ABSTRACT
Title of dissertation: EXPERIMENTAL CHARACTERIZATION OF
LASER-INDUCED PLASMAS AND APPLICATION
TO GAS COMPOSITION MEASUREMENTS
Francesco Ferioli, Doctor of Philosophy, 2005
Dissertation directed by: Professor Steven G. Buckley
Department of Mechanical Engineering
In this dissertation new applications of Laser Induced Breakdown Spectroscopy
(LIBS) are investigated. When a powerful laser beam is focused to a high enough
fluence breakdown occurs and a hot, short-lived plasma is formed. In the first part
of this dissertation, an experimental study of laser plasmas generated in air and ar-
gon is presented. The breakdown is investigated starting from the formation of the
plasma, through the subsequent phase of adiabatic expansion, until the final decay.
The results are interpreted on the basis of an hydrodynamic model that describes
the plasma as a strong shock wave propagating through the fluid. Simple dimen-
sional and energy considerations allow derivation of the general scaling laws that
govern the regimes of motion. The time and length scales appropriate to describe
the motion of the fluid at different stages are defined and, for every regime, the com-
parison between experimental observations and theory is presented. The proposed
model appears to be consistent with the observations, and the theory outlined in
the paper can be used to derive estimates of the fluid properties.
In the second part of the dissertation, atomic emission from the plasma is
used to perform direct measurements of atomic species in mixtures of hydrocarbons
and air. Atomic emission from the laser-induced plasma is observed and ratios of
elemental lines are used to infer composition in reactants and in flames. Equivalence
ratio can be determined from the spectra obtained from a single shot of the laser,
avoiding time averaging of signals with a spatial resolution on the order of a few
mm. The strength of the C, O, and N lines in the 700 - 800 nm spectral window
is investigated for binary mixtures of C3H8, CH4, and CO2 in air. The dependence
of the atomic emission on the concentration of carbon and hydrogen is investigated,
as well as the influence of experimental parameters such as the laser power and the
temporal gating of the detector.
Finally the technique is demonstrated on a reciprocating engine. The mea-
surements on the engine provide insight into the sensitivity that may be achieved in
real-world applications. It is demonstrated that the precision of the measurements
can be enhanced using the statistical technique of principal component analysis.
EXPERIMENTAL CHARACTERIZATION OF
LASER-INDUCED PLASMAS AND APPLICATION
TO GAS COMPOSITION MEASUREMENTS
by
Francesco Ferioli
Dissertation submitted to the Faculty of the Graduate School of the
University of Maryland, College Park in partial fulfillment
of the requirements for the degree of
Doctor of Philosophy
2005
Advisory Committee:
Associate Professor Steven G. Buckley, Chair/Advisor
Associate Professor Kenneth T. Kiger
Associate Professor Ken Yu
Assistant Professor Andre W. Marshall
Professor Richard V. Calabrese
c? Copyright by
Francesco Ferioli
2005
To Federica
ii
ACKNOWLEDGMENTS
I?m sincerely thankful to the many people that helped make this work possible.
Professor Paul Puzinauskas from the University of Alabama for his invaluable help
with the engine measurements. Dr. Sivanandan Harilal from the Center for Energy
Research of the University of California San Diego, for his advice on measuring
plasma radiation as well as for the access to his unpublished images of the plasma.
David Hoffmann, for his support performing shadowgraphy, and Dr. Farahat Beg
for helping measuring extreme U.V. radiation.
Finally I wish to thank my advisor, professor Steven G. Buckley for his men-
toring and the University of Modena e Reggio Emila for its support and funding
throughout these years.
iii
Contents
1 Introduction 1
1.1 Scope of the present work . . . . . . . . . . . . . . . . . . . . . . . . 1
1.2 Motivation and background . . . . . . . . . . . . . . . . . . . . . . . 3
1.3 Outline of the manuscript . . . . . . . . . . . . . . . . . . . . . . . . 5
2 Experimental Study of the Laser-Induced Breakdown 7
2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
2.2 Measurement of the Radiated Energy . . . . . . . . . . . . . . . . . . 11
2.3 The Laser Supported Wave . . . . . . . . . . . . . . . . . . . . . . . . 13
2.3.1 Dimensional analysis of the laser supported wave . . . . . . . 15
2.3.2 Maximum plasma temperature and average plasma temperature 21
2.4 Post Breakdown Evolution . . . . . . . . . . . . . . . . . . . . . . . . 27
2.4.1 The idealized point explosion . . . . . . . . . . . . . . . . . . 31
2.4.2 The self-similar region: comparison with the experimental re-
sults . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35
2.4.3 The numerical solution: comparison with the experiments . . 38
2.5 Later Stages of the Expansion . . . . . . . . . . . . . . . . . . . . . . 44
iv
2.6 Radiation from the Plasma . . . . . . . . . . . . . . . . . . . . . . . . 47
2.6.1 Spontaneous emission from a hot plasma . . . . . . . . . . . . 49
2.6.2 Lifetime of the atomic emission . . . . . . . . . . . . . . . . . 51
2.7 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54
3 Spectroscopic Measurements of Hydrocarbons 58
3.1 Optical Measurements of Gas Composition . . . . . . . . . . . . . . . 58
3.2 Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59
3.3 Spectroscopic Measurements of the Equivalence Ratio . . . . . . . . . 62
3.3.1 LIBS Measurements in a Combustible Mixture . . . . . . . . . 64
3.3.2 Effect of laser pulse energy on atomic emission . . . . . . . . . 69
3.3.3 Lifetime of the atomic emission as a function of laser pulse
energy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71
3.3.4 Quenching of atomic emission via radiationless transitions . . 74
3.4 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81
4 Real Time Measurement of the Fuel-to-Air ratio 83
4.1 Measurements on a Reciprocating Engine . . . . . . . . . . . . . . . . 83
4.2 Engine Setup . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85
4.3 Real Time Exhaust Gas Measurements . . . . . . . . . . . . . . . . . 87
4.4 Chemometric Analysis of LIBS Spectra . . . . . . . . . . . . . . . . . 90
4.5 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93
5 Future Work 96
v
5.1 An Outline for Future Research . . . . . . . . . . . . . . . . . . . . . 96
5.2 Extreme U.V. Emission from the Laser-Induced Plasma . . . . . . . . 97
5.3 Shock Wave Effect on a Dense Aerosol . . . . . . . . . . . . . . . . . 99
5.3.1 Drag of a nanometer-sized particle in a spherical shock wave . 101
5.3.2 Particle trajectory in a spherical shock wave . . . . . . . . . . 103
5.3.3 Implications for Aerosol Measurements . . . . . . . . . . . . . 106
6 Conclusions 108
6.1 Summary of the Present Work . . . . . . . . . . . . . . . . . . . . . . 108
6.2 Experimental Study of Laser Plasmas . . . . . . . . . . . . . . . . . . 108
6.3 Measurements of Hydrocarbons . . . . . . . . . . . . . . . . . . . . . 111
A Experimental Setup 113
A.1 Measurement of the Radiated Energy . . . . . . . . . . . . . . . . . . 113
A.2 Shadowgraphy Setup . . . . . . . . . . . . . . . . . . . . . . . . . . . 115
A.3 Spectroscopic measurements of the equivalence ratio . . . . . . . . . . 117
A.4 Engine experiments . . . . . . . . . . . . . . . . . . . . . . . . . . . . 119
vi
List of Tables
2.1 Energy Radiated by Laser Plasmas in Air . . . . . . . . . . . . . . . 12
2.2 Positionofthe ShockWaveasaFunctionofTime, NumericalSimulation 34
4.1 Combinations of Spectral Features that can be Related to ? . . . . . 91
vii
List of Figures
2.1 Image of the Laser Plasma in Argon . . . . . . . . . . . . . . . . . . . 14
2.2 Scaling of the Laser Spark in Argon . . . . . . . . . . . . . . . . . . . 17
2.3 Scaling of the Laser Spark in Air . . . . . . . . . . . . . . . . . . . . 18
2.4 More Images of the Laser Spark in Air . . . . . . . . . . . . . . . . . 19
2.5 Lateral Expansion of the Plasma . . . . . . . . . . . . . . . . . . . . 20
2.6 Contour of the Plasma in Air . . . . . . . . . . . . . . . . . . . . . . 22
2.7 Contour of the Plasma in Argon . . . . . . . . . . . . . . . . . . . . . 22
2.8 Volume of the Plasma as a Function of the Laser Pulse Energy . . . . 23
2.9 Plasma Temperature as a Function of Laser Pulse Energy . . . . . . . 26
2.10 Images of the First Instants of the Plasma Expansion . . . . . . . . . 29
2.11 Evolution of the Shock Wave Generated by the Laser Breakdown in
Air . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30
2.12 Position of the Shock Wave in Time in the Self-Similar Region . . . . 36
2.13 Ratio of the Length Scales r0ra . . . . . . . . . . . . . . . . . . . . . . 38
2.14 Profiles of Velocity Behind the Shock Wave at Different Times . . . . 40
2.15 Shock Position in Time, Comparison with the Numerical Solution . . 41
viii
2.16 Region Studied Experimentally and the Whole Extent of the Numer-
ical solution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41
2.17 Shock Radius at Different Energies, Comparison with the Numerical
Solution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42
2.18 Shock Propagation in Argon . . . . . . . . . . . . . . . . . . . . . . . 42
2.19 Flow Field Behind the Shock Wave at Different Times . . . . . . . . 43
2.20 Onset of Instability in the Hot Fluid . . . . . . . . . . . . . . . . . . 45
2.21 Final Distribution of Temperature and Internal Energy in Air . . . . 46
2.22 X-ray and Extreme UV Radiation Emitted from the Plasma . . . . . 48
2.23 Emission Spectrum of the Balmer-? Line of Hydrogen . . . . . . . . . 51
2.24 Evolution in Time of the Balmer-? Line of Hydrogen . . . . . . . . . 52
2.25 Intensity of the H and N Lines as a Function of Time . . . . . . . . . 53
2.26 Normalized Intensity of the 656 nm H Line . . . . . . . . . . . . . . . 53
3.1 Emission Spectrum in the 690-790 nm Region . . . . . . . . . . . . . 61
3.2 Single Shot Gas Composition Measurements . . . . . . . . . . . . . . 63
3.3 Transmitted Laser Pulse Energy as a Function of Propane Concen-
tration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66
3.4 Averaged LIBS Signal as a Function of the Mole Fraction of Propane 67
3.5 Absolute Intensity of the N Line as a Function of Laser Pulse Energy 69
3.6 Ratio of Atomic Lines (C/N+O) as a Function of Laser Pulse Energy 70
3.7 Ratio of the Normalized C to N Spectral Lines as a Function of Time 72
3.8 LIBS Measurements Taken in a Flame . . . . . . . . . . . . . . . . . 73
ix
3.9 Effect of Propane Concentration on the Lifetime of the N Atomic Line 75
3.10 Intensity of the N, O and C Lines as a Function of C3H8 Concentration 76
3.11 Comparison Between Methane, Propane and Helium . . . . . . . . . . 77
3.12 Comparison of the Emission Spectra of methane and carbon dioxide . 78
3.13 Ratio of the C to N Lines as a Function of the Mole Fraction of CH4
and CO2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79
3.14 N and O Line Intensities as a Function of the Equivalence Ratio for
CH4 and C3H8 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 80
4.1 Ratio of the Spectral Lines as a Function of the Engine Equivalence
Ratio . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84
4.2 Comparison of the Single Shot Spectra . . . . . . . . . . . . . . . . . 86
4.3 Ratio of the N and O Line to the C Line as a Function of ? . . . . . 88
4.4 Single Shot LIBS Spectrum from the Engine Exhaust . . . . . . . . . 89
4.5 LIBS Measurements Plotted in Function of the Principal Components 92
4.6 Principal Component Analysis of LIBS Spectra . . . . . . . . . . . . 94
5.1 X-ray and E.U.V. Plasma Radiation for Different Pulse Energies . . . 97
5.2 X-ray Emission from a Laser Plasma . . . . . . . . . . . . . . . . . . 98
5.3 Shock Wave-Induced Coagulation of an Aerosol . . . . . . . . . . . . 99
5.4 Trajectory of a Nanometer-Sized Particle in the Shock Wave . . . . . 103
5.5 Relative Reynolds and Mach Numbers for Particle Through the Shock
Wave . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 104
5.6 Displacement of an 800 nm Particle in the Shock Wave . . . . . . . . 105
x
A.1 Measurement of the Radiated Energy: Experimental Setup . . . . . . 114
A.2 Setup for Shadowgraphy . . . . . . . . . . . . . . . . . . . . . . . . . 115
A.3 Setup for gas Composition Measurements . . . . . . . . . . . . . . . . 117
A.4 Setup for Measurements on the Engine . . . . . . . . . . . . . . . . . 120
xi
LIST OF SYMBOLS
Aik Einstein spontaneous transition coefficient, s?1
cij Number of collisions between particles i and j
cp Specific heat at constant pressure, J/kgK
cv Specific heat at constant volume, J/kgK
C Cunningham coefficient
d Particle diameter, m
D Velocity of the shock wave, m/s
E Energy, J
qi Degeneracy of the state i
h Enthalpy, J; Planck constant, Js
J0 Light flux, J/m2s
k Boltzmann constant, J/K
kn Knudsen number
Iik Radiant power, W
n Number concentration
N Number per unit volume, m?3
Pik Transition probability
p Pressure, N/m2
r Radius of the spherical shock wave, m
r0 Characteristic length of the laser wave, m
ra Acoustic radius, m
xii
T Temperature, K
t Time, s
t0 Duration of the laser pulse, s
ta Acoustic time, s
u Fluid velocity, m/s
v Particle velocity, m/s
V Non-dimensional volume of the plasma
V Volume of the plasma, m3
Wq Ionization probability
Z Partition function
Greek Letters
? Lateral expansion of the plasma, experimental constant
? Ratio of the specific heats
? Experimental exponent, internal energy of the fluid
epsilon1 Internal energy, J/kg
? Angle
? Mean free path, m
? Dynamic viscosity, kgm2/s2
? Kinematic viscosity, m2/s
? Similarity variable for the point explosion
? Density, kg/m3
? Experimental coefficient, energy coupling into the shock wave
xiii
? Frequency, s?1
? Angle
? Equivalence ratio (normalized air to fuel ratio)
? Thermal diffusivity, m2/s
? Experimental exponent, internal energy of the fluid
? Angular frequency, s?1
xiv
Chapter 1
Introduction
1.1 Scope of the present work
ThisdissertationdiscussestheapplicationofLaserInducedBreakdownSpectroscopy
(LIBS) to the analysis of combustion processes. LIBS is a plasma spectroscopy tech-
nique that employs the focused radiation of a relatively high peak power laser pulse
to produce a hot plasma in the medium to be analyzed. As the plasma cools, elec-
trons decay from excited quantum levels, emitting energy in the form of monochro-
matic radiation. The position of the atomic emission lines depends on the energy
gap between the quantum levels involved in the transition and, therefore, on the
electronic structure of the atoms. If the light coming from the plasma is spectrally
resolved, the position of the atomic lines allows detection of the elements present in
the target medium. The intensity of the atomic lines depends, among other things,
on the number of atoms present and therefore on the concentration of the analyte.
LIBS has been used as an analytical technique for more than thirty years and ap-
1
CHAPTER 1. INTRODUCTION
plied to gas, solid and liquid targets [1, 2, 3, 4]. The unique advantages of LIBS over
other diagnostic techniques is the ability to provide real-time measurements with
almost no sample preparation. LIBS has been applied to most of the elements on
the periodic table and the detection limits are on the order of parts-per-million on
a mass basis for most atoms. Detection limits are highly dependent on the matrix
and on the plasma parameters. Despite extensive research, possible applications of
LIBS to the fields of combustion and fluid dynamics are still largely unexplored and
will be the subject of the present work.
In this dissertation a new method to optically measure optically the fuel-to-air
ratio in a combustible mixture is developed. A pulsed laser is focused in a mixture
of air and hydrocarbons and the emission lines of carbon, nitrogen and oxygen are
detected simultaneously to quantify the fuel-to-air ratio. In order to investigate the
potential of LIBS as a diagnostic tool for combustion, the technique is demonstrated
both in a laboratory setup and on a reciprocating engine. Due to the strength of
the emission from the plasma, the proposed technique proves to have an excel-
lent signal-to-noise ratio. The main problems encountered during the experiments
concern reproducibility and quantification of the results. The concentration of a
chemical element in the plasma is only one of many factors influencing the strength
of an atomic line. For this reason, measuring concentration from the strength of
spectral lines alone is often a complex task.
In order to improve the accuracy of LIBS for measuring hydrocarbons, a de-
tailed study of the main factors influencing the measurements is carried out. The
research is two-pronged: the basic physics responsible for the formation, expan-
2
1.2. MOTIVATION AND BACKGROUND
sion and recombination of the plasma are investigated, and then the influence of
the experimental parameters more relevant to measurements of hydrocarbons are
discussed.
1.2 Motivation and background
Methods of quickly and rapidly measuring gas composition in combustion sys-
tems are of great practical interest. In particular, optical techniques can be used
effectively in many situations where intrusive measurements are not convenient.
The real-time, in situ nature of many optical measurement techniques make them
amenable to control applications requiring on-line data streams, while simultane-
ously avoiding probe effects that may perturb the sample. In combustion processes,
fuel efficiency and emission of pollutants depends dramatically on the local fuel-to-
air ratio. For this reason, time-resolved measurements of fuel/air distributions may
be used to improve existing combustion systems. Raman spectroscopy is widely
used to measure turbulent mixing of fuel and oxidizer in nonpremixed flames [5];
this technique has recently been used to measure unburned fuel, N2, and O2 con-
centrations inside a cylinder of a reciprocating engine [6]. Further work on engines
has included the use of tracer laser-induced fluorescence [7] for temperature and
equivalence ratio measurements. Other combustion diagnostic techniques include
the use of tunable diode lasers, FTIR spectroscopy, and spray diagnostics [8].
Most existing techniques for equivalence ratio measurements can only be ap-
plied in a known regime, i.e. either before, during, or after the combustion event
3
CHAPTER 1. INTRODUCTION
occurs, since the methods determine equivalence ratio by measurement of 1) mix-
ture fraction of reactant or product species, 2) condensed-phase concentration, or 3)
flame emission. In this work, the use of LIBS is demonstrated in reactants, products
and flames, for different types of hydrocarbons, over a wide range of concentration.
