ABSTRACT
Title of Dissertation: CRYOGENIC DESIGN AND THERMAL
ANALYSIS OF THE CURIE CRYOTRAP
Rebecca Osborn
Master of Chemical Physics, 2022
Dissertation Directed by: Dr. Timothy Koeth
Department of Material Science
The decay rates of electron capture (EC) radioisotopes, such as 7Be, are demonstratively
susceptible to alteration with change to the electron orbital structure [1] [2] [3] [4]. The Cryogenic
Ultra-high vacuum Radioactive Isotope Experiment (CURIE) Project aims to isolate the various
charge states of the low-Z radioisotope 7Be stably to perform novel half-life measurements. To
achieve this, the system must be cooled to 4K to reach extreme high vacuum (XHV) conditions
in excess of 10?15mbar and to ensure single ion resolution detection. The cryogenic design
which achieves this is presented here. The design consists of the actively cooled 45K radiation
shield, and the 4K stage which houses the Penning trap. The 4K stage is brought to XHV and
maintained at these pressures through the design of a rotary ?cryovalve?. This thesis details
the entire apparatus, the heat loads incident on both stages through simulation, and outlines an
experimental method for testing the ?cryovalve?.
CRYOGENIC DESIGN AND THERMAL ANALYSIS OF THE CURIE
CRYOTRAP
by
Rebecca Osborn
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
Master of Chemical Physics
2022
Advisory Committee:
Dr. Timothy Koeth, Advisor/Chair
Dr. Michael Coplan
Mr. Arkadiy Klebaner
Dr. Patrick O?Shea
Acknowledgments
I would like to express my upmost gratitude to the following people and organizations who have
made this thesis possible:
First, to Lockheed Martin (LM) for generously funding this research, and to Dr. Scott Anderson
and many others at LM for smoothly facilitating this relationship.
To Dr. Timothy Koeth for his excellent mentorship, and for having the very cool idea to undertake
this project in this first place. I have learned and grown an immense amount under his leadership.
To my committee: Dr. Michael Coplan, Mr. Arkadiy Klebaner, and Dr. Patrick O?Shea. I am
very grateful for their support and expertise. In particular, Arkadiy?s guidance in all things cryogenic
engineering has made this thesis possible. I?d like to thank him for his constant optimism and kindness.
To Dr. Ned Allen, who read my undergraduate thesis and then introduced me to this world of
chemical and nuclear physics. Had it not been for him, I never would have been a part of this project.
To Scott Moroch and Ariana Bussio who have both singlehandedly moved this project miles. A
huge thanks to them, as well as to the rest of the Koeth Group, for helping me think through the majority
of this thesis, and for carrying this project on to its ultimate goal.
To Dr. Wendall Hill and Ms. Souad Nejjar for many prompt email responses and quick signatures,
with my best interest always in mind, as I navigated the world of earning this degree.
To my many proofreaders, including Dr. Michael Coplan, Mr. Alan Bornstein, and my dad, Mr.
Thomas Osborn. Thank you for your discerning eye and attention to detail.
Finally, to my family and my friends, who I am very lucky to be loved by. Thank you for listening
to me and encouraging me through all of my endeavors. To Maeve, who can?t read yet, but who has been
one my greatest sources of joy these past two years. To Grover, who fits into the same category. And to
Marco, who has been another great source of joy and my biggest supporter.
ii
Table of Contents
Acknowledgements ii
Table of Contents iii
List of Tables v
List of Figures vi
List of Abbreviations viii
Chapter 1: Introduction 1
1.1 Background and Significance . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2
1.2 Objectives and Approach Taken . . . . . . . . . . . . . . . . . . . . . . . . . . 5
1.3 Principles of Cryogenic Engineering Design . . . . . . . . . . . . . . . . . . . . 8
1.3.1 Conduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
1.3.2 Thermal Contact Resistance . . . . . . . . . . . . . . . . . . . . . . . . 10
1.3.3 Radiation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
1.3.4 Thermal Contraction . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12
1.3.5 Stress and Strain . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
1.3.6 Gas Flow in Vacuum Systems . . . . . . . . . . . . . . . . . . . . . . . 14
1.4 Prior Art . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
1.4.1 Long-term Storage through Extreme High Vacuum . . . . . . . . . . . . 16
1.4.2 Cryogenic Valves . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16
1.4.3 Cryogenic Apparatus . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
Chapter 2: Overview of the Apparatus 19
2.1 The Magnet . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20
2.2 The Cryocooler . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21
2.3 Thermal Strap Design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22
Chapter 3: Design of 45 Kelvin Stage 24
3.1 Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24
3.2 G-10CR Support Design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26
3.2.1 Simulation Results and Conductive Heat Loads through G-10CR Supports 26
3.2.2 Support Location and Strength Simulation Results . . . . . . . . . . . . . 27
3.3 Radiation Heat Load Calculations . . . . . . . . . . . . . . . . . . . . . . . . . 30
3.3.1 45K Chamber Lower Radiation Shield . . . . . . . . . . . . . . . . . . . 31
iii
3.3.2 Use of MLI to Limit Radiative Heat Load . . . . . . . . . . . . . . . . . 33
3.4 Total Heat Loads on 45K Stage . . . . . . . . . . . . . . . . . . . . . . . . . . . 36
3.5 Temperature Rise Studies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36
3.5.1 Material Properties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37
3.5.2 Initial Temperature for Model . . . . . . . . . . . . . . . . . . . . . . . 37
3.5.3 Thermal Resistance in Joints . . . . . . . . . . . . . . . . . . . . . . . . 39
3.5.4 Gradient Along Length of the 45K Stage . . . . . . . . . . . . . . . . . . 41
3.5.5 Simulation Results and Significance to Design Choices . . . . . . . . . . 41
3.6 Thermal Contraction Studies . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43
3.6.1 Material Properties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43
3.6.2 Simulation Results and Significance to Design Choices . . . . . . . . . . 43
Chapter 4: Design of 4 Kelvin Stage 45
4.1 Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45
4.2 G-10CR Support Design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48
4.2.1 Simulation Results and Conductive Heat Loads through G-10CR Supports 49
4.3 Radiation Heat Load Calculations . . . . . . . . . . . . . . . . . . . . . . . . . 54
4.4 Total Heat Loads on 4K Stage . . . . . . . . . . . . . . . . . . . . . . . . . . . 55
4.5 Temperature Rise Studies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56
4.5.1 Material Properties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56
4.5.2 Initial Temperature for Model . . . . . . . . . . . . . . . . . . . . . . . 56
4.5.3 Thermal Resistance in Joints . . . . . . . . . . . . . . . . . . . . . . . . 57
4.5.4 Length of the 4K Stage . . . . . . . . . . . . . . . . . . . . . . . . . . . 58
4.6 Thermal Contraction Studies . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61
4.6.1 Material Properties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61
4.6.2 Simulation Results and Significance to Design Choices . . . . . . . . . . 61
4.6.3 Overall Trap Shift Due to Contraction . . . . . . . . . . . . . . . . . . . 62
4.7 Achieving Extreme High Vacuum (XHV) . . . . . . . . . . . . . . . . . . . . . 63
4.7.1 The Cryovalve . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68
4.7.2 Cryosorptive Surfaces for Cryopumping . . . . . . . . . . . . . . . . . . 71
4.7.3 Testing the Valve . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74
Chapter 5: Conclusions 82
Appendix A: 85
A.1 Additional Constants and Equations . . . . . . . . . . . . . . . . . . . . . . . . 85
A.1.1 A and B constants for Clausius-Clapeyron vapor pressure equation . . . . 85
A.1.2 Transmission probability coefficient for a rectangular slit . . . . . . . . . 85
References 86
iv
List of Tables
3.1 45K G-10CR support heat loads . . . . . . . . . . . . . . . . . . . . . . . . . . 27
3.2 Tabulated layer densities of interest from Figure 3.9. . . . . . . . . . . . . . . . . 36
3.3 Total heat loads in watts, W, on the 45K stage. . . . . . . . . . . . . . . . . . . . 36
3.4 Maximum temperature of 45K stage for various thermal resistance values. . . . . 41
4.1 Total conductive heat load contributed by G-10CR supports . . . . . . . . . . . . 50
4.2 Heat loads through stage 1 and 2 G-10CR supports with varying offset. . . . . . . 54
4.3 Radiative heat loads onto 4K stage. . . . . . . . . . . . . . . . . . . . . . . . . . 55
4.4 Total heat loads in mW on the 4K stage due to all non-negligible sources. . . . . 56
4.5 4K stage end temperatures for various joint thermal resistances and stage lengths 59
A.1 A and B constants of typical molecular species present in vacuum systems for
calculation of vapor pressure with the Clausius-Clapeyron equation. . . . . . . . 85
v
List of Figures
1.1 Labeled cross-sectional view of the CURIE assembly. . . . . . . . . . . . . . . . 6
2.1 Labeled cross-sectional view of the entire cryogenic design. . . . . . . . . . . . . 19
2.2 Labeled cross-sectional view of cryocooler chamber. . . . . . . . . . . . . . . . 23
3.1 SolidWorks assembly of the 45K shield. . . . . . . . . . . . . . . . . . . . . . . 25
3.2 45K mechanical support made from G-10CR. . . . . . . . . . . . . . . . . . . . 27
3.3 on Mises stress on 45K stage. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28
3.4 Displacement in z-direction of 45K stage. . . . . . . . . . . . . . . . . . . . . . 28
3.5 Von mises stress on left-hand G-10CR support. . . . . . . . . . . . . . . . . . . 29
3.6 Von mises stress on right-hand G-10CR support. . . . . . . . . . . . . . . . . . . 30
3.7 SolidWorks model of 45K chamber. . . . . . . . . . . . . . . . . . . . . . . . . 32
3.8 Theoretical heat flux through N layers of MLI superinsulative wrapping for a
layer density of 37 layers/inch. . . . . . . . . . . . . . . . . . . . . . . . . . . . 34
3.9 Theoretical heat flux through N layers of MLI superinsulative wrapping adjusted
to match experimental result for 45 layers at a layer density of 45 layers/inch. . . 35
3.10 Thermal conductivity of 6061 aluminum as a function of temperature. . . . . . . 37
3.11 Temperature gradient across 45K chamber. . . . . . . . . . . . . . . . . . . . . . 38
3.12 Temperature gradient on 45K stage with 1 K/W of thermal resistance. . . . . . . 42
3.13 Temperature gradient on 45K stage with 20 K/W of thermal resistance. . . . . . . 42
3.14 Coefficient of thermal expansion (CTE) of 6061 aluminum as a function of temperature. 44
3.15 Thermal contraction of 45K stage. . . . . . . . . . . . . . . . . . . . . . . . . . 44
4.1 SolidWorks assembly of the 4K stage. . . . . . . . . . . . . . . . . . . . . . . . 47
4.2 Central 4K mechanical support. . . . . . . . . . . . . . . . . . . . . . . . . . . . 49
4.3 Von Mises stress on 4K stage. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51
4.4 Displacement in z-direction of 4K stage as a result of strain. . . . . . . . . . . . . 51
4.5 Von Mises stress on G-10CR support located at cryovalve. . . . . . . . . . . . . 52
4.6 Von Mises stress on G-10CR support located at trap base. The four internal points
are not attached to the 4K stage on this support. Therefore, the bottom face
deforms the most. Despite the exaggerated stress load, no thermal short occurs. . 53
4.7 Von Mises stress on G-10CR support located around titanium support. . . . . . . 54
4.8 The thermal conductivity as a function of temperature for OFHC copper RRR 50. 57
4.9 Temperature gradient on 4K stage at thermal resistance of 0.5 K/W. . . . . . . . . 59
4.10 Temperature gradient on 4K stage with thermal resistance of 5 K/W. . . . . . . . 60
4.11 Coefficient of thermal expansion (CTE) for OFHC copper. . . . . . . . . . . . . 62
vi
4.12 Thermal contraction of the 4K stage. . . . . . . . . . . . . . . . . . . . . . . . . 63
4.13 Illustration of the change in location of the Penning trap. . . . . . . . . . . . . . 64
4.14 Vapor pressures (mbar) of various gases present in vacuum systems as a function
of temperature (K). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65
4.15 Exploded view of the UMD cryovalve design, with Flange 1 shown. . . . . . . . 69
4.16 Photograph of the assembled cryovalve, ready for testing. . . . . . . . . . . . . . 70
4.17 Cross-sections of the four bottom flanges manufactured for the testing of the
UMD cryovalve. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71
4.18 Simplified geometries used for modeling in MolFlow. . . . . . . . . . . . . . . . 73
4.19 Pressure profiles from MolFlow simulation along length of 4K stage with internal
cryopumping. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73
4.20 Pressure profiles from MolFlow simulation along length of 4K stage with 10 mm
cryovalve aperture. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74
4.21 Pressure profiles from Molflow simulation along length of 4K stage with 0.01 gap
to imitate the cryovalve seal. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75
4.22 Conductance through slit-like sealing interface in l/s for a range of slit heights
from 10 ?m to 250 ?m. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 78
4.23 77K Cryostat designed and built for UMD group cryogenic testing. . . . . . . . . 79
vii
List of Abbreviations
CURIE Cryogenic Ultra-high vacuum Radioactive Isotope Experiment
CTE Coefficient of Thermal Expansion
DSV Diameter of Spherical Volume
EBIT Electron Beam Ion Trap
EC Electron Capture
LN Liquid Nitrogen
MLI Multilayer Insulation
OFHC Oxygen-Free High Conductivity
RRR Residual Resistance Ratio
UHV Ultra High Vacuum
ULV Ultra Low Vibration
XHV Extreme High Vacuum
viii
Chapter 1: Introduction
In 1896, Madame Marie Curie coined the term ?radioactivity?. Since then, radioactive
elements have provided better tools to diagnose ills and treat them in medicine, create beneficial
common household items like smoke detectors, and produce clean-energy alternatives. Along
with this wide range of applications, research during this past century has also solidified our
understanding of radioactive decay as an immutable fact, dictated by the stochastic laws of
quantum mechanics. However, one form of decay could bring this fact into question. Decay
by electron capture (EC) ? also called ?inverse beta decay? ? relies on a proton-rich nucleus
capturing a bound state electron to facilitate decay. Interestingly, several experiments have
demonstrated that manipulation of the electron structure and density has a slight but measurable
impact on the half-life of radioisotopes which decay through EC [1][2][3][4]. These results
indicate that radioisotopes which decay by EC are uniquely dependent on an external factor:
their electron orbital structure. This further suggests a claim that dramatic manipulations of this
structure could lead to equally dramatic changes in the half-life of such isotopes.
