CERENKOV LIGHT PRODUCTION 
I N A WATER MODERATED 
NUCLEAR REACTOR 
by 
Robert William Madey 
Thesis submitted to the Faculty of the Graduate School 
of the University of Maryland in partial fulfillment 
of the requirements for the degree of 
Doctor of Philosophy 
1963 
APPROVAL SHEET 
Title of Thesis : Ce r enkov Light Production in a 
Wat e r Mo derated Nuclear Reactor 
Name o f Candidate : Rob e rt William Madey 
Doctor of Philosophy, 1963 
Thesis and Abstract Appr oved : , dd 
Dick Duffey - P~ or 
Nuclear Reactor ir e c t o r 
Chemical Eng in eering 
Department 
D.s.t E:: Approved : 
c,L 2 7J1 f b.J 
{ /; J 
( 
' I 
(I 'f) I ...I,  
't' 
I I ABSTRACT (! I / 
( 
Title of Thesis: Cerenkov Light Production in a Water 
Moderated Nuclear Reactor 
Robert William Madey, Doctor of Philosophy, 1963 
Thesis directed by Dr. Dick Duffey, Professor 
An experimental investigation of the production 
of Cerenkov radiation in a water moderated nuclear 
reactor is conducted using a photomultiplier as a 
light sensor. The variations in light intensity 
are studied during various phases of reactor opera-
tion, namely: startup, steady state and shutdown. 
The relevant theory is presented as an aid in in-
terpreting and extrapolating the experimental results. 
It is found that for transients such as startup, 
the light signal is directly related to reactor power 
for periods (e - folding time) faster than about 20 
seconds. Additional transient data acquired from 
measurements performed on a TRIGA pulsed-type r eactor 
illustrate the excellent agreement between the Cerenkov 
detector and a conventional ionization chamber for 
measuring pulse characteristics such as peak power, 
pulse half-width, and prompt period. The proportional-
ity between reactor power and Cerenkov signal is no 
longer valid for whole core measurements made at steady 
state power level because of the gradual increase of the 
Cerenkov signal as a result mainly of fission product 
I 
contr ibution s . Se l e ctive s c anning of the Ce renkov 
s pectrum throu gh the us e of inter fe r e nc e fil t e rs 
0 0 
ov er th e wav e l en g th ran ge 3500 t o 5 5 30 A r e sults 
i n a lowe r buildup fraction. I ndications are that 
measurements further into the short wavelength 
r eg ion may yield a light sen s or, and hence a good 
powe r detector, independent o f any fission product 
buildup. The decrease in th e Cerenkov light intensity 
after shutdown is measured for reactor operating times from 
20 minutes to 4 hours. Comparison of the empirical 
data with theoretical considerations results in good 
agreement for shutdown times r anging from 500 seconds 
to 10,000 seconds. 
Spectral measurements made through 17 fe et of water 
with a Hilger quartz spectrograph show a spectral distri-
0 0 
bution ranging from 2500 A to 6000 A. A calculated spectral 
distribution is compared with t h e measured spectrum after 
correcting for water attenuation. 
ACKNOWLEDGEJ:1ENT 
The a uth or wishes t o e xpress his appreciation to Dr. 
Dick Du ffe y f or t he oppor t unity to und e rtake t h i s work 
an d f or his interest and encouragement throughout t he 
cou rs e o f the inve stigation . He i s e specially grateful 
to Dr . C. O. Muehlhause for sug g es tin g the problem and to 
Dr . J o s e ph Silve rman for many stimu l a t i ng discussions 
regar d i ng th e problems encountered in this work. 
Grateful recognition is also extended to the many 
fri ends who assiste d in t}:le experiments and preparation 
o f th e thesis mat erial. Particular notice is taken of the 
i nvaluab l e help g iven by Mr. Chieh Ho in maintaining the 
ope rational status of the University of Mary land Reacto r . 