In combustion process exhaust streams, LIBS has primarily been used to measure
inorganic species such as toxic metals, which typically occur in particulate form
[9] [10] [11]. Few studies have been undertaken to directly measure hydrocarbons.
Related to the work presented in this dissertation, Phuoc and White used simulta-
neous measurements of the H line at 656.3 nm and the O triplet near 777 nm to
determine averaged equivalence ratio in nonreacting and reacting jets of CH4 and
air [12]. Recently, Sturm and Noll [13] have examined averaged LIBS emission of
various C, H, O, and N ratios in mixtures of air, CO2, N2, and C3H8 to determine
calibration curves for various elements, and elemental ratios as a function of mixture
composition.
The interest in the laser breakdown is not limited to spectroscopy. Application
of laser induced plasmas includes laser ablation, material processing and nuclear fu-
sion. Since the early 1960, extensive theoretical and experimental research has been
undertaken to describe the physical process involved in the laser breakdown [19].
The first part of the present research is dedicated to the study of the basic phenom-
ena that occur during the formation, expansion and decay of laser-induced plasmas.
4
1.3. OUTLINE OF THE MANUSCRIPT
1.3 Outline of the manuscript
Chapter 2 of this manuscript is devoted to an experimental study of the laser break-
down. The evolution of the plasma is investigated from the initiation, during the
laser pulse, to the subsequent expansion and decay. The main objective of the re-
search is to derive a detailed energy balance on the laser spark. In the first part of
the Chapter, an hydrodynamic model of the plasma expansion is presented. Dimen-
sional analysis allows to derive the general scaling laws that control the different
phases of the gasdynamic process. Equations are derived to estimate important pa-
rameters, including dimensions and temperature of the plasma, and the final energy
distribution. The theoretical results are compared with the experimental obser-
vations. In the second part of the Chapter, the basic phenomena leading to the
emission of atomic lines from the plasma are discussed.
The results described in Chapter 2 are applied in Chapter 3 to measurements
of different hydrocarbons. In a laboratory set up, air is mixed with different hydro-
carbons over a wide range of concentrations. LIBS is used to obtain a quantitative
measure of the fuel-to-air ratio in the mixture. The relative accuracy and the ex-
perimental calibration of the technique is discussed. In order to demonstrate the
reliability of the technique and to improve the sensitivity, the influence of the main
experimental parameters is analyzed. In particular, the effect laser power and de-
tector timing on the recorded spectra is investigated. Finally nonlinear effects that
have an influence on the strength of atomic emission are discussed.
In Chapter 4 optical measurements of the fuel-to-air ratio are demonstrated
5
CHAPTER 1. INTRODUCTION
in a situation of actual interest. LIBS is used to analyze the exhaust gas of a recip-
rocating engine in real time. The purpose of these measurements is to demonstrate
the technique in a real combustion system. The data acquired from the engine are
processed using the tool of Principal Component Analysis, which improves the ac-
curacy of the measurements.
Some interesting phenomena that were observed during the experiments are
presented in the fifth Chapter. The exhaustive analysis of these findings is left to
future research. Finally, the sixth Chapter summarizes the main results and findings
of the research.
6
Chapter 2
Experimental Study of the
Laser-Induced Breakdown
2.1 Introduction
When a powerful pulsed laser beam is focused to a small spot in a gas, a breakdown
may occur. If the electromagnetic field generated by the incident beam exceeds a
threshold value, ions are generated. The absorption cross section of ions is much
larger than that of neutral atoms and photons are absorbed as a result of free-free
transitions of electrons in the ion field. As energy is absorbed other electron-ion
pairs are generated, further increasing the absorption coefficient of the fluid. The
result is a cascade phenomenon which results in substantial absorption of the laser
pulse, forming a hot plasma which rapidly expands in the cold gas. A detailed
description of the physics of laser-induced ionization is given in references [14] [15]
[16] [17] [18], and is not within the scope of the present work. Among the first to
7
CHAPTER 2. EXPERIMENTAL STUDY OF THE LASER-INDUCED BREAKDOWN
research the laser breakdown, Russian physicist Yu. P. Razier identified two possible
mechanisms to describe the plasma expansion subsequent to the breakdown [19]:
1. A small absorbing layer of the gas is heated by the laser radiation and rapidly
expands. A shock wave propagates in the undisturbed gas in every direction.
The gas behind the shock wave is heated and ionized, creating an optically
thick layer that absorbs more energy from the laser beam. In this way the
absorption zone moves in the direction of the laser beam while a strong shock
wave is sent into the fluid. As noted by Razier, this phenomenon is similar to
the detonation of explosive materials, in which a shock wave is driven by the
release of chemical energy, and has been defined a Laser Supported Detonation
[14].
2. The heated gas becomes incandescent. The emitted radiation heats a layer of
gas in the proximity of the plasma, which ionizes and becomes optically thick.
In this case the energy is transported not by a hydrodynamic disturbance,
but by radiation. A ?radiation wave? is formed that propagates in the fluid,
moving the absorption zone towards the laser beam.
Both mechanisms result in a wave that propagates in the direction of the laser
beam and both mechanisms are governed by the same energy balance. The laser
energy increases the internal energy of the fluid engulfed by the expanding wave. In
a quasi-steady, one-dimensional formulation, the mass rate of gas addition per unit
surface in the growing plasma is ?0D, where D is the velocity of the wave and ?0 is
the density of the undisturbed gas. Consequently the energy balance can be written
8
2.1. INTRODUCTION
as:
?0Depsilon1(T) = J0 (2.1)
where J0 is the absorbed light flux (in J/m2s) and epsilon1(T) (J/kg) is the specific inter-
nal energy of the fluid (this energy balance ignores the kinetic energy of the fluid
set in motion).
From these considerations, Razier derived estimates for the plasma tempera-
ture behind the wave and for the velocity of the wave that are in good agreement
with experimentally measured values. Both the Laser Detonation and the Radia-
tion Wave mechanisms predict a temperature of the plasma behind the wave on the
order of 105 K and a velocity of the wave close to 105 m/s (for the experimental
conditions described in [19]). As noted in [19], under the experimental conditions
commonly encountered (laser pulse energy < 10 J and pulse duration ? 10 ns) both
mechanisms predict similar results, most often within the margin of experimental
error, and it is difficult to distinguish between them on the basis of experimental
measurements. Today it is believed that both regimes can be attained during laser
breakdown, but the conditions determining the controlling mechanism are not com-
pletely understood [14].
Despite their similarities, Laser Supported Detonations and Radiation Waves
are governed by different sets of equations. In the first case the equations of hydro-
dynamics apply, and a shock wave is coincident with a back-propagating wave. In
the case of a Radiation Wave, the energy transport can be described by the heat
equation (including transport by radiation), but with temperatures of the order of
9
CHAPTER 2. EXPERIMENTAL STUDY OF THE LASER-INDUCED BREAKDOWN
105 K, the radiation thermal diffusivity coefficient ? (m2/s), should be considered a
nonlinear function of temperature [20]. The strong dependence of ? on temperature
gives the transport of energy by radiation the character of a wave, although a proper
shock wave might not be present in the fluid. In particular, a Radiation Wave can
travel faster than the normal detonation velocity, and during the first stages of the
expansion, the pressure behind the wave might not be in local equilibrium. For these
reasons the distribution of temperature, density and pressure behind the two types
of waves is considerably different [14]. Transport mechanisms for the laser supported
wave have been studied extensively (although mainly with one-dimensional models
that do not fully account for the lateral expansion of the plasma described in the
reminder of the Chapter) and detailed descriptions can be found in references [21]
[22] [23] [24] [25] [26] [27] [28] [29]. As described by Razier, after sufficient time has
passed following the end of the laser pulse, the shock wave that emerges from the
breakdown assumes the character of a point explosion and can be described by the
theory developed by G. I. Taylor [30] and L. I. Sedov [31].
In this chapter the results of an experimental investigation of the laser break-
down are presented. The plasma formation, expansion, and subsequent dissipation
are investigated, and the results are interpreted on the basis of simple energy and
dimensional considerations. We describe the formation of the plasma during the
laser pulse as a Laser-Supported Detonation. Such a model is consistent with the
experimental observations. As discussed in [14], scaling laws similar to those pre-
sented can also be derived also in the case of a Radiation Wave [14]. Later sections
describe the fate of the energy in the fluid after the laser pulse.
10
2.2. MEASUREMENT OF THE RADIATED ENERGY
2.2 Measurement of the Radiated Energy
For laser pulse energies sufficiently exceeding the breakdown threshold, approxi-
mately 90% of the laser energy is absorbed in the plasma [32] [33], while the rest is
either transmitted through the plasma or reflected by the focussing optics. The en-
ergy deposited in the plasma is dissipated by different mechanisms: part is radiated
into the cold environment, part is coupled into the expanding shock wave, and part
is dissipated by conduction and convection.
Electromagnetic radiation is generated in the highly ionized gas by Bremsstra-
hlung, at the expense of the kinetic energy of the electrons. To assess the fate of the
energy released in the fluid during the laser breakdown, it is necessary to determine
the amount radiated as a function of the laser pulse energy. The radiated energy is
measured by an energy meter facing 90? with respect to the direction of the laser
beam. A Nd:YAG laser with pulse width t0 = 10 ns FWHM generates the plasma in
air. A detailed description of the experiment is given in the Appendix. To estimate
the energy radiated over the whole 4pi solid angle it is assumed that the plasma
radiates like a point source with spherical symmetry. Table 1 shows the estimated
total radiated energy obtained from measurements.
For laser pulse energies in the range between 70 and 550 mJ, the radiated
energy is only 4 ? 5% of the energy deposited in the plasma. In order to validate
the hypothesis of spherical symmetry the detector is moved in the direction perpen-
11
CHAPTER 2. EXPERIMENTAL STUDY OF THE LASER-INDUCED BREAKDOWN
Table 2.1: Energy radiated by laser plasmas in air, for different values of the laser
pulse energy.
Deposited energy Total radiated energy Percentage radiated
mJ mJ %
74.4 4.6 6.2
168.3 6.9 4
258.7 10.4 4
311.3 15.2 4.9
524.6 17.9 3.4
dicular to the laser beam using a precision translation stage with a total travel of 38
mm. In the case of a point source, the energy radiated on the surface of the detector
should exhibit a 1/r dependence on the distance from the plasma. Due to the finite
dimensions of the plasma, the measured energy departs a little (less than 10%) from
this rule. Nevertheless, it is estimated that, in the absence of dramatic variations
in the gradient of the radiation field (in the second derivative of the radiative en-
ergy with respect to space), the total radiated energy should not differ greatly from
the values reported in Table 2.1. Overall, the values reported represent an order-
of-magnitude estimate and express the fact that only a small fraction of the total
energy is dissipated by radiation. Similarly, the x-rays and extreme-UV radiation
emitted by the plasma were measured with a diamond photodiode (from Alameda
Applied Science Corporation). Although x-ray radiation is clearly detectable, the
energy radiated at these wavelengths is much less than 1% of the total deposited
12
2.3. THE LASER SUPPORTED WAVE
energy.
2.3 The Laser Supported Wave
The amount of energy radiated by the plasma appears to be modest. To a first
approximation, for the purpose of writing a detailed energy balance on the laser
spark, it is thus possible to ignore radiation and to consider the process adiabatic
within a suitable control volume. In the present section, a description is given of
the gas-dynamic phenomena taking place during the energy deposition time, t0.
Assuming an adiabatic flow and an inviscid fluid [46], the plasma is governed by the
Euler equations for conservation of mass, momentum and energy, supplemented by
an equation of state. The set of governing equations can be written in the customary
way [20]:
D?
Dt +???u = 0, (2.2)
?u
?t +u??u =
1
??p, (2.3)
?
?t
parenleftbigg
?epsilon1+ ?u
2
2
parenrightbigg
= ???
bracketleftbigg
?u
parenleftbigg
epsilon1+ u
2
2
parenrightbigg
+pu
bracketrightbigg
+?Q, (2.4)
where Q (J/kg s) is the energy released in the fluid per unit mass, per unit time.
Assuming an equation of state similar to the perfect gas law, the internal energy of
the fluid epsilon1 (J/kg) can be written as:
epsilon1 = cvT = 1? ?1p?, (2.5)
13
CHAPTER 2. EXPERIMENTAL STUDY OF THE LASER-INDUCED BREAKDOWN
where ? is the effective ratio of the specific heats, assumed to be constant. Using
these equations we are interested in finding the position of the Laser Supported
Wave in space at the end of the laser pulse.
Figure 2.1 shows an image of the strongly luminous plasma generated in an
atmosphere of argon (at atmospheric pressure), at the end of the laser pulse. The
images were taken with a Roper Scientific PI-Max camera, able to acquire pictures
with nanosecond resolution, and the energy deposited into the plasma was approxi-
mately 89 mJ. The experiment is described in more detail elsewhere [33] [34]. After
10 ns the plasma is already several mm in length. The direction of the laser is
from the left to the right, in the plane of the pictures, and the laser supported wave
propagates from right to left as it expands radially.
Figure 2.1: Image of the laser plasma in Ar, 10 ns after the initiation of breakdown,
with a deposited energy of 89 mJ.
14
2.3. THE LASER SUPPORTED WAVE
2.3.1 Dimensional analysis of the laser supported wave
We are interested in finding the position of the wave, r, at the end of the laser pulse.
In spherical coordinates, the radius r and time t are the dimensional variables of
the problem while longitudinal and azimuthal angle, ? and ?, are dimensionless
variables. After time t0 has passed, energy E has been deposited in the fluid. With
the formulation given by Equations 2.2-2.4, if the ambient pressure is negligible
compared with the pressure behind the shock wave, the only dimensional parameters
of the problem are t0,E, and the density of the undisturbed gas ?0, while ? is a
non-dimensional parameter. The problem can be described in terms of the non-
dimensional parameter ? and the non-dimensional variables:
r
(E?0)1/5(t0)2/5,
t
t0, ? and ?. (2.6)
In particular, the angles ? and ? are needed, since the laser comes from a definite
direction in space, and, as shown in Figure 2.1, the Laser Supported Wave is not
spherically symmetric. The problem has a characteristic time, t0, and a character-
istic length, r0 = (E?0)1/5(t0)2/5. Applying the Buckingham ? theorem, the distance
travelled by the wave in a given direction, in the time t0 is given by:
r =
parenleftbiggE
?0
parenrightbigg1/5
(t0)2/5g( tt
0
,?,?,?) (2.7)
where g is an unknown non-dimensional function. At the end of the laser pulse the
value of the independent variable is tt0 = 1. The value of g(?,?,?) is still unknown,
but with these assumptions, Equation 2.7 provides a scaling law for the Laser Sup-
15
CHAPTER 2. EXPERIMENTAL STUDY OF THE LASER-INDUCED BREAKDOWN
ported Wave. In particular, at the end of the laser pulse, the dimensions of the
plasma should scale with the fifth root of the deposited energy. Figure 2.2 shows, in
the left column, the images of a luminous plasma generated in argon at the end of a
10 ns laser pulse (p = 1 atm), for different values of deposited energy. To verify the
scaling law of Equation 2.7, the images on the left column were normalized, dividing
by the fifth root of the deposited energy. Figures 2.3 and 2.4 show similar images
for a plasma generated in air at ambient pressure. When normalized, the plasmas
generated by laser pulses with different energies appear similar, and it is possible
to obtain a quantitative agreement with the scaling law of Equation 2.7 (as shown
in the remainder of this section). The evident difference in the shape of the plasma
between air and argon is probably due to the different thermodynamic properties
that determine, among other things, the speed of sound in the two gases. More
research is needed to model in detail the behavior of the different gases.
For a 10 ns laser pulse with a deposited energy of 100 mJ, the character-
istic length ro (for a gas at standard density) is 0.38 mm in air and 0.35 mm in
argon. The dimension of the plasma at the end of the laser pulse will be propor-
tional to r0. For example, the dimension of the plasma at the point of maximum
lateral expansion (i.e., the distance travelled by the Laser Supported Wave in the
direction perpendicular to the beam, at the point of maximum lateral expansion)
will be r = ?r0 where the constant of proportionality ?, is found experimentally to
be 2.76 for air and 2.34 for argon. Figure 2.5 shows the comparison of the radial
expansion measured experimentally to the theoretical scaling law for, plasmas in air
and argon. The boundary of the wave in the images from Figures 2.2, 2.3 and 2.4
16
2.3. THE LASER SUPPORTED WAVE
Figure 2.2: Images on the left column show the laser plasma in argon, after 10 ns,
for different value of deposited energy: a) E = 7 mJ, b) E = 89 mJ, c) E = 199
mJ. The right column shows the same images normalized.
17
CHAPTER 2. EXPERIMENTAL STUDY OF THE LASER-INDUCED BREAKDOWN
Figure 2.3: Images on the left column show the laser plasma in air, after 10 ns, for
different value of deposited energy: a) E = 3 mJ, b) E = 36 mJ, c) E = 74 mJ.
The right column shows the same images normalized.
18
2.3. THE LASER SUPPORTED WAVE
Figure 2.4: More images of the laser plasma in air. Deposited energy d) E = 147
mJ e) E = 206 mJ.
19
CHAPTER 2. EXPERIMENTAL STUDY OF THE LASER-INDUCED BREAKDOWN
is not perfectly sharp and the exact wave position is defined, somewhat arbitrar-
ily, as the point where the light intensity drops below the 5% of the maximum value.
Figure 2.5: Lateral expansion of the plasma as a function of the deposited energy.
Comparison of the theoretical scaling law (lines) with the experimental data for air
(circles) and argon (triangles).