The CURIE project, partially outlined in this thesis, aims to investigate this claim in the
low-Z isotope 7Be by ionizing, transporting, storing, and interrogating an ensemble of ions in the
CURIE CryoTrap. At the heart of this experiment is the need to store 7Be ions for several weeks to
months to confirm statistically a change in decay rate. This is achieved through cryogenic storage
1
temperatures that generate extreme high vacuum (XHV) conditions, eliminating essentially all
collisions with background molecules. This thesis is a comprehensive detailing of the cryogenic
design which will achieve these conditions for the CURIE apparatus.
1.1 Background and Significance
The radioactive low-Z isotope 7Be belongs to an exclusive group that only decays by
electron capture. In this process, the nucleus captures an atomic-bound electron, generating a
neutron from a proton and emitting an electron neutrino. 7Be has a natural half-life of 53.29
days, decaying through the mode shown in Equation 1.1. In 10.4% of these decays, the daughter
nucleus, 7Li, remains in an excited state and emits a 477.5 keV gamma-ray.
7Be+ e? ?7 Li+ v(Q = 872keV ) (1.1)
7Li? ?7 Li+ ?(10.4%) (1.2)
Emilio Segre first suggested in 1947 that this decay method would have a considerable
dependence on the electron density at the nucleus [5]. He suggested that perturbations of this
density, whether by alteration of chemical form, pressure, or temperature, would have a measurable
impact on the half-life. Since then, several experiments have demonstrated this phenomenon by
embedding 7Be in various chemical compounds with alterations of the half-life of 7Be of about 1-
1.5% [1][6]. These findings illustrate that the half-life of 7Be is indeed manipulable and suggests
that other electron-capture-only isotopes would be as well. However, no experiment has ever
2
isolated one such isotope in an altered ionization state to measure the change in decay rate. In
many ways, this is the most obvious and ?textbook? solution to this question: to dramatically
alter the electron orbital structure through ionization of an ensemble, store the ensemble in
an environment where recombination cannot occur, and perform a half-life measurement. The
capability to perform such an experiment, however, has only been made possible in the last few
decades. The difficulty of any experimental measurement lies largely with the long storage times
required.
Ideally, we will store on the order of 103 ions. To signify statistically meaningful alteration
in the decay rate, weeks to months of measurement are required. To store ions stably for this
length of time, the half-life of ion loss through charge exchange and collisions with background
molecules must be significantly longer than the half-life we wish to study. Isolated 7Be3+, with
only one 1s electron, is anticipated to have a significant extension of the half-life to 106.4 days [7].
For the halting of 7Be4+, this would be the half-life of interest. Therefore, required storage times
remain on the order of weeks to months. Achieving this is quite a feat for any ion trap. However,
a number of technological improvements over the last decades have made storage demonstration
of this order possible. Notably, the CERN Baryon Antibaryon Symmetry Experiment (BASE)
has achieved antiproton lifetimes of about 405 days by way of a predicted vacuum pressure of
< 10?17 mbar [8]. The ARTEMIS trap at GSI, and the ALPHATRAP at the Max Plank Institute
have also reported comparable storage times [9] [10].
The CURIE (Cryogenic Ultra-high vacuum Radioactive Isotope Experiment) cryogenic
assembly, detailed in this thesis work, is the cooling system for a precision 4 Kelvin (K) Penning
trap built for the long-term storage of ions in XHV regimes. While this apparatus will have a
long life at the University of Maryland with many scientific applications, the Koeth Group will
3
use the apparatus to investigate the halting of the half-life of 7Be through ionization and long-
term storage. The system will non-destructively measure an ensemble of ? 500 ions, with single
ion resolution to detect the slight mass change in the decay from parent 7Beq+ to daughter 7Liq+.
While specifics of these detection methods merit extensive detail and discussion, they are outside
the scope of this work.
The value and impact of this work range over several fields of scientific study. To the
world of radiochemistry, it will provide long-awaited measurements of the altered half-lives of
ionized 7Be and address fundamental questions about electron capture decay and its dependence
on electron orbital structure. This work also has broad implications for nuclear astrophysics
and the study of stellar-plasma evolution. Solar neutrinos are dominantly created through the
destruction of 7Be in the Sun through both electron and proton capture. Better predictions of
the rates at which these two reactions happen will improve our understanding and measurement
of solar-neutrino fluxes in the Standard Solar Model (SSM). Currently, the uncertainty in the 8B
neutrino flux measurement, occurring from 7Be proton capture, is about 20% [11]. Measurements
of the half-lives of hydrogen and helium-like 7Be will further understanding of the branching ratio
in the the p-p II chain, and can reduce uncertainty in the SSM. Additionally, these measurements
can provide insight into the rate of free-electron capture in the Sun.
The study of fully ionized 7Be opens doors to a multitude of new science and technology.
Our current understanding of the laws that govern radioactive decay dictate that a fully ionized
7Be ion cannot decay. By removing the bound electrons from 7Be and storing the fully ionized
nucleus in an environment where charge exchange is extremely unlikely, we test this understanding
and are faced with two possibilities. The first is that radioactive decay of 7Be is halted, marking a
ground-breaking achievement, never seen since Madame Curie first coined the term ?radioactivity?
4
over a century ago. The second is the existence of higher-order decay processes, a stunning
discovery.
Both of these outcomes would have exceptional value to the nuclear physics community,
but the first has immediate technological implications. If the radioactive decay of 7Be can be
halted, it can also be restarted. As discussed, 10.4% of these decays result in the release of a
477.5 keV gamma-ray. This leads us to the natural question of how the controlled release of such
energy might be exploited for the benefit of our changing planet. In a world where a zero-carbon
future is, currently, exceptionally dependent on lithium-ion batteries, halted 7Be could offer a
hopeful alternative.
1.2 Objectives and Approach Taken
The CURIE project has three overarching tasks essential to success: (1) ionization of the
ions, (2) transportation by focusing and steering into a Penning trap, and (3) long-term storage.
This thesis primarily focuses on this third task, but a brief overview of the first two will be
provided.
To access the four ionization states of 7Be (7Be1+, 7Be2+, 7Be3+, and 7Be4+), a room-
temperature Electron Beam Ion Trap (EBIT) has been designed and built. The EBIT uses an
electron beam to partially or fully ionize neutral atoms by electron-impact ionization. Using
this method, the EBIT is capable of ionizing 1% of neutrals and generating virtually any highly
charged ion [12]. 7Be neutrals are introduced into the system by laser ablation. A Nd:YAG laser
vaporizes the neutrals from a small target, creating a cloud for the electron beam to intersect, and
generating the four ionization states. 7Be neutrals will be plated onto a 5 mm by 5 mm target
5
Figure 1.1: Cross-section of the entire CURIE assembly. The EBIT produces the four ionization
states of 7Be. The series of Sikler lenses and the Wien filter allow for focusing, steering, and
charge state selection of the ions. The ions are then decelerated by the pulsed drift tube into the
Penning trap, where they will be stored at 4K and XHV.
and mounted in the EBIT for ablation. The UMD group has identified an experienced European
group capable of producing the ablation targets to high uniformity and specified density.
Once an ensemble of ions in all four ionization states is created, the ions will be ejected
from the EBIT and travel down a transfer line. The ion beam traverses a series of three Sikler
lenses, with an intermediate Wien filter. The Wien filter allows selection of the desired charge
state and the Sikler lenses both focus and steer the beam into the Penning trap. The Wien filter,
also referred to as a ?velocity selector?, uses a crossed variable electric field and a constant
magnetic field. The ions exiting the EBIT are accelerated by an electric field and, therefore, have
a range of velocities dependent on their charge state. The Lorentz force equation (Equation 1.3)
thus allows selection of a charge state in the Wien filter according to the exit velocity of the ion
6
through variation in the strength of the electric field.
F = qE+ qv ?B (1.3)
The Sikler lenses both steer and focus the beam. The design combines an Einzel lens,
consisting of three cylindrical electrodes that focus a charged beam, with diagonal slits on the
middle electrode for steering in the x-y plane. The focal point of the electrodes is adjusted
through alteration of the applied voltage.
Upon exiting this beam line, a pulsed drift tube will decelerate the ions before their entry
into the Penning trap. The drift tube consists of two cylindrical electrodes in series. The first
electrode is grounded, and the second is held at a higher potential. As the beam travels through,
the second potential is pulsed to 0 V to decelerate the beam.
At this point, the ion beam is injected into the Penning trap. A Penning trap, developed by
Frans Michel Penning, utilizes a combined quadrupole electric field with a uniform magnetic field
to confine ions axially and radially. Further details on the Penning trap are provided in Chapter
4. Once injected, the success of the experiment is dependent on achieving long storage times ?
on the order of weeks to months ? through XHV conditions. This is realized through cryogenic
temperatures of ? 4K in the Penning trap region. Two critical outcomes occur once the trap
reaches this cold temperature. The first is that the majority of background gases condense onto
the surrounding cold surfaces. Helium will be the primary gas still present and the vacuum will
reach extremely low pressures below 10?15mbar. At these levels, the probability of ion-electron
recombination will be negligible. This is vital: if fully-ionized 7Be4+ were to regain an electron,
the resulting 7Be3+ has the same q/m ratio to the zeroth order as 7Li3+, making the two difficult
7
to distinguish.
The cryogenic temperatures also allow for resistive cooling of the ion ensemble to reduce
the oscillation amplitude through the dissipation of kinetic energy into resistive elements, allowing
for single ion detection [13]. The axial oscillation of the ions induces an image current that
is dissipated through a resistive circuit. The circuit represents a heat bath at 4K. The charged
particles are brought into thermal equilibrium with the circuit, greatly reducing the kinetic energy
[13]. The remaining small amplitude oscillations allow for extremely precise ion detection and
distinction.
While significantly more detail is owed to the complex systems outlined above, they are
not the focus of this work. Instead, this thesis will describe, in depth, the engineering behind
the cryogenic systems used to cool the Penning trap for successful long term ion storage. It will
discuss the many calculations and simulations behind the design, outline the assembly in detail,
and predict the ultimate performance. The careful engineering noted in this work is essential to
attain the scientific goals of the CURIE project, which are broad and significant.
1.3 Principles of Cryogenic Engineering Design
The field of cryogenic engineering is well-established, with a wide range of applications
from technology to medicine. While the design detailed in this thesis work is largely customized
to the specific application of the CURIE project, the principles which dictated the many choices
made are well-defined and understood. In general, cryogenic designs must successfully accomplish
two conflicting tasks: (1) supporting the internal cold systems within the larger (and hotter)
structures while (2) minimizing the heat transfer between the two. To best understand how these
8
goals are reached, the principles of heat transfer and material properties need to be explored.
In general, there are three types of heat transfer: conduction, radiation, and convection. The
first two are of most concern in a cryogenic vacuum system (below around 10?6mbar convection
ceases to have a measurable impact) and will be explored in more detail in the following sections.
Other important considerations to cryogenic design will be discussed as well, including heat
capacity at cold temperature, limitations of high-contact resistance, and thermal contraction.
1.3.1 Conduction
Conduction is the transfer of heat from one adjacent molecule to another. The conductive
heat flow is expressed by Equation 1.4, in one-dimension, where k(T ) is the thermal conductivity
of a given material, and A(x) is the cross-sectional area [14].
Q = ? ?Tk(T )A(x) (1.4)
?x
If the cross sectional area is constant, the conductivity can be found using Equation 1.5
[14].
? TH
Q = ?A k(T )dT (1.5)
L Tc
The conduction calculations in this thesis are mostly performed using SolidWorks, providing
significant ease in calculating these integrals for variable k(T ) and cross-sectional area.
The thermal conductivity of the most prominent materials in this design ? aluminum 6061
and oxygen-free high conductivity (OFHC) copper ? are respectively given in Figures 3.10 and
4.8. It is important to note that, particularly at low temperatures, the thermal conductivity of
9
high-purity metals like OFHC copper is dominated by impurity defects and can become difficult
to predict. The OFHC copper specified in this work is defined by a residual resistance ratio (RRR)
of 50, where RRR is the ratio of the electrical resistivity at room temperature and 4K [15]. The
RRR of OFHC copper ranges from 50 up to 2000. At the high end of this scale, the copper is
exceptionally pure but also much weaker, as everything which strengthens it has been removed.
Annealing can help, but copper with high RRR is expensive and in short supply. For the analysis
in this work, an RRR of 50 was chosen.
?293K
RRR = (1.6)
?4K
1.3.2 Thermal Contact Resistance
On the topic of conduction, it is important to address the limitations of heat conduction
through solid-solid interfaces at cryogenic temperatures. In this cryogen-free system, multiple
connection interfaces are required to cool the entire apparatus. Inevitably, the introduction of
joints generates thermal contact resistance from imperfections at the surfaces of materials leading
to poor contact. High contact resistance can dramatically increase cool-down times and the
temperature gradients [16].