To all these individuals, and to my wi fe Gloria for 
her constant encourag ement, assistance an d patient under-
standing, I extend my thanks. 
TABLE OF CONTENTS 
Chapter Page 
I. I NTRODUCTION 1 
A. The Cerenkov Effect 1 
1. History 1 
2. Descriptive Account 1 
II. CERENKOV RADIATION IN WATER MODERATED 
REACTORS 7 
A. Source of Cerenkov Radiation 7 
1. General 7 
2. Beta Radiation 9 
3. Gamma Radiation 9 
III. EXPERIMENTAL DESIGN 17 
A. Brief Description of the Reactor 17 
B. Detector, De tector Assembly, 
Associated Electronic Equipment 19 
c. Detector Light Check Source 33 
IV. SPECTROGRAPHIC STUDY OF THE LIGHT 35 
V. ANALYSIS OF THE LIGHT INTENSITY AS A 
FUNCTION OF REACTOR POWER 44 
A. Introduction 44 
B. Signal Response 47 
1. Theoretical 47 
2. Experimental 54 
a. Transient 54 
b. Steady State 67 
c. Shutdown 71 
TAB LE OF CONTE NT S (CONT'D) 
Ch a pter Page 
d. Filter Tests 83 
VI . SUMMARY 88 
APPENDIX A 96 
A. Theoretical Eval uation of the 
Cerenkov Light Intensity and 
Spectral Distribution 
SELECTED BIBLIOGRAPHY 116 
LIST OF TABLES 
Table Page 
I. Refractive Index of Water at 20?C 
for Various Wavelengths 8 
II. Relative Importance of Photoelectric, 
Compton and Pair Absorption Coefficients 
for Water 11 
III. Groups of Mercury Lines Useful for Wave-
length Identification 36 
IV. Cerenkov Transient Data 62 
v. Fractional Buildup of Cerenkov Signal 
After a Reactor Operating Time of One 
Hour 84 
VI. Threshold Kinetic Energies for Electrons 
in Some Common Gases at Normal Temperature 
and Pressure 93 
VII. Fission Produc t Gannna Energy Group 
Definitions 103 
LIST OF FIGURES 
Figure 
1 . Hu yghens Construction to Illustra te 
Coherence 3 
2 . Formation o f t he Cerenkov Cone 5 
3 . Mass Absorption Coefficients for 
Water as a Function of Photon Energy 13 
4 . Initial Reactor Core Geometry, #1 18 
5. Fina l Reactor Core Geometry, :/12 20 
6 . Vertical Cross-Section of the University 
of Maryland Reactor 21 
7. Top View of the University of Maryland 
Reactor Core 22 
8 . Photomultiplier Detector Assembly 24 
9 . Pass Band Characteris tics of Inter-
ference Filters 26 
10. Photomultiplier Spectral Sensitivity 
Characteristic 28 
11. Photomultiplier Bleeder Ne twork 29 
12. Photomultiplier Current Amplification 
vs Interstage Voltage 31 
13. System Block Diagram 32 
14. Panelescent Light Spectral Energy 
Distribution 34 
15. Hilger Quartz Spectrograph 37 
16. Spectral S@nsitivity fo r Kodak 
Spectroscopic Plate Type 103a-0 39 
17. Mercury Arc Spectrum Calibration Curve 41 
18 . Measured vs Calculated Cerenkov 
Spectral Distribution 42 
19. Reactor Operational Phases; Power as 
a Function of Time 45 
LIST OF FIGURE S (CONT'D) 
F i gur e Pa ge 
20. De l ayed Gamma Effect on Ceren k ov Signal 
Re sponse for a Shift in Reactor Power 53 
21 . Ceren k ov Signal vs Neutron Power Level, 
Tes t a 56 
22. Ce r en k ov Signal vs Neu t ron Power Level, 
Te st b 57 
23. Cerenk ov Signal vs Neu t ron Power Level, 
Test c 58 