The data presented in Figures 2.2-2.5 suggest that the scaling law in Equation
2.7 agrees well with experimental observations for laser pulses with energies in the
range between 10 and 250 mJ. The scaling law (2.7) appears valid for both air and
argon, although the simple analysis proposed cannot explain the different shapes of
the plasma obtained in air and argon. There are, however, other length scales that
might be considered in the formulation of the problem, and their relevance should
be discussed. One is the beam waist at the focal spot. Due to optical aberration
the diameter of the beam at the focus is finite and depends on the focusing optics
used. This length can be evaluated using approximations from Gaussian optics
20
2.3. THE LASER SUPPORTED WAVE
[36]. For the experimental conditions presented in this paper, the beam waist is
on the order of 10 ?m, much smaller than the characteristic length r0. A second
length scale is the absorption mean free path of the photons in the optically thick
plasma. This quantity determines the length of the energy absorption zone behind
the Laser Wave. There is no simple way to estimate this length scale; we note that,
for gas pressure close to ambient, the absorption of the laser by the plasma is almost
complete, suggesting that the mean free path of the photons is considerably smaller
than the dimensions of the plasma. It is possible that the existence of other length
scales is responsible for the small differences in the shape of the plasma that can be
observed in Figures 2.2-2.4, especially for the breakdown in air at high energy.
2.3.2 Maximum plasma temperature and average plasma
temperature
Figures 2.6 and 2.7 show the measured contour of plasmas in non-dimensional co-
ordinates for air and argon (derived from one of the images in Figure 2.2-2.4). As
above, the contour of the plasma is defined as the position where the radiated in-
tensity drops below 5% of the maximum value. Assuming cylindrical symmetry, it
is possible to determine the volume of the plasma in non-dimensional coordinates
by numerical integration. This non-dimensional volume V relates the characteristic
length r0 to the physical volume, V, such that V = Vr30; we find V = 110 for air
and V = 60 for argon. With the non-dimensional volume we can predict the plasma
volume as a function of deposited energy from r0 (Equation 6), as shown in Figure
21
CHAPTER 2. EXPERIMENTAL STUDY OF THE LASER-INDUCED BREAKDOWN
2.8.
Figure 2.6: Contour of the plasma in air at t=10 ns.
Figure 2.7: Contour of the plasma in argon at t=10 ns.
As pointed out in [14], the values of temperature, density and pressure are
not constant throughout the volume of the plasma. The temperature of the plasma
in the absorption layer was estimated by Razier [19] who used an experimental
measurement of the beam waist at the focal spot to determine the light flux J0
in Equation 2.1. The conditions of conservation of mass, momentum and energy
22
2.3. THE LASER SUPPORTED WAVE
Figure 2.8: Volume of the plasma as a function of the laser pulse energy based on
the experimentally determined V (for gases at standard density). Air: solid line;
Ar: dashed line.
through the shock wave lead to the relations:
?u = ?0D, p +?u2 = ?0D2, and epsilon1+ p? + 12u2 = 12D2 + J0?
0D
(2.8)
where D is the velocity of the Laser Supported Wave and ?,p,u, and epsilon1 are the
density, pressure, velocity and internal energy of the gas behind the wave. Using
the equation of state (2.5) it is possible to derive the shock adiabat of the wave and
determine the value of D and epsilon1. In particular, the wave travels with sonic velocity
with respect to the gas behind it, satisfying the Chapman-Jouguet condition, and
there is a maximum value of the compression ratio of the gas behind the front
(depending on the effective ratio of the specific heats, see [19] and also [20] for more
details). From the internal energy it is possible to estimate temperature assuming
equilibrium. Once the energy balance in Equation 2.1 is corrected to account for
lateral expansion of the plasma, multiplying J0 by an empirical coefficient close
23
CHAPTER 2. EXPERIMENTAL STUDY OF THE LASER-INDUCED BREAKDOWN
to 0.5 [19], the calculated values agree well with the temperature value measured
experimentally. In particular, for the experimental conditions used in [19], the
plasma temperature (measured spectroscopically) was found to be on the order of
? 105 K. The model of a laser-driven shock wave assumes that the fluid expands
adiabatically behind the wave (see also [14]), and the average temperature of the
plasma is at least one order of magnitude smaller than the maximum temperatures
attained in the absorption zone.
The volume of the plasma at the end of the laser pulse defines the region
where the known energy E is deposited. Since the expansion wave is supersonic
with respect to the undisturbed fluid, conservation of mass requires that the average
density of the plasma is equal to that of the undisturbed gas. Knowing the volume
of the plasma V, at the end of the laser pulse, the average internal energy of the
fluid can be calculated from the relation:
?0Vepsilon1 = E. (2.9)
For gases at high temperature the internal energy can be approximated with inter-
polation formulae of the form [20]:
epsilon1 = aT???, (2.10)
where ? and ? are empirical coefficients that can also be used to determine an
effective ratio of the specific heats:
24
2.3. THE LASER SUPPORTED WAVE
? = 1 + ?1??. (2.11)
In particular, for air in the temperature range from 10000 K to 250000 K, the
internal energy can be approximated with the formula [20]:
epsilon1 = 3.34106
parenleftbigg T
104
parenrightbigg1.5parenleftbigg ?
?0
parenrightbigg?0.12
, J/kg (2.12)
corresponding to ? = 1.24. The local value of the density is not known (only the
average value ?0), but it cannot exceed the limiting value of ? = ?01+?1?? (=? 9.3?0).
Moreover, Equation 2.9 ignores the fact that the fluid is set in motion and some
energy is converted in kinetic energy. With these approximations, it is possible to
estimate a reference average temperature. Inserting Equation 2.12 into Equation
2.9 and substituting the expression for V one obtains:
T = 104
parenleftbigg E
3.34?0Vr30
parenrightbigg2/3
, K. (2.13)
The plasma temperature was measured spectroscopically in [33] a few tens of
ns after the breakdown initiation. The ratio of atomic emission lines of N+ was
used to determine the electron population distribution among different quantum
energy levels. Assuming the distribution to be in Boltzmann equilibrium between
the energy levels, an estimate of the bulk electronic temperature was obtained. The
experiment and the technique are described in more detail in [33]. Figure 2.9 shows
the comparison between the measured temperatures and the estimates obtained from
Equation 2.13. The temperatures predicted by Equation 2.13 are approximately 8%
25
CHAPTER 2. EXPERIMENTAL STUDY OF THE LASER-INDUCED BREAKDOWN
lower than the experimental value, but, overall, Equation 2.13 describes the relation
between deposited energy and bulk plasma temperature at the end of the laser
pulse quite well. Both the theoretical and the experimental values reported for
temperature should be regarded as estimates; for example the experimental values
are spatially distributed but might not exactly represent the average value for the
whole plasma. In addition, when considering the spatial distribution of temperature,
radiation flux should be considered. Because energy is transferred by radiation at
the speed of light, even if the total radiated energy is modest, the radiative heat flux
might be considerable. The temperature distribution inside the plasma, where the
absorptionmeanfree pathofthe emittedphotons isshort, mightdependsignificantly
on energy transfer by radiation.
Figure 2.9: Plasma temperature as a function of laser pulse energy. Comparison be-
tween experimental measurements (dots) and theoretical estimates (solid line). The
dashed line represents the fit of Equation 2.13 to the experimental data with an
empirical parameter.
26
2.4. POST BREAKDOWN EVOLUTION
2.4 Post Breakdown Evolution
After the end of the laser pulse the shock wave expands in the undisturbed gas, cool-
ing the plasma by adiabatic expansion. When the characteristic length r0 becomes
much smaller than the radius attained by the shock wave, the wave assumes the
character of a Taylor-Sedov Blast Wave i.e., a spherically symmetric point explosion.
There are two distinct regimes of motion with different dimensional constraints. Due
to the localized energy release in the absorption zone, the Laser Supported shock
wave travels much faster than the Taylor-Sedov shock wave corresponding to instan-
taneous release of the same amount of energy, see also the next section. We note that
for every kind of energy release, there exists a finite energy release time scale and
a corresponding energy release length scale. For example, during the first moments
of a nuclear explosion, an extremely hot plasma appears, often called the ?fireball?
[37]. The fireball is normally described as a radiation wave. For the nuclear test
explosion in New Mexico in July 1945, where the energy released was approximately
1014 J, the fireball had reached the radius of 14 m after 0.1 ms (with an expansion
velocity of 1.4105 m/s). Only at this point did a shock wave emerge from the radi-
ation wave. In this respect, the Taylor-Sedov solution of the point explosion should
be considered an asymptotic theory that is valid at distances sufficiently large that
the dimensional argument of Taylor and Sedov can be applied.
To investigate the gas-dynamic evolution of the laser breakdown, shadow-
graphic measurements are performed. A sheet of light from a second laser is used
to illuminate the plasma at right angles. The two lasers are accurately synchro-
27
CHAPTER 2. EXPERIMENTAL STUDY OF THE LASER-INDUCED BREAKDOWN
nized and, for measurements taken closer to the breakdown event where precision
is more critical, the timing is accurate within ?30 ns (at later stages the timing
was checked less frequently, but it is still considered accurate within ?100 ns). A
detailed schematic of the experiment is given in the Appendix. The technique of
shadowgraphy measures variations in the index of refraction of a gas due to density
gradients. In particular, shadowgraphy is sensitive to the second derivative of den-
sity with respect to space. After the end of the laser pulse the shock wave rapidly
loses strength and the temperature behind the wave drops. The gas engulfed by
the shock wave following the laser pulse ionizes (see also Section 4.2), but is far less
luminous than the very hot gas in the absorption zone of the Laser Supported Wave,
and does not appear in the images taken with an exposure time of few nanoseconds
(such as Figures 2.2 or 2.3). The shock wave rapidly leaves the plasma core formed
during the laser pulse, which stops expanding. The strongly luminous plasma com-
pletes the greatest share of its expansion during the first 10 ns. After few tens of
nanoseconds the continuous radiation emitted by the plasma begins to dim, as a
consequence of the adiabatic expansion.
Figure 2.10 compares the plots of the measure radiated intensity, the nanosec-
ond exposure photographic images (from the same plasma) and the shadowgraphs.
Figure 2.11 shows the evolution of a shock wave generated by a laser breakdown in
air with a total absorption of 93 mJ in air. After approximately 100 nanoseconds
from breakdown initiation, the gas expansion can be detected in the shadowgraphic
images. This is consistent with a strong acoustic disturbance emerging from the
plasma at the end of the laser pulse, i.e., with the model of a shock wave that is
28
2.4. POST BREAKDOWN EVOLUTION
Figure 2.10: Comparison of the of the radiated intensity, the 1 nanosecond ex-
posure photographs, and the shadowgraphs during the first instants of the plasma
expansion. Images correspond to an energy release of approximately 93 mJ and are
approximately to scale.
coincident with or ahead of the edge of the luminous plasma. As we will see below,
it is at this point that the Taylor-Sedov theory becomes useful.
Most of the continuous radiation emanating from plasma core has faded after
few hundreds of nanoseconds. During this period energy is transferred to the layer
of gas surrounding the plasma core. Atomic emission, from both neutral and ionic
lines, persists much longer in time, several ?s for ionic lines, and tens of ?s for
29
CHAPTER 2. EXPERIMENTAL STUDY OF THE LASER-INDUCED BREAKDOWN
neutral line emission.
Figure 2.11: Evolution of the shock wave generated by the laser breakdown in air
(E = 93 mJ).
To explain with more clarity the behavior of the expanding shock wave, we
recall briefly the relevant parts of the theory of point explosions. An exhaustive
30
2.4. POST BREAKDOWN EVOLUTION
description of Similarity methods in applied sciences is given in [31], [35] and also
in [38] [39] [40].
2.4.1 The idealized point explosion
When the the length and time scales r0 and t0 become small compared with radius
of the shock wave, the solution of the propagating wave can be found as if the
energy were released instantaneously from a point source. The formulation of this
problem is given in Equations 2.2-2.5. If we assume that the ambient pressure is
negligible with respect to the pressure behind the shock wave, the only dimensional
parameters of the problem are the deposited energy, E, and the ambient density,
?0. As above, ? is a non-dimensional parameter. Assuming spherical symmetry,
the radial coordinate, r, and time, t, are the only variables. Defining the similarity
variable
? = r
parenleftBig ?0
Et2
parenrightBig1/5
, (2.14)
the Buckingham ? theorem requires the radius attained by the shock wave at the
time t to be [20]:
R =
parenleftbiggE
?0
parenrightbigg1/5
(t)2/5g(?0,?), (2.15)
where g is a non-dimensional function and g(?0,?) a particular value of this function
that does not depend on r or t independently. For each value of the similarity
variable ?, the value of g(?0,?) is a constant. Customarily the value of the constant
is grouped with the energy, and the position and velocity of the shock wave are
31
CHAPTER 2. EXPERIMENTAL STUDY OF THE LASER-INDUCED BREAKDOWN
given by the relations:
R =
parenleftbigg?E
?0
parenrightbigg1/5
(t)2/5, D = dRdt = 25
parenleftbigg?E
?0
parenrightbigg1/5
(t)?3/5. (2.16)
Since the function g does not depend on the variables, the problem is self-
similar. This means that the shapes of the distribution of ?, p and u do not change
in time and scale in a similar way (i.e., satisfy the same one-parameter group of
scaling transformations [35]). In order to obtain a complete solution it is necessary
to determine the distribution of the fluid variables at a particular time, t = t1, which
yields the value of the function g for every value of r. After this,, the property of self-
similarity can be exploited to scale the results for every t [31]. Briefly, it is possible
to express the distribution of velocity and pressure as a function the velocity and
pressure behind the shock front, leaving the non-dimensional parameter ? = ?(?)
in Equation 2.16 as the only unknown. The value of ? is found from the energy
balance on the sphere encompassed by the shock wave:
integraldisplay R
0
parenleftbigg?u2
2 +
p
? ?1
parenrightbigg
4pir2dr = E (2.17)
The first term on the left-hand-side of Equation 2.17 represents the kinetic
energy of the fluid and the second tern describes the internal energy. Substituting
the analytical expressions for u and p (as a function of ?) into (2.17), the value of
? is found to be 1.175 for air with ? = 1.4 and ? 2 for a perfect gas with ? = 1.66
[31], [47]. The density, pressure and velocity of the gas behind the discontinuity are
given by the limiting formulas for strong shocks:
32
2.4. POST BREAKDOWN EVOLUTION
? = ?0? + 1? ?1, p = 2? + 1?0D2, and u = 2? + 1D. (2.18)
Behind the wave the gas is compressed to a temperature of the order of:
T = T0?0p
0
2(? ?1)
(? + 1)2 D
2, (2.19)
where T0 is the ambient temperature. As t ? 0, D ? ? and T ? ?. The
presence of a plasma core that does not obey the scaling symmetry of Taylor and
Sedov avoids this non-physical singularity. For an energy release of 100 mJ in air,
Equation 2.16 predicts a plasma radius of 0.39 mm after 10 ns, at least three times
smaller than that attained by the (non-spherical) Laser Supported Wave at the end
of the laser pulse and with an error in the energy density of the fluid of a factor of
24. As noted above the self-similar Taylor-Sedov solution is only valid following the
point at which the shock wave travels far away from the kernel of hot gas
As the blast wave expands, it loses its strength. Once the ambient pressure,
p0, is comparable with the pressure behind the wave it cannot be disregarded, and
the dimensional parameter p0 enters in the formulation of the problem. Now the
problem has a characteristic length and a characteristic timescale given by [31]:
ra =
parenleftbiggE
p0
parenrightbigg1/3
, ta = (E)
1/3?1/2
0
p5/60
(2.20)
where the acoustic radius, ra, represents the radius of the sphere whose internal
energy is comparable with the energy release E (and which is proportional to the
acoustic radius defined recently by Li?n?an et al. [41]). At this stage of the expansion,
33
CHAPTER 2. EXPERIMENTAL STUDY OF THE LASER-INDUCED BREAKDOWN
Table 2.2: Position of the shock front as a function of time, in non-dimensional
coordinates (from [31]).
r/ra t/ta r/ra t/ta
0.1867 0.01403 0.9801 0.6296
0.2669 0.0323 1.2524 0.6811
0.3342 0.05431 1.321 0.8299
0.489 0.1231 1.5171 1.108
0.6003 0.1842 1.8751 1.4636
0.6003 0.2333 2.3222 1.8973
0.6812 0.2807 2.8641 2.7763
0.7566 0.3667 3.6983 5.3764
0.9566 0.4323 7.0791 7.518
the problem can be expressed in terms of the non-dimensional variables r/ra, t/ta.
When the radius of the shock wave is comparable with ra (more precisely, when
r ? 0.18ra, as discussed in [31]), Equation 2.16 ceases to be a good approximation
for the position and velocity of the shock wave. The position of the shock in time
is given by:
r = raf(r/ra,t/ta,?) (2.21)
Since the non-dimensional function, f, depends on the non-dimensional radius
and non-dimensional time, the problem is no longer self-similar. Once the solution
34
2.4. POST BREAKDOWN EVOLUTION
for g is known as a function of the non-dimensional variables, Equation 2.21 can be
used as a scaling law for every blast wave. At the end of the Second World War,
calculations were carried out to numerically solve the propagation of the weak blast
wave, using the self-similar solution as initial condition for the one-dimensional gas-
dynamic problem. To arrive at a solution, J. Von Neumann used the pioneering
idea of a stored computer program to perform one of the very first Computational
Fluid Dynamics simulations in 1955 [42]. The results of an equivalent simulation,
carried out by Soviet scientist Korobe?inikov and co-workers in the late fifties [47],
and presented in great detail in the book by Sedov [31], will be used in this paper.
For air with ? = 1.4, the position of the weak blast wave as a function of time, in
non-dimensional coordinates, is given in Table 2.2.
2.4.2 The self-similar region: comparison with the experi-
mental results
For a 100 mJ laser pulse in air at standard conditions, the characteristic acoustic
radius is approximately ra = 9.4mm and the characteristic time is ta = 33.1?s.
To compare the experiments with theory, the position of the shock wave in time is
estimated from the shadowgraphs. As discussed above, at the end of the laser pulse
the plasma is considerably bigger than the dimensions predicted by Equation 2.16.
The experimentally measured dimensions of the plasma can be used to determine
the radius attained by the shock wave at 10 ns. Figure 2.12 shows the fitting of the
experimental data to a relation of the form of Equation 2.16, once the dimensions
35
CHAPTER 2. EXPERIMENTAL STUDY OF THE LASER-INDUCED BREAKDOWN
of the plasma core are taken into account to provide the correct initial conditions
(that is, the radius at t = 10 ns). Figure 2.12 and the measurements of the shock
wave velocity published in [43] and [44] show that the the Laser Supported Wave
acquires the character of a Taylor-Sedov blast wave after few hundred ns. However,
the fit to the experimental results is an approximation and cannot be used to derive
accurate information on the distribution of velocity and temperature. In first place,
the presence of interference fringes in the shadowgraphs are a source of experimental
errors. Moreover, the presence of a non-spherical plasma core is not contemplated
by the ideal blast wave solution.