In the CURIE system, contact resistance in joints is the main contributor to temperature
rise across the length of both the 4K and 45K stages. Estimating the magnitude of this resistance
from the equation for metal-metal contact resistance is complex. In practice, contact resistance
varies dramatically with a number of experimental factors [16][17].
In the UMD system, thermal contact resistance is limited as much as possible through
10
the use of indium seals between the 4K OFHC joints, careful tightening of joints, and the use
of brass screws so tightening occurs upon cool-down 1. On the 45K stage, copper brackets
are used on the interior of the shield so that the aluminum exterior tightens around them upon
cooling. If necessary, thermal grease can be used on low-pressure connections should a significant
temperature rise be observed after initial assembly. In general, contact resistance in joints with
indium seals or thermal grease will decrease with increased surface area. If the surface area
available is insufficient, gold-plated contacts can be considered, as the thermal resistance in this
type of joint decreases with pressure [16].
1.3.3 Radiation
Radiation is the process of heat transfer from warmer bodies to colder bodies via electromagnetic
heat waves. In cryogenics, this is typically the heat source of most concern. The Stefan-
Boltzmann Law represents the heat transfer from a radiating surface, and is expressed as Equation
1.7, where ?SB is the Stefan Boltzmann constant, equal to 5.67 ? 10?8W/(m2K4), and ? is the
ratio of the emissivity of a given surface to the emissivity of a black body [18].
Q = ? 4SB?T (1.7)
The heat flow between two surfaces is given by Equation 1.8, where E? is between 0
and 1 and is a combination of both surfaces? emissivities based on their geometric view factors
[15]. Reliable estimates of E? exist for common geometries like parallel plates and concentric
cylinders.
1Brass has a higher coefficient of thermal expansion (CTE) than OFHC copper.
11
Q = ? E A(T 4 ? T 4SB ? 2 1 ) (1.8)
SolidWorks was frequently used to calculate radiative heat loads on the system. SolidWorks
calculates the intricate view factors between more complex geometries using Equation 1.9, where
dAi and dAj are two infinitesimal surfaces, and dFij is the view factor between them [19].
cos ?i cos ?j
dFij = dA (1.9)
?R2
j
ij
Since the radiative heat load is proportional to temperature to the fourth power, the hot
surface temperature is the dominant term. It should also be noted that, for most materials,
heat capacity decreases rapidly with temperature, meaning small heat loads can lead to large
temperature rises. As a result, minimizing radiation is extremely important in a cryogenic system.
One of the most effective ways to minimize radiation losses is to add an intermediate ?warm?
stage, called a thermal shield. Typically, an actively cooled shield will be used at liquid nitrogen
temperatures of 77K, or in our case, the second stage temperature of our cryocooler of 45K.
Additional non-thermally cooled shields can be used in large number ? frequently called MultiLayer
Insulation (MLI) ? that reflect radiation and can provide ample intermediate ?warm? stages.
1.3.4 Thermal Contraction
The majority of materials contract when cooled, and this must be carefully considered
when designing a cryogenic system. If two materials are rigidly joined and not given appropriate
freedom to shrink, critical failure of parts, and subsequently whole systems, can occur. In general,
this consideration requires that any internal apparatus only be rigidly attached on one end, to
12
allow for contraction on the other. It is also important to consider material properties at joint
locations. If the coefficient of thermal expansion (CTE) of the bolt is lower than that of the
material being joined, the connection will loosen upon cooling. Common practice is to use a bolt
material which has either an equal or greater CTE, or a washer of appropriate thickness with a
very low CTE, such as titanium or invar.
1 dL
?L = (1.10)
L dT
Thermal contraction can be calculated using Equation 1.10, where ?L is the CTE of a
material, and L is the original length.
1.3.5 Stress and Strain
Mechanical stress, denoted by ?, is a measure of force per unit area, or force intensity
felt by a body. Strain, ?s, is the deformation of a body resulting from an applied stress. In the
linear region, stress and strain are related by Hooke?s law, given in Equation 1.11, where E is the
modulus of elasticity.
? = E?s (1.11)
The distortion-energy theory, also called the Von Mises theory, describes the phenomena
where a ductile material under stress will exhibit yield strengths much larger than the values found
in a simple tension test [20]. This occurs because yielding is related to angular distortion, not just
normal tension or compression. The Von Mises stress, for ductile materials, is an effective stress
where yielding is predicted to occur [20]. For planar stress, the Von Mises stress is expressed by
13
Equation 1.12, where ?1, ?2, and ?3 represent the principal stresses along the three axes [20].
[ ]
1 1/2
?? = ? (? ? ? )21 2 + (?2 ? ?3)2 + (?3 ? ?1)2 (1.12)
2
1.3.6 Gas Flow in Vacuum Systems
The kinetic theory of gases assumes that a gas consists of a large ensemble of identical
particles in constant random thermal motion, that the particles are separated by distances much
larger than their own diameter, and that the collisions are elastic [18] [21] [22]. This theory
describes ideal gases, but can be satisfactorily applied to real gases as well [18].
At very low temperatures, the attractive forces between molecules become significant as
the kinetic energy of the particles decrease. In these conditions, collisions are no longer elastic.
Instead, particles begin to stick to each other and condensation occurs [21]. For a gas like helium,
a light atom with a small with small attractive potential, the behavior can be considered very close
to ideal. Such a gas is helpfully described by the following equations.
The average thermal velocity of a gas is given by Equation 1.13, where T is the temperature,
m is the particle mass, and kB is the Boltzmann constant.
?
8kBT
vav = (1.13)
?m
Of additional interest is the average distance that a gas particle travels between collisions.
This is termed the mean free path and is calculated using Equation 1.14, where d is the diameter
of the molecule and p is the gas pressure [18].
14
?kBTl = (1.14)
2?d2p
The mean free path is used to describe the three regimes of gas flow. At high pressures,
the mean free path is small and collisions are dominated by particle-particle collisions. This
regime is called ?viscous flow?. As the pressure is lowered, ?transitional flow? is reached. In this
regime, particle-particle collisions and particle-wall collisions are equally as frequent. Finally,
once the pressure is sufficiently lowered, the ?molecular flow? regime is achieved. The mean free
path is larger than the cross section of the containing geometry and particle-particle collisions are
extremely rare [23]. Molecular flow is most relevant to the following study.
1.4 Prior Art
Experiments to measure the half-life of 7Be ionization states have been proposed, specifically
at the Isotope mass Separator On-Line facility (ISOLDE) at CERN in 2012 and by Dr. Bryan
Peterson?s group at Brigham Young University in 2010, but neither group has yet to present any
results [24] [25]. Specifically, the ISOLDE proposal outlined the use of a storage ring to make
these measurements. While possible, the difficulty in achieving XHV in a storage ring would limit
the storage times to 3-5 minutes, requiring an ensemble of ? 109 ions for statistically significant
results [25]. The half-life and branching ratios of other EC isotopes has also been investigated, in
particular that of 142Pm60+ [26]. This experiment was similarly performed in a storage ring using
the Schottky mass spectroscopy technique, a nondestructive beam noise frequency analysis [26].
15
1.4.1 Long-term Storage through Extreme High Vacuum
Several projects have had success in generating XHV conditions in a cryogenic Penning
trap for long-term ion storage. The BASE trap system at CERN achieved vacuum pressures
lower than 10?18 mbar to store an antiproton cloud for up to 405 days [27]. To achieve this,
a hermetically sealed cryogenic vacuum chamber was used with antiprotons injected through a
thin vacuum window [8]. This technique is uniquely viable for antiproton injection ? ion injection
requires other means. The ALPHATRAP experiment at the Max-Planck Institute, which aims to
measure the g-factor of highly charged ions, has estimated vacuum in excess of 10?17 mbar and
storage of a single ion for more than 2 months [9]. The project utilizes a ?cryogenically operated
valve? with a sealing flap to separate the UHV and XHV volumes along the beam-line [21]. The
ARTEMIS trap at GSI in Darmstadt similarly uses a cryogenic valve to achieve vacuum ? 10?13
mbar and storage on the order of a couple of days [28]. The PENTATRAP experiment at the Max
Planck Institute comparably achieved vacuum levels on the order of 10?13 mbar. This project did
not use a valve, instead it utilized extensive cryo-pumping at the 4K stage with charcoal adsorbers
[29]. Of note, most ion injection experiments that require long term storage utilize some sort of
valve.
1.4.2 Cryogenic Valves
The maintenance of XHV is nearly impossible to achieve without the use of a cryogenic
valve. Still, a limited number of valve prototypes currently exist. As mentioned, the ALPHATRAP
experiment utilizes a sophisticated but complex flap-like design installed along the beam-line. In
tests, vacuum conductance rates between 1.44?10?3 l/s and 4.37?10?3 l/s were measured [21].
16
The ARTEMIS project also utilizes a cryogenic valve. The valve is placed inside the field of the
superconducting magnet, and by applying a current, a shutter can be opened and closed based on
the Lorentz force equation [28].
The first appearance of a cryogenic ball-valve design is in the 2003 dissertation of Harvard
student P. Yesley. In this work, the proposed storage of anti-hydrogen required the separation of
the positron accumulation region and the trap, while still allowing for particle injection. Like the
ARTEMIS design, the ball is placed inside the superconducting magnetic field and actuated by
an applied current (? 0.25 Amps) [30]. The BASE-STEP project ? a transportable antiproton
trap built on the ideas established in the BASE trap ? is actively developing a ball-valve design.
Instead of a hermetically-sealed chamber like BASE, the design utilizes a rotatable electrode
design again actuated by an applied current [27]. Excluding the actuation method, this design is
the most similar to the UMD group design and served as a source of inspiration. While the idea
to use the superconducting magnetic field to aid in actuation is compelling, determining whether
the valve is truly open or closed becomes near impossible. The UMD design approaches the issue
using manual actuation, so that it can be easily felt if the valve is open or closed. By decoupling
the actuation bar after use, the introduction of high heat loads is also avoided.
1.4.3 Cryogenic Apparatus
The design of the 4K cryogenic Penning trap has been iterated on many times over the
years. Some, like BASE [8], ALPHATRAP [9], and PENTATRAP [29], utilize liquid cryogens
as a low-vibration cooling solution. Many, including the BASE-STEP [27], HILITE-TRAP [31],
and ARTEMIS [28] use closed-cycle cryocoolers. In general, these systems all utilize similar
17
design components: a high-conductivity assembly is attached flexibly on one end to the base of
a cooling apparatus and rigidly on the other to a Penning trap at the center of a superconducting
magnet bore. Cryogenic G-10 (G-10CR) supports are commonly used as a method of low-
conductivity support, and actively-cooled concentric thermal shields within the magnet bore are
frequently seen. Flexible copper braids, like those discussed in this thesis, are a popular tool for
flexible high-conductivity contact. While these systems have general elements in common, the
specifics of design vary significantly and the components are almost always custom designed.
The same is true for the UMD design, which takes inspiration and lesson from existing cryogenic
Penning trap projects to create a design that aims for both simplicity and sophistication.
18
Chapter 2: Overview of the Apparatus
Figure 2.1: Cross-section of the entire cryogenic design. Ions are injected through the left-hand
side (the ?beam-line side?), and stored in the Penning trap at the center of the magnet. The entire
system is cooled from the right (the ?cooling side?) by the ColdEdge ULV UHV Cryocooler.
The ?cryogenic? section of the CURIE experiment refers to everything surrounding the
4K Penning trap that actively cools and maintains the temperature of the trap. This includes the
4K stage that consists of the base of the cryocooler, the thermal straps, the oxygen-free high
conductivity (OFHC) copper bus bar, the diagnostic electronics (and their support structure), the
long cylinder (which contains the Penning trap), and the cryovalve. The cryovalve, which will
be discussed in detail in Section 4.7.1, separates the beam-line ultra-high vacuum (UHV) from
19
the internal XHV and prevents back streaming. The Penning trap, at the center of the 4K stage,
contains the assembly of ions that are stored and interrogated. The diagnostic electronics signal
wires will be fed out from the trap through a base plate, wrapped around the 4K bus bar to heat-
sink, brought out through the 45K thermal shield chamber, seen on the right of Figure 2.1, and
then brought out of the vacuum system on the ?cooling side?. These systems will generate some
Joule heating, but in general, these contributions can be considered negligible.
The thermal shield surrounds the 4K stage. It is actively cooled by the 45K stage of the
cryocooler. The shield limits thermal radiation from the surrounding room temperature vacuum
chamber to the 4K stage by providing an intermediate barrier. The shield consists of three
aluminum parts on the ?beam-line side? (the body, a ?lid?, and a cryovalve ?cap?) for ease of
assembly, and a chamber on the ?cooling side?, that connects rigidly to the cryocooler base.
To allow for thermal expansion and contraction and vibration isolation, the ?beam-line side? is
secured to the chamber through flexible OFHC thermal braids.
For both the 4K and 45K stages, extensive research, modeling, discussions with experts,
and design iterations were undertaken to have a design that is cost-effective, easily assembled,
subject to low heat loads, and mechanically stable. These design choices and their motivations
are discussed in the following work. Figure 2.1 shows the SolidWorks geometry of the entire
assembly, with important elements labeled.
2.1 The Magnet
The magnet was acquired from the Robinson Research Institute (RRI) in New Zealand. It
is a 3T magnet, shimmed to <10 ppm over a 60 mm spherical volume (DSV) and <2 ppm over
20
10 mm DSV. It has a room-temperature bore of 142 mm, is cryogen-free, and is cooled by its
own closed-cycle cryocooler. The temporal stability is < 10 ppm over 24 hours.