24. Cerenkov Signal vs Neutron Power Level, 
Test d 59 
25. Cerenkov Signal vs Neutron Power Level, 
Test e 60 
26. Cerenkov Signal vs Neutron Power Level, 
Test f 61 
27. Peak Power vs Pulse Half Width 65 
28. Peak Power vs Prompt Pe riod 66 
29. Illustrative Definition of Relative 
Buildup Fraction 68 
30. Cerenkov Signal Buildup Fraction as 
a Function of Reactor Operating Time, T 70 
31. Cerenkov Light Decay as a Function of 
Shutdown Time for a Reactor Operating 
Time, T = 20 minutes 72 
32. Cerenkov Light Decay a s a Function of 
Shutdown Time for a Reac t or Operating 
Time, T = 30 minutes 73 
33. Cerenkov Light Decay as a Function of 
Shutdown Time for a Reactor Operating 
Time, T = 45 minutes 74 
34. Cerenkov Light Decay as a Function of 
Shutdown Time for a Reactor Operating 
Time, T = 60 minutes 75 
LIST OF FIGURES (CONT' D) 
Figure Page 
35. Cerenkov Light Decay as a Function of 
Shutdown Time for a Reactor Operating 
Time, T = 120 minutes 76 
36. Cerenkov Light Deca y as a Function of 
Shutdown Time for a Reactor Operating 
Time, T = 180 minut e s 77 
37. Cerenkov Light Decay as a Function of 
Shutdown Time for a Reactor Operating 
Time, T = 240 minutes 78 
38. Perc ent Error Between Measured and Ca lcu -
lated Cerenkov Light Decay as a Function 
of Reacto4 Operating Time for a Shutdown Time = 10 s econds 82 
39. Cerenkov Signal Buildup Fraction as a 
Function of Time Us ing Interference 
Filters 85 
40. Variation of Cerenkov Threshold Energy, 
Et, as a Function of Pressure for Some 
Common Gases 94 
41. Plot o f (1 - } 2 ) a s a Function of S n 
Electron Range in H20 98 
42. Range of Electrons in H 0 as a Function 
of Energy 2 99 
43. Calculated UMR Gamma Spectrum 102 
44a. Distribution of Compton Recoil Electron 
Energies - "Prompt" Spectrum 
O<E<2.5 Mev 105 
44b. Distr ibution of Compton Recoil Electron 
Energies - "Prompt " Spectrum, 2. 5<E<8. 0 Mev 106 
45a. Distribution of Compton Recoil Electron 
Energies - "Prompt"+20 minute Fission 
Product Spectrum - O<E<2.5 Mev 107 
LIST OF FIGURES (CONT'D) 
Figure Page 
45b . Distribution o f Compton Recoil Electron 
Energies - " Prompt 11+20 minute Fission 
Product Sp ec trum - 2.5 < E < 8 .0 Mev 108 
46a . Distribution of Compton Recoil Electron 
Energies - 11 Prompt''+4 hour Fission Product 
Spectrum - 0 < E < 2.5 Mev 109 
46b . Distribution o f Compton Recoil Electron 
Energies - "Prompt"+4 hour Fi ssion 
Product Spectrum - 2.5 < E < 8 .0 Mev 110 
47. Calculated Ce r enkov Spectral Distribution 112 
48. Water At t enuation Coefficient as a 
Function o f Wavelength 114 
49. Transmitted Cerenkov Spectral Distribu-
tion Through 16 Feet of Water 115 
-CHAPTER I 
INTRODUCTION 
A. The Cerenkov Effect 
. 
1 . History1  
The discovery of the blue light emitted from trans-
parent substances when irradia t e d by radioactive sources 
dates back to Malle?i;: (1926, 1928-1929). He noted that 
the spectrum of the light was continuous and did not possess 
the line or band structure characteristic of fluorescence. 