Figure 2.12: Comparison of the experimental measurements of the shock position
(circles) with the Taylor-Sedov self-similar solution. E = 93 mJ in air at standard
conditions.
As a result of the breakdown geometry, the shock wave is not perfectly symmet-
ric and the definition of the shock radius is somewhat arbitrary. More importantly,
the distribution of velocity and pressure in the region of the plasma core is not as
36
2.4. POST BREAKDOWN EVOLUTION
prescribed by the self-similar solution which is used in Equation 2.17 to estimate
the value of the constant ?. The range of validity of the self-similar solution is only
a fraction of ra and may become comparable with the dimension of the plasma core.
Interestingly, the two characteristic length do not scale in the same way. Taking the
ratio of Equation 2.7 to the first of Equations 2.20 one finds:
r0
ra = b
p1/30 t2/50
E2/15?1/50
, (2.22)
where b is a constant close to unity. Figure 2.13 shows the ratio of the characteristic
lengths r0ra as a function of the deposited energy for air in standard conditions and
a 10 ns laser pulse. As shown, for high laser pulse energies, the dimension of the
plasma core is very small compared to the range of the self-similar solution. The
shock wave leaving the plasma core becomes stronger with increasing value of the
deposited energy. The strong shock induces ionization in the surrounding gas and
this phenomenon should become more important at high pulse energies. Preliminary
experimental observations confirmed this last consideration.
Finally, in the region where the self-similar solution holds, the thermodynamic
properties are difficult to describe, due to high levels of roto-vibrational excitation,
molecular fragmentation and excitation. This effects are often corrected by defining
a effective ratio of the specific heats, used for example in the original description of
the nuclear explosion in New Mexico [31] [20]. In reality the ratio of the specific heats
varies with r and with t, but considering a variable ratio of the specific heats would
invalidate the scaling symmetries that led to the solution, as Equation 2.5 could not
37
CHAPTER 2. EXPERIMENTAL STUDY OF THE LASER-INDUCED BREAKDOWN
Figure 2.13: Ratio of the length scales r0ra as a function of the deposited energy for a
10 ns laser pulse in air at standard conditions.
be used to eliminate the unit of temperature from the formulation of the problem. A
numerical study of point explosions accounting for real-gas thermodynamic effects
is given in [45].
2.4.3 The numerical solution: comparison with the experi-
ments
In the region described by the numerical solution, where the radius reached by the
shock wave is comparable with ra, the structure of the shock wave is considerably
different. As the wave expands over the region of self-similar motion, it becomes
more spherical and an expansion wave appears behind the discontinuity. The shock
wave is followed by a region of back-flow where the fluid moves toward the center.
This expansion wave eventually detaches leaving a region of quiet fluid near the
center. These different regions of motion are clearly shown in the shadowgraphs.
38
2.4. POST BREAKDOWN EVOLUTION
The expansion wave appears transparent in the shadowgraphic images, except in
a region near the center where the fluid appears as a dark disc due to the high
gradients of temperature and density. Figure 2.14 compares the profile of velocity
behind the shock wave (from the solution published in [31]) at the two different
times corresponding to the different regimes of motion with the corresponding shad-
owgraphs shown. In these Figures, the region corresponding to the plasma core,
where the solution is not accurate, has not been plotted. Since the shock wave trav-
els at sonic velocity with respect to the gas behind it, the motion of the shock wave
is not influenced by the behavior of the hot gas in the core. Under these conditions,
it is possible to describe the discontinuity as a shock wave propagating in air with
standard thermodynamic properties generated by an energy release:
Eeff = ?E. (2.23)
The energy Eeff is the effective initial energy that would produce the shock observed
at large distances in an idealized point explosion with constant ? = 1.4. The
characteristic length and time scales for this portion of the problem will be:
ra =
parenleftbiggE
eff
p0
parenrightbigg1/3
, ta = (Eeff)
1/3?1/2
0
p5/60
(2.24)
The results of the numerical solution reported in [31] can then be used to describe
the flow field far away from the center.
Due to the simplification of the model, the constant ? is is much less than 1.
Figure 2.15 shows the position of the shock front as a function of time for a deposited
energy of 52 mJ in air. The experimental data are compared to the numerical
39
CHAPTER 2. EXPERIMENTAL STUDY OF THE LASER-INDUCED BREAKDOWN
Figure 2.14: Approximate profiles of velocity behind the shock wave as pictured above
in the early stages of the expansion (left column) and in the weak shock region as
derived from the solution in [31] assuming spherical symmetry. E = 87 mJ in air.
The region occupied by the plasma core has not been plotted.
solution interpolated from Table 2.2, and the constant ? is found to be 0.29. Figure
2.16 shows the full extent of the region encompassed by the numerical solution in
Table 2.2, compared to the region analyzed experimentally. Laser plasmas with
coupled energies in the range between 52 and 478 mJ are shown in Figure 2.17,
which illustrates the experimentally measured shock radius and the nondimensional
solution from Table 2.2.
40
2.4. POST BREAKDOWN EVOLUTION
Figure 2.15: Shock position in air as a function of time. Comparison it of the
experimental data (circles) to the numerical solution (solid line, interpolated from
Table 2.2). Deposited energy: E = 52 mJ.
Figure 2.16: Comparison of the region studied experimentally with the extent of the
numerical solution. Deposited energy: E = 52 mJ in air.
More study is needed to gain complete understanding of the shock propaga-
tion in real gases; the value of the constant ? changes slightly with high values of
deposited energy. For a deposited energy of 478 mJ ? = 0.33 is the value that best
41
CHAPTER 2. EXPERIMENTAL STUDY OF THE LASER-INDUCED BREAKDOWN
Figure 2.17: Experimental measurement of the shock radius in air and comparison
with the numerical solution. Deposited energies: E = 52 mJ circles, E = 87 mJ
squares, E = 174 mJ triangles, E = 261 mJ diamonds, E = 478 mJ crosses.
Figure 2.18: Shock propagation in argon. Deposited energies: E = 52 mJ circles,
E = 87 mJ squares, E = 174 mJ triangles, E = 261 mJ diamonds, E = 478 mJ
crosses.
42
2.4. POST BREAKDOWN EVOLUTION
Figure 2.19: Flow field behind the shock wave at different times as determined form
the numerical solution. E = 87 mJ in air.
fit the experimental results. As noted, the numerical simulation makes use of the
self-similar solution to derive initial conditions, which is a limitation. Nevertheless,
in the range of experimental conditions considered, the numerical simulation can
be used to obtain an accurate description of the shock wave generated by laser dis-
charges, provided that the correct value for the coupled energy is used. For example,
the data published in [46] fit the simulation with a value of ? = 0.3. As discussed
in [47], results similar to those obtained for air can be used to describe blast waves
in gases with ratio of the specific heats in the range between 1.2 and 3. Although
the original simulation was carried out for air (with constant ? = 1.4), plots similar
to those presented in Figures 2.15, 2.16 and 2.17 describe, with only the change
of a multiplicative constant, the propagation of the shock wave in argon. Figure
2.18 shows the position of the shock wave as a function of time in argon for energy
releases in the range between 52 and 478 mJ. In this case the value of the exper-
imental constant ? is found to be 0.96. The apparent difference between air and
43
CHAPTER 2. EXPERIMENTAL STUDY OF THE LASER-INDUCED BREAKDOWN
argon cannot be interpreted since the multiplicative constant necessary to adapt the
numerical results to the case of a monoatomic gas is not given explicitly in [31] and
[47]. Figure 2.19 shows the the fluid velocity behind the wave at different instants
in time (as derived from the tables in [31]).
2.5 Later Stages of the Expansion
As it expands, the shock wave slows down, matching the speed of sound in the undis-
turbed gas at long distances. Asymptotic formulas for the blast wave at very large
distances from the detonation point were derived by L. D. Landau [50] (see also [51]
for a discussion of the the shock wave evolution at large distances). Reflected shocks
are still visible in shadowgraphic pictures after they travel for tens of centimeters,
as shown particularly in the third image in Figure 2.20. The compressed gas behind
the shock wave expands and cools, and the pressure behind the expansion wave is
close to ambient. Most of the absorbed laser energy is irreversibly converted into
heat and remains deposited in a small region close to the center. Shadowgraphs
show a dark, spherical region close to the center, as shown in Figure 2.14 (shadow-
graph on the right) and also in the last images of Figure 2.11; the dark region is
most probably due to high gradients of temperature and density. In air, the radius
of this opaque region is approximately r = 0.5ra (where ra is calculated using the
effective energy defined in Equation 2.23) over the whole range of pulse energy in-
vestigated. A simple model for the distribution of temperature and internal energy
can be obtained considering an ideal point explosion with energy release Eeff, in a
44
2.5. LATER STAGES OF THE EXPANSION
gas with constant ratio of the specific heats ? = 1.4. For these conditions, the final
distribution of temperature and internal energy was derived by Li?n?an et. al. [41].
Figure 2.20: Onset of instability in the hot fluid. E = 174 mJ in air; weak reflected
shocks are visible in the third shadowgraph.
The left plot in Figure 2.21 shows the final distribution of temperature as a
function of the nondimensional radius. The radius of the opaque region in shad-
owgraphs, r = 0.5ra, is also shown (with vertical dotted lines). Such distance
corresponds to the region where the gradients of temperature tapers off, providing
an experimental indication that the temperature distribution is approximately cor-
rect. The steep profile of the temperature distribution is responsible for the sharp
boundary of the opaque disk observed in the shadowgraphs. The plot on the right
45
CHAPTER 2. EXPERIMENTAL STUDY OF THE LASER-INDUCED BREAKDOWN
shows the fraction of energy stored in the fluid up to the radius r, defined as (see
[41] for more details):
h =
integraltextr
0 4pi?cp(T ?T0)r
2dr
Eeff . (2.25)
Figure 2.21: Final distribution of temperature and internal energy for air at standard
conditions from [41]. The dotted lines show the radius of the opaque disk.
These plots are not accurate for small values of r due to real gas effects and
the presence of the plasma core, but are more precise at long distances, where the
solution matches the experimental observations well. The experimental data suggest
that an amount of energy equal approximately 0.33Eeff = 0.1E is transported by
the shock wave farther than r = 0.5ra and is consumed, producing a relatively
small temperature increase in a relatively large mass of gas. After the expansion
wave detaches from the central region of fluid, approximately 90% of the deposited
energy (85% considering radiation losses similar to those estimated in section 2.2)
is is still stored in the dark region that appears in the shadowgraphs. The energy
used to dissociate the molecules will be released during recombination as discussed
46
2.6. RADIATION FROM THE PLASMA
in [45].
The small region of hot gas rapidly cools. At this stage heat conduction and
viscosity become important, changing the formulation of the problem. The spherical
mass of gas rapidly develops instability (in a time of the order of few tens of ?s for
the laser energies used in this study) collapsing along the direction of the laser
beam with a jet of gas moving toward the laser beam (see also [46]) while a toroidal
vortex perpendicular to the direction of the laser beam appears. Figure 2.20 shows
the onset of instability in the fluid. The turbulence that is generated dissipates the
deposited energy. The time scales involved are too short for the onset of natural
convection.
2.6 Radiation from the Plasma
The gas heated by the laser to high temperatures emits bright radiation due to
bremsstrahlung and ionic and atomic relaxation. The high temperature associated
with the laser breakdown becomes the source for atomic emission spectroscopy. It
is useful to analyze the emission of radiation from the plasma and compare it to the
time scales identified earlier in this Chapter. Figure 2.22 shows the emission from
the plasma during the first few hundred ns. The radiation was detected using a
diamond photodiode connected to a fast oscilloscope. Diamond has a large energy
gap between two conduction bands. Only the most energetic photons (with energy
in the 200 - 2200 eV range [65]) can promote an electron into the empty conduc-
tion band, producing an electric signal. For this reason diamond photodiodes are
47
CHAPTER 2. EXPERIMENTAL STUDY OF THE LASER-INDUCED BREAKDOWN
sensitive only to x-rays and extreme ultraviolet radiation.
Figure 2.22: X-ray and extreme UV radiation emitted from the plasma for a 100 mJ
laser pulse (approximately 93 mJ of deposited energy).
As already suggested by the short-time (ns) images of the breakdown, the
plasma emits an intense continuum radiation that lasts only few hundred ns, that
is, for the very first stages of the fluid expansion. As the plasma expands and cools
the continuum radiation fades. Atomic emission lines emerge from the background in
less than 1 ?s. The intense background radiation promotes a rapid energy exchange
within the plasma. A simple model for the atomic emission can be derived assuming
the plasma reaches local thermodynamic equilibrium after few hundred ns as a
consequence of this energy flux. Although the hypothesis of local equilibrium is
not verified for the experimental conditions investigated in this study (see [52] for a
recent discussion on the subject), such model is useful for qualitative understanding
of some features of the atomic emission from a laser plasma.
48
2.6. RADIATION FROM THE PLASMA
2.6.1 Spontaneous emission from a hot plasma
In a cooling plasma the electrons tend to reach equilibrium transferring energy by
two mechanisms: spontaneous decay from excited energy levels with the emission
of photons and collision with less energetic atoms. A simple model is sometimes
used in the literature to describe atomic emission from a laser plasma [48] [49].
Considering a partially-ionized, monoatomic gas where some electrons are promoted
to the excited quantum state i, assume that the only relevant electronic process is
spontaneous decay form the upper state i to lower states. Further assume that the
mechanism of stimulated emission is negligible. The probability per second that
a photon with energy h? = Ei ? Ek (where h is the Planck?s constant and ? the
frequency of the photon) is emitted, due to the decay of an electron from the upper
state i to the lower level k, is:
dPik
dt = Aik (2.26)
where Aik (s?1) is the Einstein coefficient of spontaneous emission (see also [53] and
[54]).
Assuming the plasma to be in Boltzmann equilibrium at the temperature T
at the end of the breakdown, the number of atoms in the state i will be:
ni = n giZ(T)e?Ei/kT, (2.27)
where n is the total number of atoms in the plasma volume, gi is the degeneracy of
the state i, Z the partition function and k the Boltzmann constant. For a partially-
49
CHAPTER 2. EXPERIMENTAL STUDY OF THE LASER-INDUCED BREAKDOWN
ionized gas it is important to consider the probability Wq of an atom to be in the
ionization state q. The number of atoms per second that undergo a transition
between the states i and k is:
nidPikdt = n giZ(T)e?Ei/kTAikWq (2.28)
In the case that absorption is much slower than spontaneous emission (for example
in a rapidly cooling plasma), the radiant power per steradian can be approximated
by multiplying Equation 2.28 by the photon energy, h? = h?/2pi and dividing by
the solid angle 4pi giving:
Iik = n giZ(T)e?Ei/kT h?8pi2AikWq (2.29)
It appears that, all other parameters being equal, the intensity of an atomic
line depends on the number of atoms of a given element in the plasma volume, and
therefore on the analyte concentration. The approximate model of Equation 2.29
implies that the number of transitions (and therefore the line strength) depends on
two parameters: the instantaneous plasma temperature and the transition proba-
bility Aik. The experimental measurements presented in the next section show that
the lifetime of atomic emission depends on both parameters.
The plasma temperature determines the equilibrium distribution of the elec-
tron population between the various energy levels [55]. It will be shown that emission
of spectroscopic lines from laser-produced plasmas cannot be explained without tak-
ing into account transient phenomena related to the plasma temperature evolution.
50
2.6. RADIATION FROM THE PLASMA
2.6.2 Lifetime of the atomic emission
The light from the plasma is focused on the tip of an optical fiber connected to
the entrance slit of a 0.3 m Acton spectrometer. The light is dispersed by a 600
grove/mm grating and imaged on the chip of a Roper Scientific PI-Max ICCD
camera. The electronic shutter of the camera is synchronized with the laser. a
detailed description of the experiment is given in Appendix A.3.
Figure 2.23: Emission spectrum of the Balmer-? line of hydrogen, taken few ?s after
the breakdown.
Figure 2.23 shows the emission spectrum from a laser-induced plasma in air.
The most prominent line is the 656 nm Balmer-? line of hydrogen from the water
vapor in the atmosphere. Figure 2.24 shows the time evolution of the Balmer-? line.
Each spectra in the graph was acquired with 1 ?s exposure of the camera, starting 1
?s after the breakdown and increasing the delay 1 ?s each time (i.e., camera gating
1 ?s, delay 1 ?s, 2 ?s, 3 ?s...).
51
CHAPTER 2. EXPERIMENTAL STUDY OF THE LASER-INDUCED BREAKDOWN
Figure 2.24: Evolution in time of the Balmer-? line of hydrogen.
The line rapidly diminishes over a few tens of ?s. Figure 2.25 shows the inten-
sity as a function of time for the Balmer-? line and for the 745 nm line of nitrogen
(from atmospheric nitrogen), for different laser pulse energies. As the energy de-
posited increases, the plasma temperature and volume increase, as described by in
Section 2.3.2. Hence at a given time the local temperature is increased with greater
energy deposition, increasing the number of excited atoms within the plasma volume
and intensifying the atomic emission.
The lifetime of the atomic emission also increases with increasing laser energy.
Both N and H lines share the same behavior. For every laser pulse energy inves-
tigated, the emission lasts through the first stages of the plasma expansion, when
the rarefaction wave develops behind the spherical shock wave. In each case the
emission decays well before the onset of instability in the fluid. The lifetime of the
emission depends on the quantum properties of the transition (such as Aik and the
52
2.6. RADIATION FROM THE PLASMA
Figure 2.25: Intensity of the 656 nm H line and 745 nm N line as a function of time
for different laser pulse energies.
energy difference between the quantum levels involved in the transition). Generally,
spectroscopic measurements are carried out during the early stages of the plasma
expansion. For many atomic lines the lifetime is of the same order of magnitude as
ta, the timescale of the weak shock wave. Figure 2.26 shows the intensity of the 656
nm H line normalized by the signal at 1 ?s.