2.2 The Cryocooler
The UMD group has purchased a ColdEdge Closed Cycle Ultra Low Vibration (ULV)
Cryocooler to cool the CryoTrap assembly. This cooler minimizes the vibrations from the cold
head by suspending the cryocooler in a ?gas gap?. There is a volume of helium gas between
the cryocooler cold tip and the outer cold tip. The vibration-generating cold head is supported
by rubber bellows above the assembly that reduces the vibrations to ? 1 ?m. If necessary in the
future, the system can be upgraded through the addition of a hydraulic stand to achieve vibrations
on the order of < 10 nm. The thermal straps, discussed in the next section, also provide some
vibrational isolation. After significant discussion with industry experts, and groups who have
developed similar systems, we believe vibrations on the order of 1 ?m are satisfactory. As a
justification, the frequency shift due to vibrations from the cryocooler may be estimated using
Equation 2.1, where ?vc is the relative frequency shift, dBrel is the gradient of the magnetic field
vv dz
strength, and ?z is the peak-to-peak amplitude of the trap vibrations [32].
?vc dBrel
= ?z (2.1)
vv dz
Given the uniformity of our field (2 ppm over 10 mm DSV), the maximum magnetic field
shift is 6 ? 10?6T. Using a first order expansion (B = B0 + B1z), it can be shown that
dBrel = B ?61 = 1.2 ? 10 T/mm. While much of the vibrations generated by the cryocoolerdz
will be dampened by the thermal straps, the maximum ?z is 1?m. At this level of vibration, the
21
frequency shift, ?vc , is 1.2 ppb. The trap requires enough resolution to differentiate 7Be from
vv
7Li: a mass difference of 131 ppm. Therefore, the frequency shift due to the cryocooler vibration
will have a negligible impact.
While 100% of the cooling capacity at the 4.2K stage is transmitted through the gas gap,
only 50% is transmitted at the 45K stage. As a result, the cryocooler has a cooling capacity of
1.5W at the 4K stage, and around 15-20W on the 45K stage. The heat loads of each stage are
calculated and discussed in detail in this work, and are predicted to be significantly lower than
these thresholds.
2.3 Thermal Strap Design
In cryogenic design, flexible points of connection are crucial to allow for thermal contraction
during the dramatic temperature changes. In the UMD design, this has been accounted for by
the inclusion of flexible copper braids, called ?thermal straps?, on both the 4K and 45K stages.
Technology Applications, Inc., a company that specializes in the design and construction of these
high conductivity straps, will supply flexible braids for the UMD group.
The 4K straps attach to the cold tip of the ColdEdge cryocooler and then to the OFHC
copper receiver for the bus bar. These connections must be made extremely tight to achieve a
good thermal pathway. Common practice for these applications is to use bolts which have a larger
coefficient of thermal contraction than the joint material so that the joint tightens upon cooling
[33]. Each of the two 4K straps, visible in Figure 2.2, has a predicted thermal conductivity of 0.8
W/K.
The 45K straps attach to the outer wall of the 45K shield chamber, that surrounds the base
22
Figure 2.2: Cross-section of cryocooler chamber with 45K and 4K thermal strap assemblies from
Technology Applications Inc. visible.
of the cryocooler. A cylindrical shield connects the 45K cold tip to the top of the shield chamber.
This connection and the subsequent connection to the chamber side are welded to provide a
better thermal path. On the cylinder end, the two 45K straps attach to a OFHC copper bracket
that surrounds the 45K shield. Extra care will be taken at this juncture in order to minimize the
gap between the connections and maximize the thermal contact. Thermal grease may also be
employed. Each of these 45K straps, also visible in Figure 2.2, has a predicted conductivity of
1.99 W/K.
23
Chapter 3: Design of 45 Kelvin Stage
3.1 Overview
The heat flux from a room temperature surface to a 4K black body surface is about 460
W/m2. With a cooling capacity of 1.5 W on the 4K stage of our cryocooler, this heat load clearly
needs to be significantly reduced. The assumption that the 4K stage is a black body is inaccurate.
In reality, we can assume the 4K stage has a emissivity close to 0.1 [34][35]. Assuming 0.1, the
heat flux is reduced to 46 W/m2 ? better but still too large. While polishing and electroplating
could further reduce the emissivity, the best way to minimize the thermal radiation is to decrease
the ?hot? temperature. Typically, this is done through the addition of an intermediary cooled
thermal shield. Often, the shield is actively cooled by liquid nitrogen to a temperature of 77K.
In our case, the cryocooler has a second stage at about 45K ? hence the name used for the stage
from now on.
The shield designed for the UMD apparatus is made of 6061 aluminum. It surrounds the
entirety of the 4K stage to prevent it from seeing thermal radiation from the external vacuum
chamber at room temperature. Within the magnet bore, the shield is a cylindrical assembly, with
a removable ?lid? for easy access to the 4K stage, and a ?cap? that fits over the cryovalve after
it is assembled. All three of these parts are attached internally by half-moon brackets to limit
the radial size of the shield. It has an outer diameter of 3.3 inches or ? 84 mm. The 45K shield
24
Figure 3.1: SolidWorks assembly of the 45K shield, showing the shield ?cap?, ?lid?, and body,
and the 45K chamber. The 45K thermal straps are also visible.
also surrounds the base of the cryocooler and the connection to the 4K stage. This is called the
?45K chamber?. This chamber connects directly to the second stage of the cryocooler, and then is
connected to the 45K cylinder in the magnet bore by the Technology Applications, Inc. thermal
straps discussed in Section 2.3. To further improve the thermal pathway from the cryocooler to
the remainder of the shield, the back wall and top of the chamber are welded to each other to
improve the conductivity. This change was implemented on the recommendation of Technology
Applications, Inc.
The following sections discuss the 45K design in greater detail, including extensive modeling
and the calculations that dictate the many design choices.
25
3.2 G-10CR Support Design
The 45K supports are very similar to those designed for the 4K stage. Like the smaller
structural support disks surrounding the 4K stage, the 45K supports are made of G-10CR and
designed with four points of external and internal contact, and a maze-like structure between. The
larger diameter of the 45K supports allows for more material to be removed to reduce the thermal
pathway. The 45K stage has two supports instead of three ? a choice dictated by simulation in
Section 3.2.1. Similar to the 4K stage, one of the supports is fixed to both the 45K stage and
to the larger 300K vacuum structure. For ease of assembly, the second support is also fixed to
the 300K structure, but not to the 45K cylinder to allow for contraction. For the connection to
the 300K vacuum to be made, the supports are pushed up against the bore chamber flanges and
screwed in. This increases the surface area of the support in contact with the 300K stage, but
does not dramatically affect the thermal performance.
SolidWorks simulations are the basis for the support designs. They are discussed in the
following section.
3.2.1 Simulation Results and Conductive Heat Loads through G-10CR Supports
Figure 3.2 shows the thermal model for the right-hand side G-10CR support on the 45K
stage. The left-hand and right-hand side geometries are similar, with only a small variation in
diameter. The resulting heat fluxes through the two supports are tabulated in Table 3.1. Since the
cooling capacity of the second stage of the cryocooler is in the range of 15-25W, a heat flux of ?
160 mW through the supports is manageable.
26
Figure 3.2: 45K right-side mechanical support made from G-10CR. Thermal gradient from 300K
to 45K is shown.
Support Heat Load (mW)
Left-hand Side 73.3
Right-hand Side 89.3
Total 163
Table 3.1: 45K G-10CR support heat loads
3.2.2 Support Location and Strength Simulation Results
The 45K stage must support the weight of the 4K stage (approximately 6.8 kg), and
the surrounding G-10CR support must support this weight and the weight of the 45K shield
(approximately 5 kg). To avoid significant stress or sagging in the thermal shield, additional
SolidWorks simulations were performed to assess the strength of the G-10CR supports and their
locations. The Von Mises stress simulation in Figure 3.3 illustrates that the entire assembly
undergoes very little stress. Similarly, Figure 3.4 demonstrates that the assembly undergoes
27
negligible sagging ? a maximum of about 50 nm. Since the left-hand side G-10 support is
connected to both the 300K and the 45K supports, the right-hand side does experience more
displacement, though insignificant.
Figure 3.3: Von Mises stress on 45K stage. Maximum occurs in G-10CR support. Value in
middle of shield is noted.
Figure 3.4: Displacement in z-direction of 45K stage. Small maximum again occurs in G-10CR
support. Displacement in middle of shield is noted.
Simulations of the G-10CR supports were also performed to determine the Von Mises stress
28
experienced and the resulting displacement to ensure thermal shorts do not occur. The 45K
thermal shield weighs approximately 5 kg. Combined with the 4K stage, the total weight of the
assembly is around 11.8 kg. As an overestimate, the simulations were conducted with 40 lb (?
18 kg) imposed on the G-10CR supports. The results are shown in Figures 3.5 and 3.6.
Figure 3.5: Von mises stress on left-hand G-10CR support. As the four internal points are all
rigidly attached to the thermal shield, the stress is evenly distributed and minimal.
These simulations indicate that the stress on the G-10CR supports, even under the exaggerated
load of 18 kg, is minimal. The left-hand side support feels a maximum of 63 MPa and the
right-hand support feels a maximum of 107 MPa. Both of these are significantly lower than the
compressive yield strength of 450 MPa for G-10CR. Displacement is similarly manageable: the
left-hand side support only displaces a maximum of 0.4 mm while the right-hand side support
moves 1.6 mm. Since the left-hand side support is attached at four points to the thermal shield
29
Figure 3.6: Von mises stress on right-hand G-10CR support. As the four internal points are not
attached to the shield, the bottom face deforms the most. Still, no thermal short occurs.
while the right-hand side support is not, the latter deforms significantly more. Still, the displacement
is exaggerated by the substantial margin of safety of the applied loads, and does not create a
thermal short.
3.3 Radiation Heat Load Calculations
The thermal radiation to the 45K stage from the surrounding room temperature vacuum
chamber is a large fraction of the total heat load. To reduce this heat load, the 45K shield will be
wrapped in MLI, discussed below. It is possible that, due to certain corners, geometries, or faults
in interfacing of MLI sheets, some of the shield will be directly exposed to the 300K radiation. In
particular, the face of the shield on the ?beam-line side? may need to be uncovered. The exposed
surface area will not be known exactly until we begin wrapping the assembly. As a generous
30
estimate, it is assumed that 0.1 m2 will be exposed directly to 300K radiation. The surfaces that
will be uncovered will be either polished to a low emissivity or covered in an aluminized Mylar
film. The estimation of 0.1 m2 is an overestimation and should account for any accidental gaps
in MLI wrapping. Assuming an achievable emissivity of 0.1, hot temperature, TH, of 300K, and
cold temperature, TC, of 45K, the radiation heat load onto these exposed surfaces is calculated in
Equation 3.1. Of note, this calculation does not account for the emissivity of the 300K chamber
but instead assumes a uniform surrounding room temperature environment. Therefore, it is an
upper limit.
Q = ? ?A(T 4 ? T 4SB H C) = 4.59W (3.1)
This heat load is significant. Minimizing the surfaces on the 45K thermal shield not covered
in MLI is a high priority.
3.3.1 45K Chamber Lower Radiation Shield
In order to evacuate the 45K stage more effectively during vacuum pump down, the base
of the 45K chamber has a vent-like structure. Since this is an evacuation point, it cannot be
wrapped entirely in MLI and therefore introduces a heat path into the system. To prevent a line
of sight view from the 300K vacuum chamber to the internal 4K stage, vents are angled inward
and a square radiation shield plate is hung from the bottom. The supports for the shield plate
require a compromise: conduction through the supports is needed to actively cool and minimize
the impact of line-of-sight radiation, while the heat load transmitted to the 45K chamber needs to
be minimized. As a balance between these two goals, the supports will be made of a conductive
31
Figure 3.7: SolidWorks model of 45K chamber with aluminum supports (right) and G-10CR
supports (left) emphasizing temperature difference to lower shield and chamber.
material, likely aluminum 6061, and both the supports and the plate will be highly polished or
otherwise altered to have a low emissivity. If the hanging shield is actively cooled, the venting and
radiation plate should limit most radiation from reaching the 4K stage inside the 45K chamber.
This was confirmed with a SolidWorks model. The model assumed that 300K radiation
was incident on the hanging radiation plate and its supports, and that the plate had an emissivity
of 0.07 [35]. A second condition that the interior surface of the plate would radiate to a 4K stage
element inside the assembly through the vented structure was included. The top surface of the
chamber was cooled to 45K. The results of the model were promising: with the radiation shield
in place, only about 0.02 mW of radiation was incident on the interior 4K stage. Without the
shield, the amount increased to 113 mW1. With the shield in place, it may be assumed that the
radiation through the holes in the shield is negligible. The trade-off is, of course, an increase in
1This was modeled by changing the support material from 6061 aluminum to highly insulative G-10CR, bringing
the hanging radiation plate to approximately 300K.
32
the temperature of the 45K stage through conduction. As Figure 3.7 demonstrates, the increase
is only about 3K at the base of the 45K chamber. While the 3K loss is a concern, the reduction
in the 113 mW heat load to the 4K stage justifies the increase in temperature. Furthermore, this
3K rise can be reduced by, for example, covering the exposed pieces in highly reflective Mylar.
3.3.2 Use of MLI to Limit Radiative Heat Load
MLI is a highly reflective insulating material, also termed ?super insulation?, used in space
applications to reflect solar radiation. Each layer of MLI is composed of a thermally insulating
material, such as Mylar, with a metalized side, typically aluminum [33]. Each layer of MLI
reflects 90-99% of incident radiation, and approaches 100% reflectivity with increased layering
[36]. In cryogenic applications, it is commonly used to limit thermal radiation heat loads from
room temperature chambers to internal cold stages. The length of our 45K stage and the limited
capacity of the cryocooler requires that the 45K shield be wrapped in layers of MLI to reduce the
thermal radiation heat load.