Mallet, however, did not attempt to offer any explanation 
of the phenomenon and i t was n ot until 1934 that the 
Russian physicist, Cerenkov, studied the phenomenon more 
systemat ically. He showed, in particular, the funda-
mental difference between this light and that produced 
by fluorescence, namely the addition of known fluorescent 
inhibitors had no effect upon the light. Furthermore, 
his experiments showed the light to be partially polarized . 
The correct theoretical explanation of the phenomenon was 
not established until 1937 by Frank and Tamm. 
2. De scriptive Account1 , 2 , 3 ,4 
Whenever a fast charged particle traverses a dielectric 
medium it produces a local polarization along its path. 
The polarized atoms return to their normal states with the 
emission of light immediately after the particle has passed . 
When the velocity of the particle is less than the phase 
1 
2 
v e locity o f light i n t he same medium, the ligh t pulses f rom 
t h e ind i v idual atoms are damped out du e to destructiv e in ter-
fcrcDce . However, if the v e loc ity of the particl e is g reater 
t h a n the phase v e locity of l i gh t in the medium, the wav e lets 
f rom a ll po r tion s of the trac e a re in phase with one another 
and a r esulting r a diation known as Cerenkov rad iation is 
ob served . Re fer ring now to Fi gure 1, t he wav e l e ts which 
are sen t out while the particle travers es the distance AB 
are propagated along a wavefront BC, the velocity of propa -
gation being ii where n is the r efractive index of the 
me dium and c is the velocity o f l i ght in vacuo. Coherence 
exists whenever the time taken by the particle to trave rse 
th e distance AB is the same as the time taken by th e wave -
front to traverse the distance AC, e . g., the spherical waves 
arr i v e in phase along BC. The direction of emission of the 
radiation is along the line AC, a t r i gh t ang les to BC. The 
distance the particle travels in a time Lit is AB = vlit, 
where vis the v e locity of t he particle in the medium. In 
the same time, the light trav e ls a distance AC = ?n Lit . The 
resulting expression, known as the Cerenkov relation, 
obtained from these two expressions is: 
cose = 1 ( 1) 
Sn 
V 
where S = c and is related to the kinetic energy E of the 
particle and to its rest mass m0 by the equation: 
E = m c 2 0 ( 2) 
3 
Fig . 1 Huyghens Construction to 
I llustrate Coherence 
A 
B 
4 
Tl crcfore , Cerenkov radiation is not possible unless 
0 ~ _L < 1 which say s , in effect, that the re is a 
-= n 
cri tic al velocity below which a particle is not able to 
produc the Cerenkov effect. In gener al, the in dex o f 
refract ion is a functi on o f wavelength. Howev er , to a 
first approxi mation, n is essentially wav e len gth in-
dep cn ent over a wide range for man y media . Hence this 
critical v e locity is equal to v . = nc  In m adin d ition , when 
the velocity o f the particle is very larg e ( s .-1), th e re is 
-
a 1  m 1a  ximum angle of emission g iven b y emax = cos (n) . To 
satisfy the condition O< __l_  < 1, n must remain greater 
- Sn -
than 1. The c ontinuous s pectrum which extends over a 
wide range of wavelengths is cut of f on the short wave 
side in the x - ray region, for n is then less than unity 
and equation (1) cann ot be satisfied . The long wav e cut -
off arises due to self absorption of the radiation in the 
medium by the pre sence of atomic and mol ecular absorption 
bands . Figure 1 has been drawn in one plane only wher as 
there is compl e t e symmetry about the axis of the par t icle 
as shown in Figure 2 . 
Finally, the expression for the spectral distribu tion 
1 
of the light is
dW -= (1 ( 3 ) 
dx 
where dW is the Cerenkov radiation energy loss per unit 
ax 
path, xis the total range of the partic le within the 
medium, e is the charge of the par ticle and A is the wave -
5 
2 Format i on of the Cer
enkov Cone 
Fig. 