Figure 2.26: Normalized intensity of the 656 nm H line as a function of time for
different laser pulse energies.
53
CHAPTER 2. EXPERIMENTAL STUDY OF THE LASER-INDUCED BREAKDOWN
Even when normalized, the lifetime of the emission increases as the energy
release increases. This is attributed due to the different temperature and different
cooling rate of the plasmas. However, the intensities presented in Figure 2.25 do not
scale with ta. The spontaneous emission from a laser plasma has two characteristic
times: the reciprocal of Einstein spontaneous emission coefficient, 1/Aik (s), and
the acoustic time, ta, of the shock wave. Before the onset of instability, the cooling
rate of the plasma as a function of the deposited energy scales with ta (as discussed
in sections 2.4.1-2.4.3). Hence the parameter 1/Aik is related to radiation decay by
spontaneous emission (see [54]) while ta is related to the temperature decay rate.
The lifetime of an atomic line depends on both the temperature history of the plasma
and the spontaneous decay of excited states. Indeed, for a 100 mJ laser pulse the
acoustic time is ta = 33 ?s and 1/Aik for the 745 nm N line is on the order of 100
?s (data from the NIST atomic spectra database [56]). The two characteristic times
have similar orders of magnitude. Quantitative description of atomic line emission
requires an accurate modelling of many plasma parameters [57] [58] [59] [60] and
cannot be solved with the simple approach discussed here. However, the concepts
outlined in this section are important for the correct quantification of spectroscopic
measurements as discussed in Chapter 3.
2.7 Conclusions
Four different regimes are attained during the breakdown of focused laser pulses in
air. Each regime is characterized by different length and time scales (or by the lack
54
2.7. CONCLUSIONS
of them).
? The energy-release timescale is defined by the duration of the laser pulse. The
corresponding length scale r0, is given by Equation 2.7. In this phase the
rapidly expanding plasma can be described as a strong shock that produces
an optically thick absorption zone. The laser pulse is absorbed in this thin
layer, resulting in a Laser Supported Wave travelling along the beam direction,
towards the laser. The gas behind the wave expands adiabatically, resulting in
a lower plasma temperature near the center. At the end of the laser pulse the
volume of the plasma is found to be proportional to r0. The plasma volume
defines the region where the known energy E is stored, and thus the maximum
internal energy of the fluid.
? The rapidly expanding gas sends a strong shock wave into the cold gas, trans-
ferring energy to layers of fluid outside the initial plasma core. For the exper-
imental conditions analyzed in this paper, the continuous radiation produced
by Bremsstrahlung fades in a time of the order of? 10t0. The shock that leaves
the plasma can be described as a strong shock without a characteristic length
or time scale. However, for pulse energies commonly used in laboratory mea-
surements, the strong shock region is small and can become comparable with
the dimensions of the plasma core. For this reason the Taylor-Sedov theory
cannot be used to derive accurate estimates of the distribution of temperature
and velocity from experimental observations.
? When the ambient pressure becomes comparable with the pressure behind
55
CHAPTER 2. EXPERIMENTAL STUDY OF THE LASER-INDUCED BREAKDOWN
the shock, the characteristic length and time scales are given by Equations
2.20. An expansion wave develops behind the shock and a region of back flow
appears. The shock soon becomes too weak to create significant temperature
gradients in the fluid and the region behind the wave appears clear in the
shadowgraphs. At this stage the propagation of the wave can be described by
the model of a weak blast wave propagating in air. However, due to real gas
effects occurring during the first stages of the expansion, the energy apparently
coupled into the shock is only a fraction of the laser pulse energy. Once this is
taken into account, the model can be used to accurately predict the position
of the shock wave in time, for laser pulses in the range between 40 and 550
mJ.
? At infinity the shock wave becomes a sound wave. Due to viscous effects be-
hind the shock wave, most of the laser pulse energy is irreversibly converted
into heat in a region with radius r = 0.5ra. The model of a point explosion
describes well the experimental observations and can be used to derive accu-
rately the final energy and temperature distribution. In particular, for air,
almost the 90% of the laser pulse energy remains confined within a radius
r < 0.5ra. Instability rapidly develops in the fluid, and the resulting tur-
bulence dissipates the energy in a time on the order of milliseconds (for the
laser pulse energies investigated in this paper). At this stage viscosity and
heat conduction become important and have to be taken into account in the
formulation of the governing equations.
56
2.7. CONCLUSIONS
Atomic emission lines appear less than one ?s after the breakdown and last, for
the laser pulse energies used in these experiments, few tens of ?s. The lifetime of
the atomic emission is comparable with the timescale of the weak blast wave, when
the expansion wave develops behind the shock wave. For the laser pulse energies
normally used for spectroscopy, the spontaneous emission fade before the onset of
instability in the fluid.
The models presented in this Chapter could be improved by performing nu-
merical simulations. Computational models can be developed to describe the hydro-
dynamics of the laser breakdown starting from the beginning of the laser pulse. The
results could eventually be coupled to radiation models to simulate emission spectra.
However, the scaling laws described here are important as they outline a convenient
formulation of the problem. In particular, the length scales r0, t0, ra and ta should
be used to present results from experiments or models in a non-dimensional form.
Furthermore, the scaling symmetries described in this Chapter provide an excellent
way to validate numerical results. In particular, computational models should pre-
dict similar values for experimental constants such as ?, V and ? and fit the plots
presented in Figures 2.6-2.7 and Figure 2.17, as well as describing the structures
observed at latest stages of the expansion (Figures 2.21 and 2.20). The results of
these studies may have important applications in the field of laser spectroscopy and
nuclear fusion.
57
Chapter 3
Spectroscopic Measurements of
Hydrocarbons
3.1 Optical Measurements of Gas Composition
Chapter 2 was devoted to the description of the laser-induced plasma temporal
evolution. Motivation for that work was to investigate the physics phenomena that
lead to the emission of spectral lines. In the second part of this dissertation, the
concepts developed earlier in this work are applied to gas composition measurements.
In particular, LIBS will be used to measure the fuel-to-air ratio in a mixture of
air and hydrocarbons. It will be shown that quantification and repeatability of
spectroscopic measurements depends critically on understanding the influence that
experimental parameters, such as laser pulse energy and detector timing, have on
atomic emission. As already discussed in the first Chapter, the mole fraction of a
combustible mixture is one of the key parameters that controls combustion efficiency
58
3.2. METHOD
and pollutant emissions. In combustion research, the mole fraction of a mixture is
often defined in function of the stoichiometric fuel-to-oxidizer ratio, Fs/As:
? = F/AF
s/As
. (3.1)
In the remainder of this manuscript, the equivalence ratio, ? will be used inter-
changeably with the mole fraction to characterize the composition of a gas.
3.2 Method
A detailed description of the experimental apparatus is given in section A.3 of the
Appendix. Gases are mixed in a cross flow arrangement before exiting into room
air through a ceramic honeycomb. A curtain flow of argon surrounds the premixed
stream to stabilize the flow. A Nd:YAG laser is used to generate the plasma, the
pulse energy was varied between 48 and 366 mJ. This introduces sufficient energy
to create the plasma such that large fluctuations in plasma temperature (and hence
plasma emission) are avoided [61]. The breakdown takes place approximately 2 mm
above the center of the burner. The spatial resolution of the measurement can be
estimated from the characteristic dimension of the plasma, a few mm as discussed
in the previous Chapter. The emission is collected at right angles with respect to
the laser beam, and the plasma light is coupled into a spectrometer. The ICCD
camera mounted to the spectrometer is controlled by a triggering signal from the
laser Q-switch. The time-resolved measurements are characterized by two parame-
ters: the delay time with respect to the triggering signal (delay) and the aperture
59
CHAPTER 3. SPECTROSCOPIC MEASUREMENTS OF HYDROCARBONS
time of the camera?s electronic shutter (gate width).
Approximately 1 ?s after the plasma initiation (and in the absence of radia-
tionless transitions, see discussion in Section 3.6), the intensity of a single atomic
line can be described by equation 2.29. One important consequence from Equation
2.29 is that the intensity of a given line changes with time as the plasma cools. Each
atomic line has an optimal temporal detection window determined by the elemental
ionization energy and the excitation energy of the specific transition under consid-
eration. This optimum changes with the characteristics of the plasma, in particular
the temperature, which at a given time is a function of the laser pulse energy. A
possible method to normalize for pulse-to-pulse variations in the laser energy is to
normalize the peak intensities by the continuum background emission [2]. Similar
results can be obtained taking the ratio of two emission lines and, to the extent that
a set of lines have similar energies and transition probabilities, line ratios are often
more repeatable than absolute line intensities.
A typical averaged LIBS spectrum of a mixture of air and hydrocarbons
(from engine exhaust) in the 700 to 790 nm spectral region is shown in Figure
3.1. This spectral region contains strong atomic lines of C, N, and O. Three
peaks of N at 741, 743, and 746 nm (a triplet generated by the fine splitting of
the 2s22p2(3P)3s ? 2s22p2(3P)3p transition), and a peak of O at 777 nm (also a
triplet that cannot be resolved with the spectrometer used in the experiments) a
at 777 nm are clearly visible. C appears in the spectrum in two different forms:
an atomic peak at 711 nm comprised of several overlapped lines, and a broad CN
molecular emission from several vibrational transitions (degraded to the red) in the
60
3.2. METHOD
Figure 3.1: LIBS spectrum of a mixture of air and hydrocarbons in the region between
690 and 790 nm.
A2? ? X2? electronic transition in the range from 708 to 734. The CN emission
arises from recombination of C and N generated in the plasma into electronically ex-
cited CN*. Additional, weaker CN bands have band heads at 725.9 nm and at 743.7
nm, the latter band head underlying the nitrogen peaks. At lower wavelengths, the
B2? ? X2? CN band, degraded to the violet (with band heads at 359, 388, and
421 nm) represents the brightest emission in the entire spectral region between the
ultraviolet to the near infrared.
To obtain the intensities of particular spectral lines, a linear baseline is fit to
the peak. This baseline is subtracted from the integral of the peak to correct for
the presence of background radiation. From Equation 2.29, as the intensity of each
spectral line is proportional to the number of corresponding atoms in the plasma
volume, to first order (in the absence of interferences) relative concentrations of
elements can be determined by taking the ratio of the integrals of corresponding
61
CHAPTER 3. SPECTROSCOPIC MEASUREMENTS OF HYDROCARBONS
elemental peaks. It is important to note that this way of defining the spectral inten-
sity is somewhat arbitrary. In particular, as shown in Figure 3.1, the background
signal is much stronger in the region of the 711 nm C peak than in the region of the
N and O peaks. For consistency, the algorithm used to compute the spectral inten-
sity is unchanged throughout the measurements, i.e., the peaks are always defined
in the same way.
3.3 Spectroscopic Measurements of the Equiva-
lence Ratio
Figure 3.2 shows the comparison between 300 single shot measurements taken in
each of three different mixtures of air and propane: 0% (pure air), 1% propane by
volume, and 2% propane by volume. Each data point represents the ratio of the
signal from the 711 nm carbon line to that of the combined 746 nm N line and 777
nm O line, as obtained from individual laser pulses. The delay and gate for these
measurements were 3 and 15 ?s respectively, and the laser pulse energy was 86 mJ.
The relative standard deviation is between 2.7% and 3% of the mean value for each
of the three data series and the variation of the data about the mean value follows
a Gaussian distribution, typical of a Poisson process. The offset reported in the
ratio on the y axis in Figure 3.2 for pure air is a result of the data processing. The
spectra show that the intensity of the 711 nm C peak does go to zero in pure air,
but a large background is still present.
62
3.3. SPECTROSCOPIC MEASUREMENTS OF THE EQUIVALENCE RATIO
Figure 3.2: Ratio of the integrated spectral peak area of the 711 nm C to the combined
signal from the 746 nm N line and 777 O line obtained in different mixtures of
propane and air: 0% C3H8 (circles), 1% C3H8 (diamonds), and 2% (triangles). All
measurements were taken with a delay and gate of 3 and 15 ?s respectively.
The background is most probably due to the effect of the CN band (CN is
highly luminous and the signal from the 400 ppm of CO2 present in air might still
be visible) or to the overlap of some other molecular band. Since the origin of the
background is not investigated in this here, it is not appropriate to subtract the
signal due to background radiation. In order to better explain the effect of laser
power on the background (see section 3.3.3) the measurements are presented un-
normalized. As shown in the next sections the presence of the offset in the y axis
does not compromise the technique. The spectrum presented in Figure 3.1 presents
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CHAPTER 3. SPECTROSCOPIC MEASUREMENTS OF HYDROCARBONS
many features that can be related to the equivalence ratio. For example the absolute
intensity of the C, N or O lines, or any combination of them, can be used to obtain
a measure of the fuel/oxidizer concentration. As above the combination of C/N+O,
provides the best signal to noise ratio and is be used throughout this Chapter unless
specified. The single-shot data in Figure 3.2 were acquired at 10 Hz. Hardware
limitations control the repetition rate of the measurement. The actual time required
for acquisition of a single measurement is only slightly more than the sum of the
delay and gate width of the detector, i.e. 18 ?s or less in these measurements. Hence
LIBS could be employed in high speed flows where fluctuating velocities are on the
order of meters per second or faster.
The data in Figure 3.2 illustrate the potential of LIBS to yield quantitative
information on the composition of an unburned mixture of air and hydrocarbons.
To investigate the potential of LIBS in combustion applications it is necessary to
investigate the behavior of each atomic line as concentrations of fuel and oxidizer
are varied over a wide range.
3.3.1 LIBS Measurements in a Combustible Mixture
Measurements in a flame, or in a combustible fuel-air mixture, can be obtained in a
similar manner to the data presented in Figure 3.2; the background luminosity of a
flame and atomic chemiluminescence are negligible compared with plasma emission
in these time-gated measurements. However, LIBS measurements in combustible
mixtures have some obvious drawbacks. In particular, the typical pulse energies
64
3.3. SPECTROSCOPIC MEASUREMENTS OF THE EQUIVALENCE RATIO
needed to form a breakdown using a nominally 10 ns Nd:YAG pulse are sufficient
to ignite flammable hydrocarbon/air mixtures. The first measurement is not af-
fected by ignition since the time required for data acquisition (?s) is much smaller
than the time scales required for ignition, but repeated measurements under similar
conditions in flammable premixtures would require extinguishiment between laser
pulses or sufficient time between measurements (on the order of a fraction of the
second for the present measurements) for a flame to regain equilibrium following the
expansion caused by the plasma. These considerations depend on the application,
in particular on the flow velocity, equivalence ratio, and plasma energy. For the
10 Hz measurements performed in combustible mixtures in this work, a significant
effect on the flame structure was not observed.
For some in-flame measurements, beam steering was observed to interfere with
plasma formation. The index of refraction of a gas depends on temperature, and
thus as rays of the focusing laser beam encounter the flame, they are diffracted
according to Snell?s law. The gradient of the index of refraction is expected to be
roughly normal to the flame surface, which is non-uniform. The steering of each
portion of the beam is thus different, potentially defocusing the beam and/or mov-
ing the focus. Practically, the effects of such aberration depend strongly on local
conditions and may be observed by plotting the fraction of laser energy transmitted
through the plasma as a function of the mixture composition in a particular flow
geometry. In the absence of such aberration, approximately 90% of the laser energy
is absorbed during the breakdown event and the remainder is transmitted [32].
Figure 3.3 shows the percentage of transmitted energy for a 117 mJ laser
65
CHAPTER 3. SPECTROSCOPIC MEASUREMENTS OF HYDROCARBONS
Figure 3.3: Transmitted laser pulse energy as a function of propane concentration.
pulse as a function of the mole fraction of propane in air. The energy absorbed
in the plasma is close to 90%, in accord with the data reported in literature [32]
[34], except for the data point in a nearly stoichiometric propane and air flame,
in which the transmitted energy is almost 72%. Neglecting this aberrant point, a
slight dependence of the absorbed energy on gas composition is observed in Figure
3.3, consistent with results published in literature that suggest the deposited energy
depends slightly on the gas composition [33].
Figure 3.3 illustrates that for these experimental conditions, optical aberra-
tion is only important for mixtures near stoichiometric. The decrease in absorbed
energy is not observed in a rich flame (0.06 mole fraction of propane in air), and was
also not noticed in other experimental settings, in particular during measurements
in a turbulent flow of hot exhaust gas from an engine (T > 600 K). The problems
associated with optical aberration in flames can be avoided by increasing the laser
power such that the absorbed energy always exceeds the effective breakdown thresh-
66
3.3. SPECTROSCOPIC MEASUREMENTS OF THE EQUIVALENCE RATIO
old. For example, in the near-stoichiometric flame through which 72% of the laser
pulse was transmitted, the pulse energy corresponding to breakdown (in air or in
rich mixtures) is increased from approximately 54 mJ to 94.5 mJ. Measurements of
the absorbed energy at a given detector delay and gate allows quantification.
Figure 3.4: Averaged LIBS signal as a function of the mole fraction of propane,
delay 1 ?s, gate 5 ?s.
Figure 3.4 shows the LIBS ratio of the 711 nm C line to the combined of N
and O lines at 745 and 777 nm respectively, over a wide range of mole fractions of
propane in air. These measurements were taken with a delay of 1 ?s and a gate
width of 5 ?s, and a constant energy (90 ? 5 mJ) deposited in the plasma. The vari-
ation in absorbed energy due to gas composition is modest (< 2 mJ) and is ignored
(see discussion in the next Section). Each data point in Figure 3.4 is an average of
300 laser shots; given the Poisson distribution of the single shot data (Figure 3.2) it
is expected that the standard deviation of the averaged data scales as 1?N , where
67
CHAPTER 3. SPECTROSCOPIC MEASUREMENTS OF HYDROCARBONS
N is the number of averaged measurements, and the estimated standard deviation
for the average of 300 shots is less than the 0.2% of the mean value. Other sources
of systematic error (e.g. rotometer values) may be significant and could explain
some fluctuations in the data, but are not included here. As observed in Figure 5,
with this choice of delay and gate, the LIBS ratio of C/(N+O) describing mixture
fraction of C3H8 between 0 and 0.25 can be fit with good accuracy (R2 < 0.99) with
a second order polynomial.