A rule of thumb: MLI density should be limited to a layer density of about 45 layers/inch
[37]. Above this density, thermal shorts are likely to occur, increasing the conductive heat load
onto a system and negating the benefit of MLI. Careful wrapping is key to the efficacy of MLI
performance [37]. To allow the diameter of the 45K stage to be larger, it may be desirable
to decrease the layering of the MLI surrounding the 45K shield. The increase in heat load by
decreasing the layering to 15 or 30 layers of MLI is not exceptionally well defined, as these are
less experimentally studied. An estimation is attempted below.
The heat transfer through N thermal layers is calculated theoretically by Equation 3.2,
33
Figure 3.8: Theoretical heat flux through N layers of MLI superinsulative wrapping for a layer
density of 37 layers/inch. TH is 300K, TC is 45K, and the emissivity is 0.03 [38].
where ?SB is the Stefan-Boltzmann constant, TH is the hot temperature, and TC is the cold
temperature [38].
1 ?SB?
q = (T 4H ? T 4(N + 1) 2? ? C
) (3.2)
The temperature of an intermediate screen, i, can be calculated using Equation 3.3 [38].
1
T 4 = T 4 + (T 4 ? T 4i C i+ 1 H C
) (3.3)
Figure 3.8 is a graphical representation of Equation 3.2 for an emissivity of 0.03, a warm
temperature of 300K, and a cold temperature of 45K. From this figure, the heat flux at 45
layers is approximately 150 mW/m2. This is significantly lower than the industry experimental
expectation: for 45 layers of MLI on a flat plate (with a layer density of 45 layers/inch), a heat
34
Figure 3.9: Theoretical heat flux through N layers of MLI superinsulative wrapping adjusted to
match experimental result for 45 layers at a layer density of 45 layers/inch. TH is 300K, TC is
45K, and the emissivity is 0.03 [38].
load of 1 W/m2 is typical2 [37]. Figure 3.9 is the same theoretical trend from Equation 3.2,
but with the 45-layer point adjusted to the experimental prediction of 1 W/m2. The discrepancy
between these two curves can be attributed to the differences in layer density and imperfections
encountered when wrapping MLI ? corners and odd geometries make small thermal shorts unavoidable.
The heat fluxes for 15, 25, and 35 layers are extracted into Table 3.2. Additionally, the
expected heat load for our model is listed, with 30% uncertainty added to the predicted heat flux.
The total surface area covered in MLI on the 45K shield is approximately 1.65 m2. In reality, the
45K stage will not be uniformly 45K across its entire length, but will likely increase to around
80K. The assumption that the thermal shield is uniformly 45K gives a higher heat load than the
actuality, setting an upper-bound.
2To account for inevitable wrapping error, an uncertainty factor of 30% should be added.
35
N (layers) 15 25 35 45
Heat Flux (W/m2) 2.92 1.80 1.30 1.00
Heat Load (W) 6.26 3.86 2.79 2.14
Table 3.2: Tabulated layer densities of interest from Figure 3.9.
3.4 Total Heat Loads on 45K Stage
The most significant contribution to the heat load on the 45K stage is radiation. In particular,
radiation to uncovered surfaces. While these areas will be minimized, it is vital to account for
some error in wrapping. For instance, the far ?cap? end of the cylindrical shield will likely be
covered in MLI, however this surface may be wrapped in significantly fewer layers or covered in
a single aluminized Mylar film. In the worst case, this surface will be uncovered but polished.
Table 3.3 lists the contributions to the total heat load on the 45K stage. The conduction through
the G-10CR supports is negligible. The radiation onto surfaces covered in MLI is listed for 45
and 25 layers in our current design.
45K Stage Heat Sources Heat Load (W)
Conduction through Supports 0.160
Radiation through MLI 2.14 - 3.86
Radiation on Uncovered Surfaces 4.59
Total 6.89 - 8.61
Table 3.3: Total heat loads in watts, W, on the 45K stage.
3.5 Temperature Rise Studies
The 45K stage is assembled such that the 45K chamber is in contact with the cryocooler,
that is then connected to the remainder of the 45K cylindrical shield. Simulations were done
in two parts. The prescribed conditions and loads were applied to the 45K chamber, and the
36
temperature at the thermal strap points of assembly noted. Using the thermal resistance of the
straps, the temperature rise across them was calculated; this was used as the initial temperature for
the cylindrical shield temperature gradient model. In each of these simulations, the appropriate
heat loads were applied.
3.5.1 Material Properties
Figure 3.10: Thermal Conductivity of 6061 aluminum as a function of temperature [39].
The temperature variation of thermal conductivity shown in Figure 3.10 of 6061 aluminum
was gathered from a NIST database [39].
3.5.2 Initial Temperature for Model
Creating a thermal model for the 45K stage is more involved than for the 4K stage. To best
approximate the initial temperature at the base of the thermal straps and start of the cylindrical
37
Figure 3.11: Temperature gradient across 45K chamber with appropriate radiative and conductive
heat loads applied.
38
shield, the thermal gradient across the 45K chamber was modeled first. The top surface of the
vertical cylindrical shield on the 45K chamber was initialized at 45K. According to heat load
maps provided by ColdEdge Technologies, with expected heat loads less than 10 W, an initial
temperature around 43-45K is expected. Radiation from the larger 300K vacuum chamber was
applied to the bottom surfaces, that are not wrapped in MLI, and 1.8 W/m2 was applied to the
remaining surfaces, mimicking 25 layers of MLI ? an upper limit of 45 layers will likely be used.
A 2.3 W heat load was applied at each of the positions where the straps connect. This is based
on the estimate that 4.6 W of heating occurs from radiation and conduction on the cylindrical
portion of the shield.
As Figure 3.11 shows, the temperature at the base of the straps is 52.5K and 54.8K. Each of
the thermal straps then has a 1.99 W/K conductivity. As with the 4K stage straps, the temperature
drop across the thermal straps can be calculated using Equation 3.4. We again assume a heat load
of 4.6 W on the cylindrical portion of the shield, which indicates a temperature rise of 1.15K
across the straps. Therefore, the initial temperatures at the surface of the clamp will be 53.7K
and 56.0K.
?T4K = RQ (3.4)
3.5.3 Thermal Resistance in Joints
Overall, the thermal resistance of the joints on the 45K stage will be higher than on the 4K
stage. On the 4K stage, careful assembly is essential: the success of the experiment depends on
achieving a temperature as close to 4K as possible at the trap. To achieve this, indium seals will be
39
put in place and surfaces polished to ensure tight seals upon cooling. So long as the temperature
of the shield is below 77K (LN temperature), radiation to the 4K stage is manageable. A critical
part of the shield is the connection between the thermal strap clamp and the cylindrical shield.
OFHC copper has been chosen for the clamp, however the shield is made of 6061 aluminum,
which contracts slightly more than OFHC copper upon cooling. As a result, the seal weakens
upon cooling. To mitigate this, thermal grease can be employed to improve the contact in this
low-pressure seal.
The joints of the cylindrical shield body, ?lid?, and ?cap? will tighten upon cooling. The
brackets which hold the three parts together are made of OFHC, again to encourage conduction.
These brackets are on the inside of the assembly, so the surrounding shield will tighten around
the brackets when cooled. It is imperative that these parts are machined to a high tolerance to
ensure a precise fit.
As with the 4K stage, the exact thermal resistance in the joints is difficult to predict and a
series of simulations were performed for a range of resistance values from 1 to 20 K/W. While it is
possible to model and predict the contact resistance between these copper and aluminum surfaces,
there are so many factors experimentally that any prediction is unlikely to be very reliable [40].
Therefore, the temperature gradient is calculated for only this range of contact resistances. If,
upon assembly, higher contact resistances are experienced, the seals will be further tightened. In
the simulations, the same value was used for each joint was applied, with the exception of the
joints between the three 6061 aluminum pieces. As these are in low-pressure contact, they were
modeled as isolated surfaces, with the only heat pathway delimited through the copper brackets.
40
3.5.4 Gradient Along Length of the 45K Stage
With the results of the 45K chamber thermal model, a secondary thermal model can be
constructed for the cylindrical shield using initial temperatures of 53.65K and 55.95K on the
surfaces of the thermal strap clamp. The appropriate radiation heat loads were applied, assuming
25 layers of MLI (a lower limit), uncovered ?cap? end and conduction through the G-10CR
supports. Additionally, the range of thermal resistances from 1 W/K to 20 W/K discussed in the
previous section were applied to the copper-aluminum joints. The results are listed in Table 3.4.
3.5.5 Simulation Results and Significance to Design Choices
The greatest concern, with the increase of the 45K shield temperature, is the resulting
increase in thermal radiation to the 4K stage. However, while the increase in radiation load
between a shield maintained at 45K and one at ? 80K is significant, it is acceptable. In the initial
radiation analysis for the 4K stage, outlined in Section 4.3, it was assumed that the entire shield
is at 60K. If that temperature were to increase to 80K, the heat load would only increase by 27
mW, or 1.8% of the total 4K heat capacity. Therefore, the results shown in Table 3.4 indicate the
temperature rise across the 45K thermal shield will remain manageable for the requisite cooling
of ions.
Thermal Resistance (K/W) Max Temperature (K)
1 61.5
5 64.7
10 68.6
15 72.5
20 76.6
Table 3.4: Maximum temperature of 45K stage for various thermal resistance values.
41
Figure 3.12: Temperature gradient on 45K stage with 1 K/W of thermal resistance applied to
copper-aluminum joints. Maximum temperature near trap is noted.
Figure 3.13: Temperature gradient on 45K stage with 20 K/W of thermal resistance applied to
copper-aluminum joints. Maximum temperature at temperature near trap are labeled.
42
3.6 Thermal Contraction Studies
The following section details a SolidWorks study done to determine the change in dimensions
of the 45K stage due to thermal contraction. Since the 4K stage is secured to the 45K stage, and
the 45K stage secured to the 300K stage, any contraction due to temperature changes will shift
the 4K stage and the Penning trap. It is important to calculate the displacement of the Penning
trap with respect to the uniform field region at the geometric center of the magnet. This study
assumes that the assembly consisting of the shield body, ?lid?, and ?cap? is cooled to 45K and
fixed at the left-hand G-10CR support. The assumption that the entire structure is cooled to 45K
is an approximation. There will be a thermal gradient across the 45K stage (see Figures 3.12 and
3.13). However, about 95% of thermal contraction occurs before a structure reaches 77K, making
this an appropriate approximation [41].
3.6.1 Material Properties
The coefficient of thermal expansion curve for 6061 aluminum was extracted from the
NIST database and is shown in Figure 3.14 [39] .
3.6.2 Simulation Results and Significance to Design Choices
The results of the thermal expansion simulations are illustrated in Figure 3.15. At the point
where the 4K stage is rigidly attached to the 45K stage, the aluminum shield is calculated to
contract by about 0.87 mm, and at the far end of the shield a maximum of 7.87 mm of contraction
will occur. The thermal straps have a predicted lateral motion of approximately 0.5 inch or 12.7
mm, and therefore will tolerate a change in length of ? 8 mm.
43
Figure 3.14: Coefficient of thermal expansion (CTE) of 6061 aluminum as a function of
temperature [39].
Figure 3.15: Thermal contraction of 45K stage, with the points of interest (the cryovalve position
and the maximum contraction) labeled.
44
Chapter 4: Design of 4 Kelvin Stage
4.1 Overview
The heart of the 4K stage is the cryogenic cooled ion trap, or Penning trap, that will store
the 7Be for interrogation and precise measurements. As stated in Section 1.2, the Penning trap,
first developed by Frans Michel Penning, combines a quadrupole electric field with a uniform
magnetic field to confine ions. The traditional Penning trap incorporates hyperbolic electrodes
and is described by the ideal quadrupolar potential given in Equation 4.1, where d is the characteristic
trap size [42].
U0
U = (2z2 ? x2 ? y2) (4.1)
2d2
2
d2
1 ?
= (Z20 +
0 ) (4.2)
2 2
Stable, harmonic motion confines ions in the axial direction. However, a particle cannot
be trapped in a stable potential well constructed using only electrostatic potentials, according to
Earnshaw?s theorem [43]. Therefore, a magnetic field is required for confinement in the radial
direction. In all, ion motion is described by cyclotron, magnetron, and axial motion, each with a
well-defined frequency. Detection of these frequencies is the foundation of the measurements.
45
To allow for injection along the beam line, the UMD trap uses an orthogonalized cylindrical
trap with open endcap electrodes. For this geometry, the electrostatic potential at the center of
the trap can be represented by a Legendre polynomial series. The Gabrielse solution, developed
in the 1980?s, eliminates the 4th and 6th order terms, and minimizes the 8th [44].
( )
1 ?? r k
U = U0 Ck Pk(cos ?) (4.3)
2 k=0 d
The trap is at the center of a magnet from RRI, cooled by the cryocooler, and contained
within a cylinder capped by a cryovalve downstream from the ion source. Cooling the trap to as
close to 4K as possible is essential. Cooling minimizes the thermal motion of the ions, reduces
electrical noise to aid the detection electronics, and adsorbs background gases onto cold surface
walls. Adsorption is crucial, as it allows us to reach the desired XHV level.
To confirm statistically the halting or alteration of radioactive decay, ion confinement on
the order of weeks to months is necessary. To achieve this, it is critical that the stored ions do not
collide with background gases. In this case, the energy of the ions will decrease and, in turn, the
magnetron orbit radius will increase, ultimately growing too large and leading to loss of the ion.