Particle 
Light 
6 
leng th of the light . Since the intensity of ligh t of 
\vavelength .\ may be writt e n as W = N ? h ~ w~1e re N is t he 
p A p 
number of Cerenkov light pho tons and h is Planck 1 s con-
stant, the expression for the production of light in 
units of photons per unit path as derived by Frank and 
Tamm is g iven by: 
(1 (4) 
The rate of loss of energy du e to Cerenkov light produc-
tion over the entire spectrum amounts to about 0.1%3 of the 
energy loss by ionization for a relativistic particle, 
so some idea may be obtained o f the weakness of the radia-
tion . Unlike fluorescence, the spectrum is continuous 
extending from the ultra-violet to ?the infra-red; the in -
t ensity and spectral distribution being determined by 
the energy of the exciting radiation and the phys ical 
characteristics of the medium. Furthermore, it is in-
terest ing to note that t he radiation depends uniqu e ly 
on t he charge of the particle an d not on its mass as 
contrasted to, say, bremsstrahlun g whose radiation yield 
is very sensitive to the mass of the moving particle . 
Provided the energy of the charged particle exceeds the 
threshold for the Cerenkov effect in the medium under 
consideration , the form of the spectral distribution is 
theoretically independent of the particle energy . 
CHA PTER II 
CERENKOV RADIATION I N WATER MODERATED 
REACTORS 
A. Sourc e of Ce r enkov Radiation 
1 . Gene r a l 
The Cerenkov light intensity produced in a trans-
parent die lectric medium is de p endent upon the nature 
of the particl e s appearin g in the medium and upon its 
physical prop erties . In the experimental investigation 
describ ed herein, the Cerenkov light intensity f rom the 
core of a light-water mod e rat e d reactor has been investi-
gated under varying conditions of reactor operation. The 
index of refraction of light-water is approximately 4 3 as 
indicated b y Table I. Hence, only particles havin g a 
velocity greater than i c, (where c is the velocity of 
10 ' 
light, 3 x 10 cm per sec), are able to produ ce light 
by the Cerenkov effect. 
The kinetic energy of particles having such a velocit y 
as calculated from equation (2) is seen to be: 
260 kev for electrons 
475 Mev for protons 
960 Mev for deuterons 
2 Bev for alpha particles 
The three latter particles have energi es much too high to 
be of importance in reactors. On the contrary, there exists 
7 
8 
Table I - Refractive Index of Wat5r at 20?C For Various Wavelengths 
0 
Wavelength {A2 Refractive Index 
12560 1. 3210 
6708 1. 3308 
6563 1.3311 
6438 1. 3314 
5893 1. 3330 
5461 1 . 33Li-5 
5086 1. 3360 
4861 1. 3371 
L:.8 00 1. 3374 
Li-047 1 . 3428 
303Li- 1. 3581 
Temperature Coefficient of Index of Refraction: 
- 1 . 0 x 10 - 4 per ?C 
9 
in the reactor a lar ge numb er o f e lectrons havin g 
energies grea t er than or equ a l to 260 k ev . These fast 
e l e ctrons can be produc e d eith er directly as beta 
particles from radioactive nucle i or i ndirectly by gamma 
rays . 
2. Beta Radiation 
The constituent materials o f the University of 
Mary land reactor are essentially the water moderator, 
the uranium elements clad in alumin um , and the aluminum 
f uel element containers , experimental ports and t ank . 
The aluminum cladding of th e e lements stop, to a great 
ext ent, the beta particles emitted b y the fission pro ducts. 
Based on be ta ray spectra of the fission product s of 
U- 235, 13 , 23 it is conservat ively es timated that l ess than 
fiv e percent of the total number of beta particles pro -
duced per fission penetrate the aluminum cladding . On 
the other hand, b e ta particles emitted by the aluminum 
slow down in the water and are capable of producin g 
the Cerenkov effect. Al-27, under bombardment by n eu trons 
giv es rise to Al-28 which is rad ioactive and emits beta 
particles having a maximum energy of 2.86 Mev and gamma 
ray s of approximately 1 . 8 Mev . 6 The hal f - life of Al - 23 
is 2 .3 minutes and the b e ta particles are of sufficient 
en e r gy fo r producing light b y the Cerenkov effect. 