Figure 3.4 illustrates quantitative concentration measurements with LIBS us-
ing an experimental calibration. A detailed calibration curve is required for each
specific application. Determination of laser absorbtion on a shot-to-shot basis was
necessary to compare measurements taken in cold gases to some of those taken in
flames due to the fluctuating absorption of the laser. In the case of turbulent flame
measurements multiple energy-dependent calibrations would be required, and mea-
surements of the absorbed energy with each shot would allow proper quantification
for a measured laser absorption. In general, depending on the absorbed energy,
detector timing and range of concentrations, the relation between the LIBS signal
and concentration may be nonlinear, and the choice of experimental parameters
depends on the actual application. The influence of experimental parameters, in
particular laser pulse energy, detector timing, and the chemical matrix, on the LIBS
measurements is the subject of the remainder of this Chapter.
68
3.3. SPECTROSCOPIC MEASUREMENTS OF THE EQUIVALENCE RATIO
3.3.2 Effect of laser pulse energy on atomic emission
As already discussed, the instantaneous intensity of the atomic emission depends
on the plasma temperature. Plasma volume, temperature and cooling rate depend
strongly on the energy coupled in the breakdown. Therefore, the absolute intensity
of an atomic peak depends on the fraction of the laser pulse energy that is actually
absorbed in the plasma. For each value of the fuel-to-air ratio, and for each choice
of delay and gate, increasing the laser energy increases the emission of N, O and C.
Figure 3.5: Absolute intensity of the 745 nm N line as a function of laser pulse
energy for different concentrations of propane in air, with delay and gate each 1 ?s.
Figure 3.5 shows the intensity of the 745 nm N line as a function of the
concentration of propane for several values of pulse energy ranging from 48 to 165
mJ. Each data point is derived from a single 10-shot average spectrum taken with a
delay and gate of 1 and 5 ?s, respectively. Based on statistics of the data in Figure
3.2, the fluctuations due to shot to shot instabilities are on the order of 1% of the
69
CHAPTER 3. SPECTROSCOPIC MEASUREMENTS OF HYDROCARBONS
mean value for a 10 shot average. As illustrated, line intensity decreases almost
linearly with increasing concentration of fuel, and the behavior is similar for each
pulse energy. Therefore, it should be possible to produce a calibration curve similar
to Figure 3.4 for each laser pulse energy.
Figure 3.6: Ratio of atomic lines (C/N+O) as a function of laser pulse energy for
different concentrations of propane in air, with delay and gate each 1?s respectively.
Figure 3.6 shows the ratio of the 711 nm C line to the combined signal of the
745 nm N and 777 nm O lines. In a given measurement there are three measurands,
C, N and O, which in principle allows the solution of up to three variables (although
in this case N and O are directly related and thus not independent). Provided that
calibration curves (or suitable interpolations) are known for each value of the laser
pulse energy, two lines (C and one of the others) can be used to solve for pulse
energy and hydrocarbon concentration. It is interesting to note that the intensity
of the signal reported in Figure 3.6 for pure air (0% mole fraction of propane)
70
3.3. SPECTROSCOPIC MEASUREMENTS OF THE EQUIVALENCE RATIO
depends on laser power, because the intensity of the background depends on laser
power. In these experiments the background was subtracted by fitting a baseline
under the peaks. The baseline was determined by averaging a few points at fixed
locations on each side of the spectral feature. This simple approach, unchanged
for the different measurements, does not fully compensate for the effect of laser
power on the background (which changes, for example, the peak width). Therefore,
the computed spectral intensity seems to change as a function of the laser energy.
Again, this phenomenon does not present a significant problem once the effect of
the experimental parameters is known in detail.
3.3.3 Lifetime of the atomic emission as a function of laser
pulse energy
The discussion in the preceding section illustrates the effect of laser power as a
function of hydrocarbon concentration. Figure 3.5 shows that nitrogen emission
intensity decreases with concentration of propane. Moreover, the ratio of the C to
the N and O lines shown in Figure 3.6 is dependent on the laser pulse energy. An
increase in the effective lifetime of the emission with increasing laser pulse energy
is one of the primary reasons for this variation. As discussed in Section 2.6.2,
the lifetime of the 745 nm N line increases as the energy coupled into the plasma
increases (Figure 2.25). The 711 nm C line and the CN molecular emission have
similar behavior, but decay more slowly than the N and O lines, which have almost
identical temporal behavior.
71
CHAPTER 3. SPECTROSCOPIC MEASUREMENTS OF HYDROCARBONS
Figure 3.7: Ratio of the normalized C to N spectral lines as a function of time for two
different laser powers (86 mJ squares and 268 mJ circles), with a 0.1 propane mole
fraction for both measurements. Each point is obtained averaging 10 laser shots
Figure 3.7 shows the ratio of the 711 nm C line to the 745 nm N line alone (each
atomic line has his own characteristic lifetime, for simplicity the behavior of only two
lines is compared) at two different pulse energies for 0.1 mole fraction of propane in
air, acquired with a gate width of 1 ?s. At first the ratio increases in time, because
the N line decays faster than the C line. The C to N ratio reaches a maximum during
the later stages of the plasma, when the C emission is actually stronger than those
of N. At these timings the absolute intensity of the atomic lines has decreased more
than ten times from their maximum value, and the fluctuations in the data are due to
low signal to noise ratio. Eventually the ratio approaches unity as the plasma cools
and both lines disappear in the background noise. With increasing laser energies
the curves shift in the direction of increasing time. There are two main implications
72
3.3. SPECTROSCOPIC MEASUREMENTS OF THE EQUIVALENCE RATIO
of the observed behavior for LIBS measurements of hydrocarbons:
Figure 3.8: Comparison of LIBS measurements taken in a flame (squares) with
measurements taken in a cold mixture (circles, diamonds and triangles), taken with
a delay and gate of 1 and 5 ?s, respectively.
? First, performing measurements at shorter times (shorter delay and gate) cap-
tures less C emission, eventually reducing the sensitivity at very short times.
Figure 3.8 shows single shot data obtained in lean and burning mixtures of
propane in air, taken with a delay and gate of 1 and 5 ?s respectively. The
ratio of atomic lines C/(N+O) shown on the y-axis is different than that re-
ported for the same concentration in Figure 3.2 (delay and gate 3 and 15 ?s
respectively) as it depends on the detector timing. Comparison and analysis
of Fig. 3.2 and Fig. 3.8 shows that the single shot measurements at the given
concentrations are less resolved on the C/(N+O) axis with shorter detector
73
CHAPTER 3. SPECTROSCOPIC MEASUREMENTS OF HYDROCARBONS
timings, reducing the sensitivity of the measurement.
? The second issue arises when directly comparing measurements obtained with
different laser powers. If the pulse energy is changed, but the delay and gate
are kept constant, the temporal profile of the atomic lines shifts with respect
to the data acquisition window. This produces nonlinear variations in the
relative intensities of the atomic lines, generating errors in the measurements.
Using a short delay and gate combination minimizes this variation for the C/N or
C/(N+O) ratio, and may be useful in hydrocarbon mixtures with relatively wide
concentration fluctuations, where the absorbed energy may vary and measurements
of absorbed energy may not be possible. As discussed, another approach is to use
energy-dependent calibrations and measurements of the absorbed energy. In general
delay, gate and laser power have to be optimized for each application.
3.3.4 Quenching of atomic emission via radiationless tran-
sitions
The measured lifetime of the atomic lines of N and O varies as a function of the
concentration of propane. Figure 3.9 shows the lifetime of the 745 nm N line in two
different mixtures of propane and air (pure air and 0.1 mole fraction of propane),
with each data point representing the average of 10 laser shots, collected with a gate
width of 1 ?s at the delay shown on the x-axis. The atomic lines appear weaker
and decay more quickly in a rich mixture of propane. The observed decay cannot
be explained, on the basis of Equation 2.29, by a reduced concentration of N atoms
74
3.3. SPECTROSCOPIC MEASUREMENTS OF THE EQUIVALENCE RATIO
in the plasma volume. Rather, the decay is similar to the quenching of atomic
emission due to radiationless decay observed in other emission techniques such as
Laser Induced Fluorescence [54].
Figure 3.9: Effect of the concentration of propane on the lifetime of the N atomic
emission.
The quantum level Ei of an atom can be depopulated not only by sponta-
neous emission, but also by collision-induced radiationless transition [54]. In this
case the energy is transferred to another atom (or molecule) upon collision without
the emission of a photon. The probability of collisional quenching depends on the
concentration of collision partners, the collisional cross section, and the mean veloc-
ity of the molecules. Following the approach of Section 2.6.1 the collision probability
can be written as:
dPcollik
dt = vNb?
coll
ik (3.2)
75
CHAPTER 3. SPECTROSCOPIC MEASUREMENTS OF HYDROCARBONS
where Nb is the number of collision partners per unit volume (m?3), b, v the mean
molecular velocity and ?collik the collisional cross section. In presence of collisional
quenching the total number of transitions per second, from the upper state i becomes
(see equation 2.28):
dni
dt = n
parenleftbigg g
i
Z(T)e
?Ei/kTAikWq +vNb?coll
ik
parenrightbigg
. (3.3)
Comparing equation 2.28 and 3.3 appears that, in the presence of collisional quench-
ing, the intensity of the emission line (given by Equation 2.29) at any time, and the
atomic lifetime decreases. As discussed in section 2.6.2, since T = T(t), v = v(t) and
possibly Nb = Nb(t), Equation 3.3 cannot be used to obtain quantitative estimates
of the emission lifetime.
Figure 3.10: Normalized intensity of the N (746 nm) O (777 nm) and C (711 nm)
lines as a function of the concentration of propane, with delay of 3 s and gate of 15
?s.
76
3.3. SPECTROSCOPIC MEASUREMENTS OF THE EQUIVALENCE RATIO
Figure 3.10 illustrates the normalized intensity of the 711 nm C, 745 nm N an
777 nm O atomic lines as a function of the concentration of propane in air. Data were
taken with a delay of 3 ?s and a gate of 15 ?s, each data point corresponds to the
average of 300 shots. The carbon signal appears to saturate at higher concentrations
of propane, while the behavior of the N and O lines is highly nonlinear. When the
mole fraction of propane exceeds 0.3 the atomic emission of N and O are completely
quenched at the given detector timings, and a shorter delay is required to detect a
signal from N or O.
Figure 3.11: Normalized intensity of the N (746 nm) line as a function of the concen-
tration of propane. Comparison between methane, propane and helium, with delay
of 3 ?s and gate of 15 ?s.
Figure 3.11 compares the intensity of the 745 nm N line at 3 ?s delay and 15
?s gate as function of the mole fraction of diluent for binary mixtures of propane,
methane and helium in air. While the behavior remains linear for increasing mole
77
CHAPTER 3. SPECTROSCOPIC MEASUREMENTS OF HYDROCARBONS
fraction of He, similar quenching is observed for propane and methane, with increas-
ing decay associated with C3H8, which has more carbon atoms and a higher C/H
ratio than methane. The experimental data suggests that C, or a recombination
molecule of carbon, act as collisional partner for N and O.
Applications of LIBS in combustion systems would likely require the measure-
ments in mixed hydrocarbons and/or mixtures of reactants and products. While
the measurements presented in Figures 3.9 and 3.10 suggest that C plays a major
role in the behavior of the atomic emission, hydrogen also as an effect on the LIBS
signal. Comparisons with CH4 and CO2 diluents in air are useful, as both molecules
have the same number of carbon atoms so the substitution of CH4 for CO2 repre-
sents significant hydrogen addition, and O2 is in high concentration in both cases,
although the concentration of O2 is not the same in the two mixtures.
Figure 3.12: Comparison of the emission spectra of methane and carbon dioxide.
Figure 3.12 compares two spectra acquired with delay and gate of 3 and 15 ?s,
78
3.3. SPECTROSCOPIC MEASUREMENTS OF THE EQUIVALENCE RATIO
obtained in binary mixture of 25% carbon dioxide or methane in air. The molecular
emission of CN is considerably higher in the spectra obtained with methane, while
the N emission is lower. Further experiments have shown that the addition of
even relatively small quantities of H2 (1-2 % by volume) to a mixture of carbon
dioxide and air increases the CN emission perceptibly. However, such increase is
small enough that the effect water vapor in ambient air can be neglected in most
applications. A possible explanation is that the presence of hydrogen changes the
relative concentrations of the molecules that recombine in the cooling plasma; this
would also change concentrations of the emitting and quenching species, thereby
also changing the intensity of the N lines.
Figure 3.13: Ratio of the C to N lines as a function of the mole fraction of methane
and carbon dioxide in air, taken with a delay of 3 ?s and gate of 15 ?s.
Figure 3.13 illustrates the ratio of the C to N line as function of mole fraction
in mixtures of methane and carbon dioxide in air, taken with a delay and gate of 3
79
CHAPTER 3. SPECTROSCOPIC MEASUREMENTS OF HYDROCARBONS
and 15 ?s. Each data point is the average of 300 laser shots. For methane this ratio
is nonlinear, while the relationship remains linear over a wide range of mole fraction
for carbon dioxide. Propane is similar to methane, but cannot readily be compared
on Figure 3.13 since the total concentration of carbon atoms is different. These
experiments show that chemical composition, and in particular the abundance of C
and H, plays a major role in LIBS emission of mixtures of air and hydrocarbons.
Although more research is required on this topic, it is expected that hydrocarbons
with similar chemistry would share similar behavior.
Figure 3.14: Normalized intensity of the N and O spectral lines plotted as a function
of the equivalence ratio for methane and propane.
Figure 3.14 shows the intensity of the 745 nm N and 777 nm O lines of propane
and methane plotted as a function of the equivalence ratio. The plot is similar
to that presented in Figure 3.11, but the data collapse onto a single curve when
plotted as a function of the equivalence ratio, illustrating the similarities as function
80
3.4. CONCLUSIONS
of atomic composition. A detailed model of the molecular quenching (that includes
the transient effects arising during the plasma decay) could possibly explain the
observations and be used to further generalize the results outlined in this Chapter.
3.4 Conclusions
The results presented in this Chapter illustrate the use of LIBS as a diagnostic tech-
nique for combustion systems. While limitations exist, there are several combustion
applications that could benefit from this new diagnostic tool. Applications under
development include real time measurements on automobile engines and measure-
ments of the mixing of air and helium in supersonic flows (with applications to fuel
injection in hypersonic and supersonic flows). In the field of combustion, LIBS can
be used to investigate mixing in turbulent flames or to study ignition of turbulent
reacting flows (in this case the laser would be used both as an ignition source and
as a diagnostic tool). Given the high signal to noise ratio of the LIBS technique and
the robustness of the measurement in reactant, products and flames, measurement
of mixture fraction in turbulent flames could probably be accomplished using the
methods outlined in this paper.
The measurements presented have covered several issues that are important for im-
plementation of LIBS as a combustion diagnostic:
? Practical considerations on the performance of measurements in hot, react-
ing flows have been addressed. The LIBS technique can be readily used in
reactants, in products, and even in flames. Measurements obtained in widely
81
CHAPTER 3. SPECTROSCOPIC MEASUREMENTS OF HYDROCARBONS
different regimes can be easily compared, highlighting a rather unique prop-
erty of LIBS as a diagnostic. The role of energy deposition in the plasma for
calibration under variable conditions was illustrated.
? The influence of some key experimental parameters, such as delay, gate and
laser power, on the intensity of atomic emission lines was illustrated. An
understanding of the effect that these parameters have on the lifetime of the
atomic emission is important for optimization of the technique in a variety
of operating conditions. Each application will likely require an individual
optimization, due to variations in configuration, laser plasma characteristic,
and gas composition.
? Finally, emission quenching has been qualitatively described as a function of
the concentration of C and H. In particular the similarities between two dif-
ferent hydrocarbons and the role of C and H have been highlighted. A better
understanding of the basic mechanisms governing the atomic emission of hy-
drocarbons may be exploited to further generalize the technique. For example,
it appears possible to derive a common calibration valid for mixed hydrocar-
bons, or to gather information on the molecular structure of hydrocarbons (for
example the abundance of C and H atoms) from a single LIBS spectra.
While LIBS is an established spectroscopic technique in many fields, the measure-
ments presented are among the first applications of LIBS to combustion problems;
further research is expected to yield to considerable improvements in the technique.
82
Chapter 4
Real Time Measurement of the
Fuel-to-Air ratio
4.1 Measurements on a Reciprocating Engine
The results presented Chapter 3 show how LIBS can be used to perform quantitative
measurements of hydrocarbons. Most of the nonlinear effects related to the depen-
dence of atomic emission on the experimental conditions can be overcome with a
suitable calibration. The measurements are spatially and temporally resolved and
are possible in products, reactants or flames without the knowledge of other addi-
tional parameters. The spectral emission signatures form the plasma are generally
bright, providing high signal to noise ratio that can possibly translate into good
accuracy. Measurements can be obtained from a single pulse of the laser, avoid-
ing time integration of the measurements. These reasons make LIBS attractive for
some applications. However, in order to identify applications of actual interest, it is
83
CHAPTER 4. REAL TIME MEASUREMENT OF THE FUEL-TO-AIR RATIO
necessary to demonstrate LIBS measurements in a real combustion system.
In this Chapter real-time measurements of the equivalence ratio in a recip-
rocating engine are presented. The experiments were performed at the Propulsion
Laboratory of United States Naval Academy in Annapolis during several test ses-
sions in 2002 and 2003.
Figure 4.1: Ratio of the intensity of the spectral lines from exhaust gas as a function
of the engine equivalence ratio. N1 and N2 are the two most intense lines of the 745
nm N triplet.
Figure 4.1 shows LIBS measurements of car engine exhaust. Cold exhaust gas
was sampled from the tailpipe of an engine, while the engine was run at different
equivalence ratios under a constant load. The composition of the exhaust gas was
controlled with feedback from a Universal Exhaust Gas Oxygen (UEGO) analyzer.
A few hundred spectra were collected for each setting of the engine and the average
signal was used to produce the plot presented in Figure 4.1. In the range of equiv-
84
4.2. ENGINE SETUP
alence ratios normally achieved by a car engine , ? = 0.8 ? 1.2, there is almost a
linear relationship between the ratio of spectral lines and the measured fuel-to-air
ratio. It was this first experiment that demonstrated the possibility to use LIBS to
measure combustible mixtures [62]. In this Chapter the most relevant results from
the engine tests are presented.