Collisions with background gases can also result in charge exchange, altering the stored 7Be4+ to
7Be3+. Distinguishing 7Be3+ from 7Li3+ can be difficult, and any unintentional creation of 7Be3+
should be avoided. It has been verified experimentally that the charge state lifetime is inversely
proportional to pressure, p, given by Equation 4.4 where ?m is the reduced mass of the collision
[45]. Simulations of 7Be4+ in a Penning trap indicate that a vacuum pressure at or below 10?15
mbar is required.
46
Figure 4.1: SolidWorks assembly of the 4K stage, with components labeled. The thermal straps
are attached directly to the base of the cryocooler to cool the entire structure.
?
1 kBT?m
tc = (4.4)
?SBp 3
The XHV regime has been achieved by several experiments, including the BASE project at
CERN and the ALPHATRAP experiment at the Max Planck Institute [8][9]. At 10?15 mbar the
mean free path for helium at 4K is on the order of 1.45 million km. The mean thermal velocity
of 7Be at 4K, found using Equation 1.13, is 70m/s. Therefore, theoretical storage times at this
vacuum level are on the order of 240 days, or almost eight months.
In all, the 4K stage consists of the base of the cryocooler, the Technology Applications,
Inc. thermal straps, the OFHC copper bus bar, the diagnostic electronics and surrounding support
structure, the cylinder that contains the Penning trap, and the cryovalve. This stage has an outer
diameter of 2.3 inches or ? 58 mm. The design of this assembly and the various stresses it is
subjected to are detailed in the following sections.
47
4.2 G-10CR Support Design
The success of the Penning trap experiments depends on the careful design of the surrounding
cryogenic stages. Attaining a temperature as close to 4K as possible is imperative to the successful
trapping of ions. To achieve this, heat loads on the Penning trap must be minimized. Equally
important, thermal contractions must be accounted for in the design to avoid mechanical failure.
With both of these goals in mind, the following section details how the internal 4K system
containing the Penning trap will be precisely located with minimum heat load.
The mechanical supports within the magnet bore: (1) must be mechanically strong enough
to support the concentric geometry within the bore and (2) must thermally isolate the stages.
Contact between the 4K stage and 45K stage requires careful mechanical design, and choice
of material. Three disk-like supports have been made from G-10CR for the 4K stage, and two
similar supports for the 45K stage. The disks have four points of contact with the external cylinder
and four points with the internal geometry, with maze-like slits to lengthen the thermal paths
between them.
The first of the three 4K supports is located at the base of the cryovalve. This support
consists of two halves that are formed around the cylinder for assembly purposes, and then bolted
together. The second support is located at the base of the Penning trap, and is shown in Figure
4.2. The third support surrounds the titanium cage that bridges the space between the electronics
and the thermal strap base.
48
Figure 4.2: Central 4K mechanical support made from G-10CR with four points of contact on
the internal and external surfaces and offset by 90?.
4.2.1 Simulation Results and Conductive Heat Loads through G-10CR Supports
Thermal conduction studies determined the heat loads contributed by the three supports in
contact with both the 45K stage and the 4K stage. Temperatures were initialized as 60K1 on the
outer surfaces, and 4K2 on the inner surfaces. The two halves of the two-pieced support were
bonded. This is a conservative approximation as there will likely be some degree of thermal
isolation between the two halves. The results are tabulated in Table 4.1.
160K was chosen as an estimate of the inevitable temperature rise along the 45K stage, maximizing the potential
heat load through our supports.
2Here, an initial temperature of 4K does not account for the inevitable temperature rise along the 4K stage; this
was done intentionally again to maximize the heat load.
49
G-10CR Support Heat Load (mW)
Cryovalve Support 46.3
Trap Support 2.87
Titanium Cage Support 2.30
Total 51.5
Table 4.1: Total conductive heat load contributed by G-10CR supports
4.2.1.1 Support Location and Strength Simulation Results
The entire 4K stage weighs about 7 kg, and is supported at three points along the length
of the ? 1.5 m assembly. The mechanical performance of the supports on the 4K stage was
assessed using SolidWorks to determine any potential points of failure and sag along the length.
Maintaining the position of the trap within the geometric center of the magnet is important for
the accuracy of measurements and significant sag could create a thermal short. To account for
the additional weight of the Penning trap and electronics not present in the model, 5 kg of mass
is distributed uniformly across the central geometries. Figure 4.3 depicts the stress using the Von
Mises Stress Criterion along the 4K stage. In the 4K assembly, the OFHC bus bar is unsupported
beyond the base attachment within the electronics cage. The simulation gives a maximum stress
of 23.5 MPa at the base of the bus bar. This value is significantly below the yield strength of
OFHC copper and is not of concern. Figure 4.4 shows the SolidWorks model displacements
under the same conditions as the stress modeling. The OFHC bus bar also experiences the largest
displacement: 1.2 mm down. While this displacement and stress are tolerable, a G-10CR support
could be added along the bar?s length to reduce the displacement to close to zero and minimize
the stress. In this case, the maximum stress is in the G-10CR supports instead of at the base of
the bus bar, with a small magnitude of 20-50 MPa. With a compressive yield strength of about
450 MPa for G-10CR, the supports are capable of withstanding these forces and displacements.
50
In the initial construction of the assembly, this additional G-10CR support will be omitted, but
could be added subsequently. The remainder of the copper structure does not experience stress
near the yield point of the material nor any areas of significant sag.
Figure 4.3: Von Mises stress on 4K stage. Point of maximum stress is shown at base of OFHC
copper bus bar. This maximum is still far below any point of failure.
Figure 4.4: Displacement in z-direction of 4K stage as a result of strain. This deformation is
negligible.
51
Additional models of the G-10CR supports under exaggerated stress conditions were performed
in order to assess their performance under a ?worst-case scenario?. Each support was modeled
with gravity and a 45N force applied. This assumes that each support carries a third of the total
weight, and a factor of safety of two is included. The results are shown in Figure 4.5, 4.6, and
4.7. The conditions for the support at the cryovalve differ slightly from the other supports. The
top half is mechanically fixed to the 4K stage, relieving the bottom half stress. Overall, these
supports only experience 30 to 75 MPa, significantly below the failure point of G-10CR. Another
concern is displacement causing a thermal short across the support. The greatest risk of this is for
the support located around the titanium support. However, even at this exaggerated load of 45N,
the displacement is not sufficient to cause a short.
Figure 4.5: Von Mises stress on G-10CR support located at cryovalve. As with the 45K supports,
the four internal points are rigidly attached to the 4K stage, minimizing the stress to the bottom
point of support.
52
Figure 4.6: Von Mises stress on G-10CR support located at trap base. The four internal points
are not attached to the 4K stage on this support. Therefore, the bottom face deforms the most.
Despite the exaggerated stress load, no thermal short occurs.
In the design of the 4K stage, an additional concern is the placement of the G-10CR
supports relative to the placement of the 45K supports and the possibility of an indirect but
detrimental heat pathway from the 300K stage to the 4K stage. Simulations were run with 0
mm, 38 mm (1.5 inches), 76 mm (3 inches), and 152 mm (6 inches) of offset between the 4K
and 45K stage supports. The results of the simulations are summarized in Table 4.2. When the
separation between the supports was eliminated completely (0 in), the heat load only increased by
0.1 mW from a full 152 mm separation. The relative position of the supports makes a negligible
contribution to the heat load delivered to the 4K stage.
53
Figure 4.7: Von Mises stress on G-10CR support located around titanium support. In this design,
the bottom face again deforms the most since there is no rigid connection to the 4K stage. At the
exaggerated loads, no thermal short occurs.
Offset(in) Heat Load (mW)
0 17.5
1.5 17.5
3 17.5
6 17.4
Table 4.2: Heat loads through stage 1 and 2 G-10CR supports with varying offset.
4.3 Radiation Heat Load Calculations
In addition to conductive heat loads, the 4K stage is heated by thermal radiation from the
45K thermal shield, and from any line-of-sight pathways to the 300K stage. The surface area
subject to thermal radiation from the 45K shield is approximately 0.30 m2 while the surface area
emitting thermal radiation from the 45K shield is 0.80 m2.
The radiation heat load between two surfaces is found using Equation 4.5.
54
Q = ? A ? (T 4 ? T 4SB 1 12 2 1 ) (4.5)
In Equation 4.5, ?12 is the effective emissivity and is specific to the geometries in question.
For concentric cylinders we use Equation 4.6, where A1 < A2.
?1?2
?12 =
? + A
(4.6)
1
2 (1? ? )?A 2 12
The radiation from the 45K shield is found using Equation 4.6, assuming an emissivity of
0.07 for the 4K stage and 0.1 for the aluminum stage. The result can be found in Table 4.3.
There are two holes in the 45K thermal shield: one for the beam line to enter, and one for
the cryovalve actuation. Both of these holes have a diameter of 0.014 m2. To estimate the heat
load contributed by this radiation, it is assumed that the holes are perfect black body absorbers
(? = 1) as a worst-case scenario. An uncertainty factor of 40% is added as well.
4K Stage Radiation Heat Sources Heat Load (mW)
45K Radiation 12.5
300K Radiation 198
Total 211
Table 4.3: Radiative heat loads onto 4K stage.
4.4 Total Heat Loads on 4K Stage
The major contributors to heat load on the 4K stage are conduction through the G-10CR
supports, radiation from the 45K shield and 300K vacuum chamber, and conduction from electronics
wiring. The BASE experiment estimated the conductive heat load due to wiring to be on the order
of 15 mW [8]. Using this value, the total heat load on the 4K stage is summarized in Table 4.4.
55
4K Stage Heat Sources Heat Load (mW)
Conduction through Supports 51.5
Radiation 211
Conduction through Wiring 15.0
Total 277
Table 4.4: Total heat loads in mW on the 4K stage due to all non-negligible sources.
This estimation of 277 mW aligns well with estimates from other similar projects. The
BASE-STEP experiment at CERN estimated about 350 mW on their 4K stage, and a dissertation
on the design of a similar trap for sympathetic laser cooling of beryllium ions estimated 835 mW,
with two openings of larger size in their thermal shield [27] [33].
4.5 Temperature Rise Studies
In addition to thermal conduction through the G-10CR supports, thermal studies of the
entire 4K stage were performed to determine the temperature rise over the entire assembly. These
simulations were performed using SolidWorks.
4.5.1 Material Properties
A NIST resource provided the temperature dependent thermal conductivity of OFHC copper
with an RRR of 50 for this study [39]. The behavior is shown in Figure 4.8.
4.5.2 Initial Temperature for Model
As discussed previously, the two Technology Applications, Inc. thermal straps at the 4K
stage each conduct 0.8 W/K. From the definition of thermal conductance, the temperature rise
across the straps can be approximated using Equation 3.4 to be 0.18K.
56
Figure 4.8: The thermal conductivity as a function of temperature for OFHC copper RRR 50
[39].
The simulations discussed in this section were performed with an initial temperature of
4.4K at the cryocooler end of the OFHC bar. This accounts for the relatively small temperature
rise across the two thermal straps due to their inherent thermal resistance.
4.5.3 Thermal Resistance in Joints
The UMD design currently has four mechanical joints in the 4K stage. It is imperative
that each joint forms a tight and well-bonded seal to maximize the heat conduction. For copper-
copper joints, this is typically achieved using either a thin foil of indium (0.1 mm) or gold-plating
the two contacting surfaces [46]. Indium requires far less torque to seal than gold, and is useful
for joints that cannot tolerate high torque. Gold-plating is better in applications requiring a high
level of cleanliness [46]. For our purposes, indium seals are preferred.
57
The thermal resistance of the different joints is difficult to assess. Several measurements
have been done, summarized in a manuscript by R. Dhuley, and a wide range of values were
found despite using similar techniques [17]. This work cites resistances ranging from <1 K/W
to 20 K/W at 4.2K for pressed indium seals. For our study performed with SolidWorks, four
iterations were done using values of 0.5 K/W, 1 K/W, 3 K/W, and 5 K/W, respectively. While
this variable is largely unknown, references suggest that achieving a thermal resistance below 5
K/W is feasible. Therefore, 5 K/W is an upper limit. If not initially achieved, the system would
be opened and the various joints tightened to reduce this value.
4.5.4 Length of the 4K Stage
The length of the 4K stage is largely dictated by the length of the 300K vacuum chamber.
As the 300K chamber has slightly magnetic 304 stainless steel flanges on both ends, they must be
kept sufficiently far from the superconducting magnet to avoid perturbing the field. The length of
the 300K vacuum chamber requires a 4K stage of 1.5 m (60.5 inch) in length. If this distance can
be decreased, the temperature at the cryovalve can be reduced. The following simulations aimed
to see if the temperature reduction would be substantial enough to warrant this change.
For effective cryopumping, the entire 4K assembly should remain below approximately
10K. At this temperature, the saturated vapor pressures of most gases are below 10?13mbar.
Only neon, hydrogen, and helium are still present, with helium largely dominating (see Figure
4.14) [47].
As the absolute minimum length for the 4K stage is 1 m, simulations were performed at
3 lengths: 1 m (42 in), 1.3 m (50.5 in), and 1.5 (60.5 in). In this study, all non-negligible heat
58
loads were applied, an emissivity of 0.07 was assumed, and the material properties and initial
temperatures discussed above were employed.
4.5.4.1 4K Length Simulation Results and Significance to Design Choices
1 m 1.3 m 1.5 m
0.5 K/W 5.42 K 5.51 K 5.61 K
1 K/W 6.00 K 6.16 K 6.36 K
3 K/W 6.84 K 6.96 K 7.12 K
5 K/W 7.70 K 7.77 K 7.89 K
Table 4.5: 4K stage end temperatures for various joint thermal resistances and stage lengths
Figure 4.9: Temperature gradient on 4K stage at full length with thermal resistance of 0.5 K/W
applied in all joints. Temperature at trap shown.
The simulation results shown in Table 4.5 indicate that there is an increase of approximately
0.2K between the 1 m assembly and the 1.5 m assembly. For a change in length of 0.5 m, this
is not a significant change and does not necessitate a decrease in the length of the 300K vacuum
chamber. The negative impact of the interference of the stainless steel flanges with the magnetic
field far outweighs the possible benefit of a slight temperature decrease.
59
Figure 4.10: Temperature gradient on 4K stage at full length with thermal resistance of 5.0 K/W
applied in all joints. Temperature at trap shown.
The temperature at the position of the Penning trap is of particular interest. Figures 4.9 and
4.10 show the thermal gradient and the temperatures at the cryovalve and Penning trap positions.
For thermal resistance of 0.5 K/W in the joints, the temperature is 5.3K at the trap, and for
thermal resistance of 5 K/W in the joints, the temperature is 6.8K ? a 2.5K rise with increased
resistance. This could be improved through the refinement of the OFHC bus bar connection to
improve conduction.
Of note, this study assumed no MLI was present between the 45K and 4K stage, and did
not account for improvements in conduction through the OFHC bar by annealing. Instead of
shortening the 4K stage, we can minimize the temperature through careful construction of joints,
vacuum annealing of the copper components, and minimizing the emissivity of the copper stage.
This offers a hopeful prospect: the goal of remaining below 10K is certainly achievable and
possibly by a wide margin of 3 to 4K.
60
4.6 Thermal Contraction Studies
The 4K stage is fixed to the 45K stage at the location of the cryovalve base flange. This is
to ensure the location of the cryovalve does not change dramatically in relation to the rotary feed-
through that actuates its motion and to introduce some predictability into the ultimate thermal
shift of the trap. As discussed, the 4K stage will be cradled at two other locations by custom
G-10CR disks to support its weight, but not fixed anywhere else.
To predict both the shift in the position of the cryovalve and the trap, thermal contraction
studies were performed using SolidWorks.
4.6.1 Material Properties
The data on the CTE as a function of temperature was extracted from a NIST document
[39]. The behavior is shown in Figure 4.11.
4.6.2 Simulation Results and Significance to Design Choices
In this simulation, the entire assembly, consisting of the OFHC bus bar, electronics cage,
Penning trap cylinders, and cryovalve, was modeled as globally bonded and cooled to a temperature
of 4.4K. In reality, there is a temperature gradient along the length of the assembly. However,
as stated earlier, 95% of contraction happens above 77K, making this gradient largely negligible.
The results are shown in Figure 4.12.
The positions of the cryovalve and of the Penning trap after contraction must be known.
As Figure 4.12 illustrates, the cryovalve is predicted to shift only 0.075 mm and the Penning trap
about 3.5 mm relative to the pinned G-10CR support. The maximum shift, at the cryocooler-end
61
Figure 4.11: Coefficient of thermal expansion (CTE) for OFHC copper [39].
of the OFHC bar, is approximately 7.65 mm. These results agree with the theoretical prediction;
a 25.4 mm (1 inch) in diameter solid copper beam of the same length should shrink about 7.5
mm.
4.6.3 Overall Trap Shift Due to Contraction
To predict the shift of the Penning trap upon cooling, one of the G-10CR supports is pinned
relative to the 45K stage. Similarly, the 45K stage is pinned to the room temperature stage that
will not contract. By optimizing the pinning locations, the shift of the Penning trap can be
minimized. The contraction of the 45K stage and the contraction of the 4K stage can be made
to approximately cancel each other, allowing us to predict closely with simulation exactly how
much the trap will move. For the superconducting magnet, a 1 cm2 sphere at the geometric center
62
Figure 4.12: Thermal contraction of the 4K stage undergoing cooling from 300K to 4.4K. The
contraction at the cryovalve and Penning trap are labeled, as these are the points of most interest.
of the magnet is guaranteed to be shimmed to within 2 ppm, as we require. As such, maintaining
the position of the center of the trap to be within this small sphere is of large concern. While RRI
Magnetics has since delivered a magnet with a significantly larger area appropriately shimmed,
this is, nonetheless, a valuable method for determining and minimizing the shift of the trap within
the magnet bore. From simulation, an estimate can be made of the contraction of both stages and,
based on the pinning locations, the predicted shift of the trap. An illustration of this practice and
the shifts of the two stages is shown in Figure 4.13. Ultimately, the trap will shift approximately
2.7 mm to the left of its original location.
4.7 Achieving Extreme High Vacuum (XHV)
XHV conditions can be achieved in a vacuum vessel through the adsorption of molecules
onto sufficiently cooled surface walls via attractive Van der Waals forces. This process is called
?cryopumping? and consists of three regimes.
63
Figure 4.13: Illustration of the change in location of the Penning trap due to thermal contraction
of the 4K and 45K stages. Not to scale.
First, physisorption is the sub-monolayer coverage dominated by Van der Waals forces
between adsorbed materials and the surface [47]. The binding energy required to adsorb a
molecule is typically larger than the heat of vaporization. A sub-monolayer amount of most
gases can be physisorbed in sub-saturated conditions at their boiling points.
Second, as surface coverage increases, the cryocondensation regime is reached. This
regime is characterized by Van der Waals forces among adsorbed molecules [47]. The eventual
equilibrium that is achieved between gas adsorption and desorption processes establishes the
saturated vapor pressure.
Third and finally, in the cryotrapping regime, a condensible gas is used to trap a non-
condensible gas with a higher vapor pressure[47]. This technique is used frequently to trap
hydrogen and helium ? two gases of main concern in the UMD trap at 4.2K [9]. Figure 4.14
illustrates this point well. The saturated vapor pressure, or the pressure at which the vapor phase
64
Figure 4.14: Vapor pressures (mbar) of various gases present in vacuum systems as a function of
temperature (K). Curves found from Equation 4.7 and constants found in Appendix A.1.1 [47].
is in equilibrium with the liquid phase, follows the Clausius-Clapeyron equation, a form of which
is seen in Equation 4.7 [47]. Below 10K, most gases will have fully condensed out, with the clear
exception of helium and some hydrogen.
B
log10(Psat) = A? (4.7)T
Attaining XHV on the order of < 10?15mbar is a requirement for long-term storage of
ions. Reaching this level of vacuum requires cryogenic temperatures in the trapping region to
induce cryopumping. Further, if the ion trap XHV can be isolated from the greater UHV region,
storage times on the order of a year have been demonstrated [8]. An experiment at the Max Planck
Institute has produced a vacuum below 10?17mbar through the implementation of a ?cryovalve?
65
that separates the UHV regime from the XHV ion trap region [9]. A ball-valve cryovalve for the
CURIE Project has been designed that is similar to one under development for the BASE-STEP
Experimental group at CERN [27]. The design separates the ? 10?9mbar in the ion transfer line
from the 4K XHV environment Penning trap. The ball-valve is actuated externally and tests are
underway to quantify its performance at room and liquid nitrogen temperatures. The design and
results are detailed in this work.
4.7.0.1 Formation of a Monolayer
At the cryogenic temperatures in the Penning trap system, most gases will condense on
to the walls of the assembly. This cryosorption of gas further reduces the pressure inside the
4K system. The high efficiency of cryosorption is maintained until a monolayer of gas on the
surface is formed. At this point, less gas will be adsorbed, and the pressure will begin to rise
[27]. Helium and hydrogen, specifically, will be the most abundant species due to their vapor
pressures and outgassing [18]. The time for a monolayer of helium to form, assuming an open
valve, is calculated. In this calculation, there is assumed to be no inlet valve, just an open cylinder
with negligible pressure drop across the entrance.
The rate of adsorption on a unit area is given in Equation 4.8, where st is the sticking
probability ? or the likelihood of adsorption by an incident molecule on a surface [18]. For this
study, the sticking probability is set to 1.
dna 1
= stP (2?mkT )
?
2 (4.8)
dt
For pressure, P, in Pascals, this equation can be rewritten as Equation 4.9, where M is the
66
molecular weight of the gas and T is the temperature [18].
dna 1
= 2.6? 1024P (MT )? 2 (4.9)
dt
The above equation can be rearranged to solve for monolayer formation time, TM . In
Equation 4.10, Amol is the area of a single hydrogen molecule. The internal surface area, Atrap,
of the 4K stage is approximately 0.25m2. Therefore Atrap/Amol = n, where n is the number of
particles in a monolayer.
Atrap
TM = 1 (4.10)
Amol2.63? 1024P (MT )? 2
Assuming the Bohr radius, an initial pressure of 1? 10?8 Pa (1? 10?10mbar), and room
temperature, 293K:
TM = 1.28 hours (4.11)
Vacuum pressures of order 1?10?8 Pa or 1?10?10mbar outside the 4K stage are attainable,
however, if the external pressure is as high as 1? 10?7 Pa (1? 10?9mbar):
TM = 0.128 hours = 7.68minutes (4.12)
Since the 7Be is to be stored for several weeks, it is imperative to have separation of the
vacuum regions to prevent the rapid formation of a monolayer in the 4K stage and the resulting
rise in pressure. This necessitates the cryovalve.
67
4.7.1 The Cryovalve
In order to isolate the internal XHV of the Penning trap from the UHV of the beam line,
a cryovalve has been designed. The ball-valve design was chosen to increase the sealing surface
area and to allow for a single-axis actuation method. The ball sits on a spherical seat on the
lower flange ? the entrance to the 4K stage. The ball itself is rotated by two keys within Teflon
sleeves to reduce friction with the copper walls. On one side, the key is elongated and attached to
a G-10CR T-bar assembly. To actuate it, the T-bar is engaged by an external G-10CR assembly,
turned, and then again released. Since this assembly will only be in contact with the actuation
system for seconds at most and through highly insulative G-10CR, the heat load is negligible.
The rotation of the ball is physically halted by a threaded rod in its side that is arrested by a set
screw in the upper plate and a mechanical stop block on the bottom flange.
Due to unavoidable surface roughness between the sphere and the flange seat, there will
be micro-gaps between the two. These gaps can be reduced by polishing and by increasing the
force used to engage the sphere with the seat, but the allowable size of these gaps is yet to be
determined. Considering the small magnitude of the differential pressure between the XHV and
UHV volumes, its likely the seal does not need to be exceedingly tight. To assess the necessary
force for sealing, the top plate is secured by four bolts with springs between the heads and the
surface. This allows progressive tightening of this plate onto the ball, increasing the pressure on
the lower flange seat and improving the seal. The plate itself has a conical cut on the underside
to interface with the sphere tangentially.
To further examine the sealing surface, various shapes were investigated. Four different
flanges were made, each with a varying amount of surface area in contact with the ball. The four
68
Figure 4.15: Exploded view of the UMD cryovalve design, with Flange 1 shown.
69
Figure 4.16: Photograph of the assembled cryovalve, ready for testing.
70
flanges are shown in Figure 4.17. Flanges 1 through 3 have a spherical interface, with increasing
contact area, while flange 4 is a conical shape, to provide only a tangential circle of contact.
Figure 4.17: Cross-sections of the four bottom flanges manufactured for the testing of the UMD
cryovalve with varying seal surface area. 1, 2, and 3 are spherical, and 4 is conical.
4.7.2 Cryosorptive Surfaces for Cryopumping
The sticking factor of a surface is a function of several variables including surface roughness,
material, and temperature. Typically, sticking factors decrease over time as the capacity of
the porous surface fills [48]. It is difficult to predict and model the change in sticking factor
over the time of an experiment. To have a sticking factor as close to unity and maximize
71
cryopumping, there are many types of surface coatings that can be used. These include carbon-
fibre cryoadsorbers, and various types of activated charcoal coatings and getters that maximize
the internal surface area and effectively create small pockets to trap molecules.
Carbon-fibre cryosorbers implemented in the CERN Large Hadron Collider have been
investigated for efficacy. At a surface coverage of 1018H /cm22 , the sticking factor increased
from 0.1 at 30K to 0.3 at 7K [48]. At a lower surface coverage of 1014H2/cm2 (approximately
a monolayer), the sticking factor at 6K increased to greater than 0.8 [48]. This indicates both
the effective pumping of cryosorptive materials, and the need to maximize monolayer formation
time.
4.7.2.1 MolFlow Simulations
To assess the use of a porous material such as activated charcoal to achieve XHV, simulations
in MolFlow were undertaken. In these simulations, a simplified geometry of the 4K stage was
used, and the entrance pressure was initialized at about 10?9 mbar with a series of sticking factors
applied to the wall. Figure 4.19 illustrates the efficacy of the increased sticking factor on the cold
surfaces; increasing the sticking factor from 0.5 to 0.9 reduces the pressure in the 4K stage by
approximately three orders of magnitude.
In the CURIE system, the cryovalve aperture is 0.3125 inch or 8 mm. Figure 4.20 demonstrates
the result of reducing the aperture from 15 mm to 10 mm. In this model, there is also a tube before
the entrance to the 4K stage which generates a pressure drop, approximating our actual design.
With a small aperture, a moderate sticking factor of 0.5 is sufficient to reduce the vacuum to
below 10?15 mbar at the far end of the 4K cylinder; with a considerable sticking factor of 0.9,
72
Figure 4.18: Simplified geometries used for modeling in MolFlow, with a sample pressure
gradient shown. Image 1 no initial cryopumping, while image 2 has 50.8 mm (2 in) of
cryopumping surface area prior to the valve opening.
Figure 4.19: Pressure profiles from Molflow simulation along length of 4K stage with internal
cryopumping only and varying sticking factor (SF) from 0.25 to 0.9.
73
10?17 mbar is reached.
Figure 4.20: Pressure profiles from Molflow simulation along length of 4K stage with 10 mm
cryovalve aperture.