4.2 Engine Setup
In order to demonstrate LIBS measurement in conditions similar to those that might
be encountered in applications of actual interest, an experiment is arranged to an-
alyze hot engine exhaust in real time. The experimental apparatus is described in
more detail in the Appendix. Briefly, an eddy current dynamometer loads a GM four
cylinder engine. A computerized test system controls the injectors of the engine and
measures the performances including speed torque and intake air flow. An optical
cell is mounted on the exhaust manifold close to the exhaust valve of one cylinder.
The optical cell consists of two thick fused silica window mounted at right angles
on a steel frame. This design provides optical access to the exhaust gas coming
from one of the cylinders at a position were gas temperature and velocity are com-
parable to those obtained inside a cylinder. An Nd:YAG laser is used to generate
the plasma inside the cell. Atomic emission is collected at right angles and coupled
into an optical fiber. The fiber sends the light to a spectrometer which disperses
the light onto an ICCD camera that records the spectrum. A UEGO analyzer is
placed in the optical cell to measure the fuel-to-air ratio near plasma location. The
85
CHAPTER 4. REAL TIME MEASUREMENT OF THE FUEL-TO-AIR RATIO
equivalence ratio of the engine is varied by changing the injector timing. The laser
is synchronized with the engine to always fire at the same position during the cycle.
Figure 4.2: Comparison of the single shot spectra obtained in a laboratory set up
(above) and from the engine (below).
Figure 4.2 compares the spectrum obtained in a laboratory set up (from the
experiments presented in Chapter 3) with the signal obtained from the engine. Both
spectra were obtained from a single pulse of the laser in different mixtures of air and
hydrocarbons. In both cases, camera delay and gate are 3 ?s and 15 ?s respectively.
86
4.3. REAL TIME EXHAUST GAS MEASUREMENTS
The different values on the y-axis are due to different settings of the camera inten-
sifier. Clearly, the signal to noise ratio is considerably reduced in the measurements
obtained from the engine. Nonetheless, the spectral lines of nitrogen, oxygen and
carbon are clearly visible and can be used to determine the equivalence ratio.
4.3 Real Time Exhaust Gas Measurements
Figure 4.2 suggests that detection of spectral lines is not compromised by the high
temperatures and the high velocity, unsteady flow field in the exhaust manifold.
This conforms with expectations, since the plasma temperature (several thousands
Kelvin, as discussed in Chapter 2) is much higher than those normally encountered
in combustion applications, and the time required for the measurements (18 ?s in
the present set of experiments) is negligibly short compared to the time scales of the
fluid phenomena involved. Moreover it seems to be possible to obtain measurements
through the thick optics required to sustain the stress caused by engine operation. In
particular, once the manifold has warmed up and the water that initially condenses
on the windows is evaporated, the instruments seems to perform satisfactorily for a
time sufficiently long to perform the experiments.
Figure 4.3 shows the ratio of the 745 nm N and 777 nm O lines to the 711
nm carbon line plotted as function of the equivalence ratio (as measured by the
reference UEGO sensor). The intensity of the atomic lines is calculated as described
in Chapter 3 and each data point is obtained averaging together the signal from
80 single shot spectra. Similarly to the measurements obtained in a cold exhaust
87
CHAPTER 4. REAL TIME MEASUREMENT OF THE FUEL-TO-AIR RATIO
Figure 4.3: Ratio of the 745 nm N and 777 nm O lines to the 711 nm C line as a
function of the equivalence ratio.
(and presented in Figure 4.1) there is almost a linear relation between the ratio of
spectral intensities and the equivalence ratio of the mixture. Figure 4.3 represents
a calibration curve to relate the LIBS signal to the equivalence ratio. As the error
bars on Figure 4.3 show, averaging together multiple measurements allows discrim-
ination between ?0.05 changes in the equivalence ratio for averaged measurements.
Averaged measurements similar to those presented in Figure 4.3, can have
some possible applications, but for engine research it is interesting to analyze sin-
gle shot measurements. If single shot measurements could be similarly analyzed,
the associated temporal resolution, which is only limited practically by laser repeti-
tion rate, could provide cycle-to-cycle equivalence ratio data from individual engine
cylinders. Figure 4.4 compares the ratio of the 711 nm C to 745 nm N line obtained
88
4.3. REAL TIME EXHAUST GAS MEASUREMENTS
from a single shot of the laser. The 160 data points were obtained at two different
equivalence ratios: ? = 0.95 and ? = 1.25. This plot is similar to those obtained
in a laboratory setup for mixtures of air and propane and shown in Figures 3.2 and
3.8. While a clear separation between the two equivalence ratios is visible in Figure
4.4, there is considerable scatter in the data, primarily related to the signal-to-noise
ratio in these single-shot measurements. Likely causes can be found in the opti-
Figure 4.4: Single shot LIBS spectrum from the engine exhaust. ? = 0.95 solid
diamonds and ? = 1.25 empty squares.
cal losses due to soot, water vapor and transmission through the optical elements.
Local temperature gradients can cause variations in the refractive index of the air
that affects the focusing of the laser beam. As discussed in Section 3.3.1, this could
influence both the size and the position of the plasma relative to the collection op-
tics, eventually affecting the intensity of the detected lines. Finally the non-optimal
repetition rate imposed by the engine (the laser is designed to fire stably at 10 Hz)
may affect the stability of the laser pulse. Shot-to-shot variation in the pulse power
89
CHAPTER 4. REAL TIME MEASUREMENT OF THE FUEL-TO-AIR RATIO
would affect the plasma temperature and eventually the intensity of the atomic lines
(as discussed in Chapter 2). These issues could be addressed and minimized by im-
provements in the experimental set up. For example it is possible to measure the
relative energy of each laser pulse and relate the energy to fluctuations in the signal.
Before considering modifications to the experimental apparatus, it is interesting to
investigate the possibility reduce the noise by manipulating the data.
4.4 Chemometric Analysis of LIBS Spectra
There are many spectral features apparent in either of the spectra shown in Figure
4.2 that could be related to the equivalence ratio, for example the intensity of the
atomic lines or suitable ratios of atomic lines. The variables used in the present
Chapter and in Chapter 3 are the combinations that give the best signal to noise
ratio for a particular set of measurements. An example of different variables that
could be evaluated for each spectrum and related to the abundance of fuel in air is
shown in Table 4.1. Among these variables, the ratio of the 711 nm C line to the
745 nm N line, used in Figures 4.3 and 4.4, gives the best results as a predictor of
?, but it is likely that each of the 10 variables shown in Table 4.1 contains some
information. Moreover the 10 variables are not independent, but are interrelated. It
is expected that it is possible to find a linear combination of these variables that has
the best correlation with the local equivalence ratio. Principal component analysis
(PCA) was used to determine the optimum combination of these 10 variables for
prediction of ? (see for example [63] for an introduction to principal component
90
4.4. CHEMOMETRIC ANALYSIS OF LIBS SPECTRA
Table 4.1: Combinations of several spectral features from Figure 4.2 that could be
related to the equivalence ratio: C = 711 nm C line, O = 777 nm O line, NI and
NII = first and second lines (in order of intensity) of the 745 nm N triplet, CN =
CN molecular band.
Variable Definition Variable Definition
x1 N I+ N II + O x6 C/N I
x2 N I x7 C/O
x3 O x8 C/(N I + O)
x4 C x9 C/(N I + N II + O)
x5 CN x10 CN/O
analysis).
A Matlab routine is used to calculate the 10 variables shown in Table 1 for each
spectrum in a set of data, for example the 160 spectra shown in Figure 4.4. There
are at most 10 independent (or orthogonal) linear combinations of these variables.
A principal components algorithm built into Matlab, based on multivariate analysis,
is used to calculate the linear combination of these variables that expresses the most
variance among the data; this combination is called the first principal component.
The second principal component is computed such that it is orthogonal to the first
and expresses as much of the remaining variance in the data as possible, and so on.
Since ? is the only parameter that is changed during the experiments it is expected
that the variance in the data is all related to ?. Moreover, since the variables are not
independent, the first few principal components should contain most of the variance
91
CHAPTER 4. REAL TIME MEASUREMENT OF THE FUEL-TO-AIR RATIO
and are likely to be the best linear combinations to relate spectral features with ?.
The output of the software is the 10-by-10 matrix A that transforms the
variables in Table 4.1 into the new set of principal components according to the
relation:
y = AxT (4.1)
where x is the row vector containing the 10 initial variables and y is a vector
containing the numerical value of the principal components. It is then possible to
plot the first few Principal Components and verify how they relate to ?. The new
coordinate system groups the variance in the first few variables, so that the data can
be plotted and analyzed conveniently. Figure 4.5 shows the set of data from Figure
Figure 4.5: Single shot LIBS measurements plotted in function of the Principal
Components (from the same data presented in Figure 4.4).
4.4 plotted as a function of the first two principal components. The data series
92
4.5. CONCLUSIONS
now appear more fully separated, indicating that PCA succeeded in recognizing ?
as a latent property in the data. When compared with the plot in Figure 4.4 it
appears evident that PCA significantly reduces the scatter in the data, improving
the determination of ? from LIBS spectra. For example, it is possible to estimate
the increased accuracy of the technique by the number of non-overlapping points in
Figures 4.4 and 4.5. The number of spectra for which the equivalence ratio can be
correctly resolved increases 23% using PCA, from 72% of the total in Figure 4.4, to
95% in Figure 4.5. For this set of data, the first two principal components express
the 99.3% of the variance in the data. Conveniently, principal component analysis
is fully automated and doesn?t require post-processing of the data.
PCA was applied to another set of data acquired at a later time than the
data in Figures 4.4 and 4.5. Using the same experimental parameters as in the
previous experiments, the equivalence ratio was set to 0.85, 1.00 and 1.15. The first
graph in Figure 4.6 illustrates the original data, and the second illustrates the data
following treatment with PCA. Again, it is evident that PCA significantly improves
the resolution of ? from the original data. The data in Figure 4.6 illustrate the
limits of the present experimental set up for engine measurements.
4.5 Conclusions
The results presented in this Chapter demonstrate the use of LIBS as a diagnostic
technique to obtain optical measurements of the equivalence ratio in an engine. Spa-
tially and temporally resolved measurements were obtained in the exhaust manifold
93
CHAPTER 4. REAL TIME MEASUREMENT OF THE FUEL-TO-AIR RATIO
Figure 4.6: Analysis of spectra obtained in lean (? = 0.85), stoichiometric and rich
(? = 1.15) conditions. Comparison of the original data (above) to to data treated
with PCA (below).
of an automotive engine in conditions comparable (for temperature, flow velocity,
volume fraction of soot, etc.) to those that would be encountered in situations of
actual interest, for example during measurements inside a cylinder or in a combus-
94
4.5. CONCLUSIONS
tor. Practical difficulties related with the experiment do not prevent quantitative
measurements and it was possible to synchronize the laser with the engine to obtain
measurements in a fixed position during the cycle.
The possibility of obtaining single shot measurements is discussed, since such
measurements are of primary interest for possible applications. In particular the
numerical techniques of principal component analysis can be used to significantly
improve the accuracy of the single shot data. Using principal component analysis
it was possible to discriminate between single shot measurements obtained in lean
(? = 0.85), stoichiometric (? = 1) and rich (? = 1.15) conditions. The implemen-
tation of principal component analysis is fully automated and becomes an integral
part of the calibration procedure. As a whole, these measurements suggest LIBS
measurements of hydrocarbons may become a useful diagnostic technique for practi-
cal combustion systems. The measurements presented in this Chapter demonstrate
the sensitivity and accuracy that can be achieved with the current setup. Changes to
the experimental apparatus will likely be necessary to further improve the technique.
95
Chapter 5
Future Work
5.1 An Outline for Future Research
This Chapter provides a brief description of some interesting phenomena observed
during these experiments that may be worthy of future work. Here the preliminary
results that could be used as the starting point of a new research are summarized.
The next three sections describe the emission of extreme ultraviolet radiation from
a laser-induced plasma and the effect of a spherical shock wave on nanometer-sized
particles. Both topics departs from the main body of this dissertation, but might
be of some interest in related fields of research.
96
5.2. EXTREME U.V. EMISSION FROM THE LASER-INDUCED PLASMA
5.2 ExtremeU.V.EmissionfromtheLaser-Induced
Plasma
Recently laser plasmas have been proposed as a possible source of x-ray and extreme
UV radiation [64]. A new source of high energy radiation could have applications
of considerable interest in the fields of photolithography and material processing.
As seen in Figure 2.22, the plasma emits radiation at high frequencies shortly after
the breakdown. The total energy radiated is, however, only a small fraction of the
deposited energy. Figure 5.1 shows the signal measured with a diamond photodiode
for different laser pulse energies. The electric potential measured on the y axis is
proportional to the plasma emission in the 200-2200 eV range [65] i.e., to radia-
tion in the extreme UV and soft x-ray range. As expected, the emission increases
Figure 5.1: X-ray and E.U.V. plasma radiation for different pulse energies. Dotted
line: 60 mJ; solid line: 100 mJ; dashed line 200 mJ.
97
CHAPTER 5. FUTURE WORK
Figure 5.2: X-ray emission from a laser plasma; laser pulse energy, 300 mJ.
with increasing laser energy. Radiation intensity reaches a maximum few tens of
nanoseconds after the breakdown and rapidly decays afterwards. Regardless of the
laser pulse energy, it appears that the emission of radiation occurs in two different
stages: an intense burst during the first 100 ns, and a slowly-decaying emission
lasting several hundred ns. The reason for this behavior is not known, but it might
be related to the structure of the laser supported wave during the very first stages
of the expansion.
The exact spectrum of the radiation emitted is not known. In order to gain a
qualitative understanding of the spectral distribution, a thin aluminum foil (with a
thickness of few hundred ?m) is placed in front of the photodiode. Only radiation
with a very high frequency (with energy greater than approximately 1 keV) can pass
through the foil. Figure 5.2 shows the radiation detected by the shielded photodiode
for a 300 mJ laser pulse. The radiation detected is due to soft x-rays and the profile
98
5.3. SHOCK WAVE EFFECT ON A DENSE AEROSOL
in time appears similar to that presented in Figure 5.1. More research is needed to
identify possible applications and to enhance the intensity of the emitted radiation.
5.3 Shock Wave Effect on a Dense Aerosol
During the LIBS measurements on engine exhaust, presented in Chapter 4, an unex-
pected phenomenon was observed. In the cold exhaust of the engine a large number
of carbonaceous particles, with diameters of a few tens of nm, are formed due to
homogeneous nucleation. During the experiments, the particle size distribution was
measured in real time with an optical particle counter. Meanwhile, LIBS was used
to measure the composition of the gas. A sudden change in particle size was noticed
when the LIBS laser was operated.
Figure 5.3: Effect of the shock wave on the particle number distribution of a dense
aerosol.
99
CHAPTER 5. FUTURE WORK
To investigate the phenomenon the following experiment was performed. An
aerosol was generated with an atomizer using solutions of sodium or magnesium.
The aerosol flowed through an optical cell where the laser was focused. The cross
section of the optical cell (several cm2) was much bigger then the characteristic
dimension of the plasma, thus the effect of the hot plasma on the overall temperature
was negligible. The particle size distribution was analyzed using a Scanning Mobility
Particles Sizer (SMPS). Figure 5.3 shows the particle size distribution of the aerosol
with and without the operation of the pulsed laser. As it can be seen, the number of
particles with diameter in the range between 30 and 100 nm is greatly reduced when
the laser is operated. Meanwhile the number of particles with diameter greater than
150 nm is increased.
This phenomenon is attributed to the shock wave generated by the plasma
discharge. The laser-generated shock wave transfers momentum to the particles.
The velocity of the particles depends on the diameter; therefore particles of different
sizes will acquire a relative velocity and may collide together. Upon collision, surface
forces cause the particle to stick together. The overall effect is that the number
of smaller particles is reduced while new larger particles are created. A similar
phenomenon, well documented in literature, is the agglomeration of particles due to
standing or travelling sound waves [66] [67]. Compared to the sonic case, the particle
motion in weak shock waves has been studied much less. Some relevant papers on
the subject are quoted in references [68], [69], [70], [72], [73], [74]. In particular
Goldshtein and co-workers demonstrated experimentally the displacement of small
particles and aerosol agglomeration, caused by a planar shock wave [68], [69].
100
5.3. SHOCK WAVE EFFECT ON A DENSE AEROSOL
In Figure 5.3 it is also observed that a peak of particles with diameter around
25 nm appears when the laser is operated. This peak is likely caused by re-suspension
of particles from the walls of the optical cell. The smaller particles, with a relatively
large diffusion coefficient, deposit on the walls of the cell by diffusion. When the
laser is operated, the vibrations induced by the shock wave re-suspend the particles,
increasing the number of small particles. Using this mechanism, Vanderwood and
co-workers proposed the use of shock waves to clean silicon surfaces of nanoparticles,
[75], [76].
5.3.1 Drag of a nanometer-sized particle in a spherical shock
wave
To understand the dynamic effect of the shock wave on an aerosol, it is necessary
to describe the behavior of a single particle in the flow field caused by the laser
spark. The results presented in Chapter 2 show how fluid velocity in time can be
determined accurately from the results published in literature. The trajectory of
a particle through the shock wave can be determined once the particle?s drag is
known. The simpler model to describe the motion of a solid particle is to assume an
uniform, spherical particle in a Stokes flow. With these assumptions the acceleration
on a particle is given by Stokes law:
dv
dt =
18?
?pd2(u?v) (5.1)
where v is the velocity of the particle, u the velocity of the fluid, ? the viscosity
of the fluid, ?p the particle density and d the particle diameter. Stokes equation is
101
CHAPTER 5. FUTURE WORK
valid only in the assumption of viscous flow. That is with Rer < 1 where Rer is
the relative Reynolds number based on the relative particle velocity, u?v and the
particle diameter, d:
Rer = ?0d|u?v|?