Figure 4.20 shows the pressure profile when the valve is open. This indicates that XHV
pressures are achievable, but to maintain them, the cryovalve is required. Figure 4.21 explores
the pressure profile expected with a closed valve and imperfect seal, initialized at 10?9 mbar. A
large gap of one one-hundredth of an inch is assumed between the ball and the 8 mm cryovalve
aperture. In this case, a moderate sticking factor of 0.5 reduces the vacuum to the low 10?16 mbar
range; with a sticking factor of 0.9 the pressure approaches 10?18 mbar.
4.7.3 Testing the Valve
The apparatus designed specifically for these tests is shown in Figure 4.23. It is a counter-
top cryostat to cool the cryovalve to ? 77K and measure the pressure differential across it.
74
Figure 4.21: Pressure profiles from Molflow simulation along length of 4K stage with 0.01 gap
to imitate the cryovalve seal.
While the valve will ultimately be cooled to closer to 4K, about 95% of thermal contraction
will occur by 77K, making it an appropriate initial testing temperature. To establish an upper-
limit of the conduction through the valve, tests will initially be performed at room temperature
and atmospheric pressure on the exterior of the valve. Subsequent tests will be done at 77K.
Construction of the apparatus is underway, in preparation for initial testing. As such, results have
not yet been gathered and cannot be reported in this thesis. The methods that will be followed
during testing are outlined below.
4.7.3.1 Conduction Estimation
It is valuable to have an estimation of the conductance through the valve prior to measurement.
To estimate the conduction of the valve in the open position, Equation 4.13 is used. The equation
75
is valid for conduction through an aperture in the molecular flow regime, in units of l/s [18].
?
T
Cap = 3.64A (4.13)
M
Equation 4.14 is also of value, as it provides an estimate of the conductance through a tube
of length l and diameter d, where l >> d [21]. However, for a short tube like the inlet of the
cryovalve where l and d are comparable, both Equations 4.13 and 4.14 are needed. The effective
conductance of these two considerations is given by Equation 4.15 [18].
?
T d3
Ctube = 3.81 (4.14)
M l
1 1 1
= + (4.15)
Ceff Ctube Cap
The cryovalve entrance has a diameter of 8 mm and a length of 4.5 cm. For helium gas at
room temperature, the total effective conductance for the valve when open is 2.97 l/s. At 77K,
the effective conductance becomes 1.52 l/s. The gas entering the valve will be closer to room
temperature.
The conductance of the valve in the closed position can be estimated by approximating
the space between the ball and the seat as a slit, using Equation 4.16 [21]. To be thorough,
this equation can then be combined with the conductance along the valve inlet using Equation
4.15, where Cap becomes Cslit. However, at small ?slit? heights, Ctube becomes negligible. The
?length? and ?width? of the ?slit? will change depending on the flange, so the dimensions of
flange 2 will be used as a mean value. The ?length? is the arc length of the ball in contact with
76
the flange seat, 0.23 cm. The ?width? is the mean sealing length, 3.63 cm. The ?height? is
the estimated distance between the ball and the seat due to surface roughness. In the MolFlow
simulations, a one-hundredth of an inch gap was assumed, or 250 ?m. This is quite large. In
reality, a gap closer to 50 to 75 ?m is reasonable.
vav
Cslit = a A (4.16)
4
In Equation 4.16, a is the transmission probability factor, vav is the average thermal velocity,
and A is the slit entrance area (b?h). Assuming the presence of helium gas at room temperature,
the average thermal velocity (Equation 1.13) is 1350 m/s. At 77K, this reduces to 693 m/s, and
at 4K it is 162 m/s. The transmission probability coefficient is 0.243 (see Appendix A.1.2 for
calculation details). The results of this calculation are visualized in Figure 4.22. The benefit of
reduced temperature is clear, due to slowed thermal ion velocities. However, again, the gas will
be around room temperature as it is travelling from the beam-line. This study indicates that the
MolFlow simulation shown in Figure 4.21 experienced a gas flow through the 250?m wide ?slit?
of approximately 0.5 l/s.
Assuming a ?slit? height closer to 50 ?m, a new monolayer formation time can be calculated
using Equation 4.17. At 50 ?m and room temperature, helium leaks through the valve at a
conductance of 0.052 l/s. ?P is the pressure drop across the valve. This can be estimated from
Figure 4.21, where the inlet to the 4K stage causes a pressure drop from about 1? 10?10mbar to
8 ? 10?15mbar. In reality, the pressure drop will be larger and the monolayer time longer since
the study in Figure 4.21 assumes a ?slit? height of 250 ?m, not 50 ?m.
77
Figure 4.22: Conductance through slit-like sealing interface in l/s for a range of slit heights from
10 ?m to 250 ?m. Helium gas is assumed and the curve is calculated at three temperatures: 4K,
77K, and 293K.
Atrap kBT
TM = (4.17)
Amol ?PCslit
TM = 134 years (4.18)
This is an impressive increase from the monolayer formation time found for an open
valve and certainly justifies the need for the cryovalve. This indicates that, with the valve
closed, the Penning trap can remain at XHV pressures for much longer than the duration of
any experimentation.
78
4.7.3.2 Methods
Figure 4.23: 77K Cryostat designed and built for UMD group cryogenic testing.
While the conductance through the open valve is certainly of interest, these tests primarily
aim to determine the conductance through the ?sealed? surface of the cryovalve ? or the cryovalve
in the closed position. Through these experiments, an upper limit to the conductance will be
determined, first testing at room temperature and higher vacuum pressures, and then at cryogenic
temperatures and vacuum pressures on the order of 10?4 to 10?6mbar. In actuality, this valve
will operate between vacuum pressures closer to 10?9mbar and 10?15mbar.
79
In a complex geometry such as this, analytical calculation of the gas-flow conductance is
not possible, and experimentation is required [21]. Two categories of conductance measurements
exist: intrinsic and reduced measurements. An intrinsic measurement is one where a valve is
mounted between two relatively large vessels such that the distribution of the direction of flow is
isotropic [22]. In contrast, a reduced measurement involves building the valve into a tube where
the particle flow at the entrance will be directional [22]. For the latter, additional calculations are
required to account for the increased ease of flow through the valve. While the cryostat assembly
described by Figure 4.23 is not strictly either of these categories, the pressurized entrance to the
valve is in a large volume, making an intrinsic measurement appropriate. The details of such a
measurement are discussed below.
The cryovalve experiments will be conducted in the 77K cryostat assembly, shown in
Figure 4.23. The apparatus consists of the custom-built internal cryostat, an 8 inch CF 4-way
cross chamber, a rotary feedthrough for actuation, and two pumping stations: one for each of the
vacuum volumes. Prior to assembly, all components were cleaned for UHV use.
The initial tests will be conducted at room temperature. With the valve open, the entire
assembly will be evacuated to 10?6mbar by two turbopumps. The valve will then be closed, and
helium leaked into the exterior vacuum chamber to a pressure of 0.25 atm, or ? 250 mbar. At
this point, the gas throughput Q is known from the amount of leaked helium, and the volume of
the exterior chamber will be estimated. Subsequently, a pressure ?rate-of-rise? test is conducted.
In this measurement, the pressures in the exterior chamber, P1, and interior chamber, P2, are
recorded over several hours to days so that a leak-rate can be calculated.
In general, it can be assumed that a leak induces a constant leak-rate and can be expressed
by Equation 4.19 [22].
80
?P
Qleak(t) = V = constant (4.19)
?t
The conductance is defined by Equation 4.20.
Qleak
C = (4.20)
?P
The cold test will be similarly conducted. To begin, the entire assembly will be sealed
and evacuated to at least 10?4mbar with the valve open. Once evacuated, the valve will be
closed and LN added to the designated fill area. At this point, both vacuums will improve due to
cryopumping, but the interior vacuum pressure will decrease more, leading to a pressure gradient
across the valve. A small amount of helium will be added into the exterior vacuum chamber using
a helium leak valve, further increasing the pressure difference. As at room temperature, a rate-of-
rise measurement will be performed, with the pressures on either side of the valve recorded over
several hours to days. This test will involve the same calculations as the room temperature test.
81
Chapter 5: Conclusions
Several experiments have demonstrated that the half-lives of radioisotopes that decay by EC
are susceptible to change with manipulation of their electron orbital structure. Yet, no experiment
has ever isolated the ionization states of such an isotope to measure the new, altered decay rates.
Further, no experiment has ever attempted to halt radioactive decay by fully ionizing and stably
storing such an isotope. The CURIE Project at the University of Maryland is approaching both of
these goals through the commission of a 4K CryoTrap system capable of achieving storage times
on the order of weeks to months.
Such extensive storage times are made possible by cryogenic temperatures of ? 4K in the
Penning trap region. At these temperatures, most background gases condense out to generate
XHV pressures and allow for resistive cooling of the trapped ion ensemble, thereby permitting
single ion detection. At XHV pressures, the half-life of the ions due to collisions or charge
exchanges is much longer than the half-life of partially ionized 7Be, creating an extremely stable
home for an ion ensemble. The cryogenic system that makes this possible is outlined in detail in
this thesis. It is comprised of the 45K stage that minimizes thermal radiation to the colder internal
structures, and the 4K stage that houses the Penning trap.
The 45K stage is made of 6061 aluminum and exists as an intermediate thermal barrier
between the hot room temperature chamber and the cryogenic Penning trap. It is cooled by
82
the 2nd stage of the cryocooler that has a cooling capacity of 15-20W. Extensive modeling
predicts that the applied heat loads on this system will be 160 mW due to conduction through
supports, 2.1 to 3.9 W due to radiation on surfaces wrapped in MLI, and 4.6 W due to radiation on
uncovered surfaces, totaling 6.9 to 8.6 W. Other contributions, such as conduction through wiring
and Joule heating, were justifiably assumed to be negligible. Thermal gradient studies indicate
that the 45K stage will reach a maximum temperature between 60K and 76K. The variability
comes about from the uncertainty in thermal resistances of joints, and can be minimized through
careful assembly. Thermal contraction in the design was also given careful consideration: the
Technology Applications, Inc. thermal straps serve as a point of flexibility and each stage was
only pinned at one location. Mechanical stresses were found to minimal on the system.
The 4K stage is primarily constructed from OFHC copper, and cools the Penning trap at
the center of the magnet bore. For effective ion cooling, the Penning trap should be as close to
4K as possible. Modeling indicates that the heat load due to conduction will be 66 mW, and 210
mW due to radiation. As the total cooling capacity on the 1st stage of the cryocooler is 1.5W,
these heat loads are appropriate. The maximum temperature at the far end of the stage, as a
result of these heat loads, was modeled to be between 5.6K and 7.9K. The variation here is again
due to uncertainty in the thermal resistance of joints. Of more relevance, the temperature at the
position of the trap was between 5.3K and 6.8K. This thermal rise can be minimized through
careful joint construction, annealing of the OFHC copper bus bar, and wrapping the 4K stage in a
layer of MLI. Additionally, the temperature at the Penning trap location can be brought closer to
4K through improvement of the OFHC bus bar connection to maximize conduction. Contraction
studies predict that the Penning trap will shift 3.5 mm from its position at 300K ? a tolerable shift.
As the 45K stage and 4K stages are both pinned rigidly at one position, the thermal contraction
83
of each can be used to partially negate this Penning trap shift.
While attaining XHV is largely dictated by the achievement of cryogenic temperatures,
maintaining such vacuum pressures necessitates the cryovalve. The cryovalve is a rotary ball
valve which separates the UHV beam line from the XHV trap region to slow the formation of
a condensed gas monolayer. A prototype of the design presented in this thesis has been made
and initial tests are underway to assess the seal. The conduction through the valve when open is
estimated to be 2.97 l/s at room temperature, and 1.52 l/s at 77K. When closed, the conduction
depends on the fit of the ball and flange seat, or the ?slit? height. For a fairly rough height of 250
?m, the conduction at room temperature is predicted to be 0.744 l/s. At 77K, this reduces to 0.381
l/s, and at 4K to 0.089 l/s. With decreased slit height through increased pressure or polishing,
this conduction can be reduced significantly. In conjunction with the cryovalve, cryosorptive
materials will be applied to the interior of the 4K stage to maximize the sticking surface area.
Simulations in MolFlow emphasize the importance of maximizing sticking factor on the interior
surfaces, and indicate that pressures below 10?15mbar are well within reach.
The design presented in this thesis is both simple and robust, and meets the various requirements
for success outlined by the larger CURIE project. Still, the success of any cryogenic system
hinges on careful tolerancing and assembly; these will be given extreme care as the system comes
to life. Future work will include the completion of the cryovalve testing, and possibly subsequent
iterations of the cryovalve design.
84
Appendix A:
A.1 Additional Constants and Equations
A.1.1 A and B constants for Clausius-Clapeyron vapor pressure equation
He H2 CH4 H2O Ne N2 CO C2H6 O2 Ar CO2
A 4.09 3.97 7.36 10.23 6.95 8.14 8.67 9.69 8.57 7.84 9.995
B 4.96 40.9 486.80 2612.60 109.87 379.27 441.19 1039.34 463.448 420.58 1360.35
Table A.1: A and B constants of typical molecular species present in vacuum systems for
calculation of vapor pressure with the Clausius-Clapeyron equation [47].
A.1.2 Transmission probability coefficient for a rectangular slit
Assuming the slit height, h, is much smaller than both the width, b, and the length, l, the
transmission probability coefficient is described by a = k1 ? k2 where k1 and k2 are defined in
Equations A.1 and A.2 and L = l/h [21].
( )
1
k = 1 + (1 + L2)1/21 ? L (A.1)
2
( )2
3 L? ln[L + (L2 + 1)1/2]
2
k2 = (A.2)
L3 + 3L2 ? 4? (L2 + 4)(L2 + 1)1/2
85
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