0
(5.2)
If the particle diameter becomes comparable with mean free path of the fluid
molecules, the gas cannot be assumed to be a fluid with continuum properties. In
particular, the fluid velocity with respect to the particle cannot be assumed to vanish
at the particle surface. The Knudsen number, Kn, is defined as:
Kn = ?d (5.3)
where ? is the mean free path of the molecules. For values of the Knudsen number
greater than 10?3 rarefaction effects become important [77]. A common correction
for the particle acceleration is to consider:
dv
dt =
18?
C?pd2(u?v) (5.4)
where C is the Cunningham correction factor defined as:
C = 1 +Kn(1.257 + 0.4e?1.1/Kn) (5.5)
For higher values of the relative Reynolds number, the inertia of the particle becomes
important while, for high values of the relative mach number, Mr (defined as the
ratio of the relative particle velocity, u-v, to the speed of sound), compressibility
effects become important [77]. Equation 5.4 is usually assumed to be valid for
Rer < 1 and Mr < 0.6 and can easily be integrated to obtain the particle trajectory.
102
5.3. SHOCK WAVE EFFECT ON A DENSE AEROSOL
5.3.2 Particle trajectory in a spherical shock wave
Equation 5.4 approximately describes the behavior of a solid particle of a few hun-
dred nanometers in diameter, in a viscous flow. The trajectory through a shock
wave can be found considering a particle initially at rest at a short distance from
the breakdown. Assuming spherical symmetry, the flow field as a function of time
and space is determined interpolating the tables given in [31] and [47] (considering
also the results discussed in Section 2.4.3 to obtain the correct flow field for a given
laser pulse energy). Then, Equation 5.4 is integrated twice to compute the particle
trajectory in the radial direction. A computer code was written in MatlabcircleR to
perform these tasks.
Figure 5.4: Displacement of a 100 nm particle (with density 1000 kg/m3) initially
placed at 10 mm from the breakdown point of a 300 mJ laser pulse.
Figure 5.4 shows the radial displacement, r = r(t), of a 100 nm particle with
103
CHAPTER 5. FUTURE WORK
Figure 5.5: Relative Reynolds and Mach numbers for a 100 nm particle as a function
of time. The dotted lines show the limit of validity of Equation 5.4.
density of 1000 kg/m3, initially placed at 10 mm from the breakdown point of a
300 mJ laser pulse. This set of initial conditions could represent a solid particle
suspended in air. First, the particle is pushed outwards by the expanding blast
wave, then it is moved back towards the center by the back-flow in the expansion
wave. The displacements caused by the shock wave are on the order of thousands of
particle diameters. The simulations suggest that, after the shock wave has passed,
there is a net positive displacement of the particles, that is, the particles are pushed
away from the breakdown point. However, the net displacement is small when
compared to the size of the turbulent region generated during the last stages of the
breakdown (see section 2.5). For this reason, the shock wave is not expected to have
an influence on the local concentration of an aerosol, but could have an effect on
particle collision rates.
104
5.3. SHOCK WAVE EFFECT ON A DENSE AEROSOL
The results of the simulations are consistent with the structure of the shock
Figure 5.6: Displacement, relative Reynolds and Mach numbers for an 800 nm par-
ticle as a function of time.
wave, but have not been verified experimentally. Figure 5.5 shows the relative
Reynolds and Mach numbers for the particle in Figure 5.4 through the shock wave,
as a function of time: it appears that the values remain within the range of validity
of Equation 5.4. If this results could be validated experimentally (for example
using Particle Image Velocimetry) it would be possible to use the simulations to
compute the relative velocity of particles with different sizes. Figure 5.6 shows the
displacement and the relative Reynolds and Mach numbers for a 800 nm particle
(in the same conditions as those described for Figures 5.4 and 5.5).
105
CHAPTER 5. FUTURE WORK
5.3.3 Implications for Aerosol Measurements
If the relative velocity of particles is known, then a kinetic model for the collision
of particles, similar to that presented in [78], can be developed to describe the
agglomeration of an aerosol. Consider a polydisperse aerosol, initially composed of
a number N0 of particles divided in k groups according to the diameter. Let ni be the
number of particles with diameter di, and vi their velocity. In the time ?t, a single
particle di will travel a distance ?tvi. Assuming that the particles with diameter
dj have lower velocity, di will collide with all the particles dj that happen to be in
a cylinder with base pi(di+dj)24 and height ?t(vi ?vj). The number of collisions for
the single particle di with particles dj is:
cj =
integraldisplay
V
integraldisplay ?
0
pi(di +dj)2
4 (vi ?vj)njdtdV (5.6)
where V is the volume of the aerosol. For ni particles di the total number of collision
is:
cij = ni
integraldisplay
V
integraldisplay ?
0
pi(di +dj)2
4 (vi ?vj)njdtdV (5.7)
Assuming perfectly sticking particles (although this is just an approximation), then
when two particles with diameters di and dj collide together they form a particle
with diameter (di + dj) = di+j. It is then possible to model the evolution of the
particle population. The rate of formation of particles with diameter dq will be:
nprimeq = 12
summationdisplay
i+j=q
cij (5.8)
where the summation i + j = q is intended over those particle that would yield a
particle dq upon collision. The coefficient 1/2 is inserted not to count each collision
106
5.3. SHOCK WAVE EFFECT ON A DENSE AEROSOL
twice. Any collision of a particle dq decreases nq. Therefore the rate of change of
particles dq is:
nprimeq = 12
summationdisplay
i+j=q
cij ?
ksummationdisplay
i=1
ciq (5.9)
Knowing the relative velocity of different particles as a function of space and
time, allows to solve Equation 5.7 calculating the number of collisions. Then, the
particle population evolution is completely determined. It is noticed that the ag-
glomeration of an aerosol can be investigated experimentally with experiments sim-
ilar to that presented in Figure 5.3. Therefore, a model for particle dynamics could
provide insight on quantities that are hard to measure such as drag of nanometer-
sized particles or the probability of particles to stick together upon collision.
107
Chapter 6
Conclusions
6.1 Summary of the Present Work
In this dissertation, possible new applications of Laser Induced Breakdown Spec-
troscopy are investigated. The work is divided into two distinct parts. In the first, an
experimental and theoretical study of the basic physics governing the laser-induced
breakdown is carried out. In the second part, atomic emission lines from the plasma
are used to perform gas composition measurements. In order to obtain reliable spec-
troscopic measurements, a detailed knowledge of the laser-induced plasma is needed.
Thus, the two parts of the research are deeply connected.
6.2 Experimental Study of Laser Plasmas
Laser plasmas are formed when the energy from relatively powerful laser pulses
(typically a few hundreds of mJ in a ?10 ns pulse) is absorbed by ionized gas. Af-
108
6.2. EXPERIMENTAL STUDY OF LASER PLASMAS
ter the initial breakdown, the plasma can be described as an inviscid, compressible
fluid. The laser energy is absorbed by a layer of ionized gas that is compressed by
a strong shock wave, to reach high temperatures and high densities. The absorbed
energy creates the shock. The mechanism is similar to ordinary detonations, where
a shock wave ignites an explosive releasing chemical energy. In order to understand
the plasma evolution, it is necessary to investigate the fate of the energy deposited
in the fluid. Experimental measurements suggest that only a small fraction of the
energy is dissipated in the form of radiation. The greatest part of the energy is
spent to increase the internal energy of the fluid, which rapidly expands. Dimen-
sional analysis of the problem allows the derivation of scaling laws that determine
the dimensions of the plasma, at the end of the 10 ns laser pulse, as a function of
laser pulse energy. The volume of the plasma defines the region where a known
amount of energy is stored. Thus, it is possible, using thermodynamic relations be-
tween internal energy and temperature, to estimate the plasma temperature. The
theoretical estimates are found to be in good agreement with the values measured
experimentally.
After the end of the laser pulse, the free expansion of the fluid can be described
using the theory of point explosions. Originally developed to study nuclear explo-
sions, the theory of point explosions describes the shock wave produced by the laser
breakdown (where the energy release is tens of orders of magnitude smaller). The
position of the shock wave in time is measured experimentally and compared to the
theory. This allows to accurately determine the evolution of the flow field during
the first few tens of ?s, as well as the final energy distribution. Most of the energy is
109
CHAPTER 6. CONCLUSIONS
irreversibly converted into heat and remains deposited within few tens of mm from
the breakdown point. The small region of hot gas rapidly develops instabilities and
turbulent convection dissipates the remaining energy.
The plasma emits intense radiation for few hundred nanoseconds following the
breakdown. The continuum bremsstrahlung radiation from the plasma rapidly fades
as the fluid expands. After less than a ?s after the laser pulse, atomic emission lines
emerge from the background. The emission lasts a few tens of ?s, during which
the shock wave detaches from the central, hot gas region, and fades well before the
onset of instability (for the laser pulse energies investigated in this study). The
lifetime of the atomic emission is determined by the overlap of two phenomena: the
spontaneous decay of fluorescence and the hydrodynamic evolution of the gas.
The model of shock propagation developed is in good agreement with the
experimental observations, and allows for quantitative estimates of the fluid prop-
erties. The approximate relations derived in this dissertation could be considerably
improved by means of numerical simulations. For example, computer models should
be capable of describing the plasma from the absorbtion of the laser pulse, to the
final emission spectra. Nevertheless, the approach used in this dissertation describes
a convenient non-dimensional formulation of the problem. These experimental re-
sults, when reported in non-dimensional form, could be used to validate numerical
results.
110
6.3. MEASUREMENTS OF HYDROCARBONS
6.3 Measurements of Hydrocarbons
In the second part of the research, spectroscopic emission is used to measure the
composition of mixtures of air and hydrocarbons. The 700?800 nm spectral region
contains atomic emission of C, N and O, allowing the estimation of the mole fraction
of fuel and oxidizer. LIBS measurements can be carried out in reactants, products
and even flames. Nonlinear effects, due to the high temperature gradients present
in the flame, can be corrected during calibration. There is a monotonic relation
between intensity of the spectral lines and mole fraction of fuel in a gas over a wide
range of concentrations. Measurements can be obtained with a single pulse of the
laser and are spatially and temporally resolved.
In order to optimize the technique, the dependence of the measurements on the
main experimental parameters is studied. In particular, the effect of laser pulse en-
ergy and detector timing are investigated. The energy of the laser pulse determines
the volume and temperature of the plasma. This influences both the intensity and
the lifetime of atomic emission. The timing of the camera determines the tempo-
ral interval over which spectroscopic emission are integrated to generate the signal.
The camera timing can be optimized to obtain the best signal to noise ratio for a
particular experiment.
It is noticed experimentally that high concentrations of C decrease the inten-
sity and lifetime of the N and O atomic emission lines drastically. This phenomenon
cannot be explained by the reduced concentration of N and O atoms in the plasma
volume. The reduced atomic emission lifetime is consistent with a collisional quench-
111
CHAPTER 6. CONCLUSIONS
ing model, where the excited quantum levels are depopulated by collisions with
other atoms. Likely C, or a recombination molecule containing C (for example CN,
formed in the cooling plasma), acts as an effective collision partner for N and O
atoms. Experimental measurements suggest that emission spectra is also affected
by the concentration of H. The behavior observed appears to be similar for differ-
ent hydrocarbons. The experimental calibration of the technique will thus depend
on the chemical composition of the hydrocarbon investigated. Further research is
needed to better understand the role of the chemical matrix on emission spectra.
In order to identify possible applications of the technique, LIBS is used to
analyze exhaust gas from a reciprocating engine. It is demonstrated there is a linear
correlation between the intensity of spectroscopic emission and the fuel to air ra-
tio. The measurements are performed in the hot exhaust gas, few centimeters from
the exhaust valve of one cylinder. The conditions of temperature and fluid veloc-
ity are comparable to those encountered in the combustion chamber of an engine.
Compared to the measurements obtained in a laboratory set up, the signal-to-noise
ratio in the engine measurements is considerably reduced. It is demonstrated that
the statistical technique of principal component analysis can be used effectively to
increase the sensitivity of the measurements. It was then possible to discriminate
between measurements obtained in lean (? = 0.85), stoichiometric, and rich condi-
tions (? = 1.15). These measurements define the limits of sensitivity that can be
achieved with LIBS, in the present configuration.
112
Appendix A
Experimental Setup
A.1 Measurement of the Radiated Energy
As shown in Figure A.1, the plasma is generated by Nd:YAG, Spectra Physics Pro
250laser, Q-switchedwith10Hzrepetitionrate. Thepulsedurationis10nsFWHM.
The pulse energy is accurately controlled using an optical attenuator consisting of
1/2 retardation waveplate and a polarizing cubic beam splitter. The energy of the
beam is measured using an Ophir PB50BB pyroelectric energy meter. The laser is
focused by a 75 mm focal length fused silica lens and the radiated energy is measured
with an Ophir 10A-P volume absorber energy meter. The radiation detector has
a flat response in the range between 190 and 1500 nm and is initially positioned
at 19 mm from the focus of the lens. The position is accurately controlled with a
micrometric translation stage. Since the volume absorber detector is sensitive to the
vibrations produced by the shock wave, it is protected with a fused silica window.
All the measurements are corrected for losses through the optical components.
113
APPENDIX A. EXPERIMENTAL SETUP
Figure A.1: Measurement of the radiated energy: experimental setup.
114
A.2. SHADOWGRAPHY SETUP
A.2 Shadowgraphy Setup
Figure A.2: Setup for shadowgraphy.
Illustrated in Figure A.2, a Nd:YAG lab 150 Specrta Physics laser, with a
10 ns FWHM pulse width, is used to illuminate the plasma at right angles. The
laser beam is expanded to a diameter of 50 mm by a matching pair of collimating
lenses and subsequently imaged on a SONY XCD-SX900, CCD camera. The beam
intensity is attenuated using a set of neutral density filters. The lasers and the
camera are synchronized using a Berkeley Nucleonics Delay Generator. On a pulse-
to-pulse basis, the timing between the two lasers is assumed accurate within ?10
115
APPENDIX A. EXPERIMENTAL SETUP
ns. Over a longer period of time the delay between the two lasers may drift a few
hundred of ns. To reduce this uncertainty to few tens of ns, the delay between the
laser pulses is checked periodically with a 100 ps rise-time photodiode connected to
a fast oscilloscope.
116
A.3. SPECTROSCOPIC MEASUREMENTS OF THE EQUIVALENCE RATIO
A.3 Spectroscopic measurements of the equiva-
lence ratio
As shown in Figure A.3, gases metered using rotometers are mixed in a cross flow ar-
rangement before traveling 0.5 m though a 25 mm ID tube. A fine mesh honeycomb
stabilizes a premixed flame over the burner during measurements in combustible
mixtures.
Figure A.3: Setup for gas composition measurements.
The air flow was set at 10 l/min for all of the experiments, while fuel, diluent
117
APPENDIX A. EXPERIMENTAL SETUP
CO2, or He were varied to set the mixture fraction. A curtain flow of argon surrounds
the premixed stream to stabilize the flow. 10 Hz pulses of 1064 nm light from
a Spectra Physics Quanta Ray Pro 230, Q-switched Nd:Yag laser were used to
generate the plasma. The beam is focused using a 12.5 cm focal length fused silica
convex lens. The breakdown takes place approximately 2 mm above the center of
a 25 mm ID tube. A pair of 12.5 cm focal length fused silica lens collects and
collimates the emission at right angles to the laser beam, and couples the plasma
light into a UV-grade optical fiber. The fiber transmits the light to a 0.3-m Acton
SpectraPro 300i spectrometer, where the signal is spectrally resolved and imaged
onto a Roper Scientific PI-Max gated ICCD camera. The effective dispersion of
the system with the 600 groove-mm grating employed in these measurements is
approximately 0.125 nm/pixel. The ICCD camera is fully binned in the vertical
(non-dispersion) direction. The system is coupled to a personal computer for data
acquisition. The laser pulse energy was measured with an Ophir pyroelctric energy
meter, controlled by personal computer and capable of recording measurements at
the laser repetition rate of 10 Hz.
118
A.4. ENGINE EXPERIMENTS
A.4 Engine experiments
As shown in Figure A.4, the test engine is a General Motors LD-9 dual overhead
cam four-cylinder engine. This engine, originally known as the GM Quad 4, has
four valves per cylinder, a direct-fire ignition system, and port fuel injection. In
this investigation, the ignition and fuel injection are controlled with an Intelligent
Controls IC 5460 computer controller, which directly controls the fuel injectors and
sends low-level ignition signals to an Intelligent Controls IC 5580 ignition relay
system to fire the ignition coils.
A Borghi and Saveri FE-300-S eddy current dynamometer loads the engine,
under control of a SuperFlow Pro Console test system, which also acquires engine
performance data. The measured performance data included speed, torque, relative
intake air flow, exhaust sample temperature and a reference equivalence ratio. A
number of other standard temperatures and pressures are recorded.
The reference fuel to air ratio is measured using an ECM 2400G UEGO-based
Wide-Range Air-Fuel Ratio Analyzer. A hot-wire mass-air-flow sensor output pro-
vides the relative mass air-flow measurement. An optical cell was mounted on the
exhaust manifold, roughly 15 cm from the exhaust valve of one of the cylinder.
The cell consists of two fused silica windows, 50 mm in diameter and 12 mm thick,
mounted at right angles on a cubic steel frame. The 532 nm pulse from a CFR
400 Big Sky Nd:YAG laser was used to generate the plasma. The beam is focused
using a 12.5 cm focal length fused silica convex lens. The breakdown takes place
approximately in the center of the optical cell. A triggering signal from the engine
119
APPENDIX A. EXPERIMENTAL SETUP
Figure A.4: Setup for measurements on the engine.
is used to synchronize the laser so that every measurement is taken in a specified
position during the engine cycle. For simplicity the speed of the engine was reg-
ulated to provide a signal close to 10 Hz, the default laser repetition rate set by
the manufacturer. A 12.5 cm focal length fused silica lens collects and collimates
the emission at right angles to the laser beam, and couples the plasma light into a
UV-grade optical fiber. The fiber transmits the light to a 0.3-m Acton SpectraPro
300i spectrometer, where the signal is spectrally resolved and imaged onto a Roper
120
A.4. ENGINE EXPERIMENTS
Scientific PI-Max gated ICCD camera. The effective dispersion of the system with
the 600 groove-mm grating employed in these measurements is approximately 0.125
nm / pixel. The camera is controlled by a triggering signal from the laser Q-switch.
The ICCD is fully binned in the vertical (non-dispersion) direction.
121
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