3 . Gamma Radiation 
Th e ma.i n sources o f?  t h e gamma ra d i. ati.o n 7 ' 8 ' 9 t h rou g h -
out the reactor include the following : 
10 
(a ) pr ompt f ission gamma rays 
(b) gamma r a ys f rom neutron cap ture in th e 
uran ium, cons t ruct i on ma t e rials and the 
mJd e rator 
( c ) f i ss ion p ro duct gamma r ays 
(d) gamma rays f r om the d i s int e gration of 
cap ture pro du c ts 
The fi r s t t wo s ourc es are p roport iona l t o the numb e r o f 
neu tron s p r esent in t he r eactor ; henc e a f unction of 
p ower l ev e l, whereas the l a tter t wo de pend upon the p owe r 
a nd hi s tory o f the r eacto r in a more comp l ex way . Gamma 
rays f rom in elast ic scatt e r ing in aluminum and u ran ium 
as well as n eutron capture in U- 238 and the graphite r e -
f l ecto r are not considered due to their relat i v ely low in-
tensities. 
The importanc e o f gamma r a dia tion, wi th r espect t o 
production o f ligh t by t he Ce r enk ov effect, depen ds 
e ssentially on the probab ility o f a gamma r ay producin g 
f ast e l e ctrons. Gamma rays produc e el e ctrons b y the 
. 10 11 
photo e l e ctric e ffect, Compton e f fe ct, and pair production ' 
but only tho se e l e ctrons hav in g an en e r g y g r eater ? than 
260 kev are conside r e d. Tab le II i llustrates t h e re lative 
importanc e of these proce s ses in wat e r. In the photo-
e lectric effect, the energy o f th e incident gamma ray 
photon is trans fe rred complet e ly to an orbital electron 
in an atom which is then e j ect e d with a kin e tic en e rgy 
11 
TABLE II 
Re lative Importance of Photo e l ectric, Co:npton, and Pair 
Absorption Coefficients in Water 12 
Total mass Photoelectric {~} 
Photon absorption Compton {"ft} and Pair (!J/) 
energy, co ef fie ient, 
Mev cm2 /gm % of total % of to t al 
0.10 0.171 98 . 8 1. 2 
0.20 0.137 99 .7 0.3 
0.30 0 .119 100 0 
0.40 0.106 100 0 
0.50 0. 09 66 100 0 
0.60 0. 089 6 100 0 
0.80 0.0786 100 0 
1.0 0.070 6 100 Pair 
1.5 0.0575 99.8 0.2 
2 . 0 0.0493 98 . 6 1. 4 
3 . 0 0.0396 97.2 2.8 
4.0 0.0339 94 . 7 5 . 3 
5.0 0.0301 92. 0 8 .0 
6.0 0.0 275 89 . 1 10.9 
8.0 0. 02L1.0 83.3 16 .7 
10.0 0.0 219 78 . 1 22 .9 
12 
Ek - h v - I, I bein g the ionization pot ential of the 
l ev el a t which t he e l e ctron is found, and v the 
f r equenc y of the incident gamna ray photon. For t he K 
electron level, t he ionization potent ial is approxi-
mately equal to RYZ2 (Z being the atomic nurnoe r and Ry 
the Rydberg constant which is e qual to 13.5 ev ) , e . g . 
the ionization potential f or aluminum and uranium is 
2 kev and 108 kev respe ctively . For the subsequ ent 
levels further out, the ionization potential becomes 
smal ler. A photoelectron, therefore, is a b l e to produce 
light by the Ce renkov effect if the energy of the incident 
photon is greater than hv =Ek+ I, (hv = 262 kev fo r 
aluminum). Examination of the cross-section curv in 
Figure 3 and Table II shows that gamma rays with ener gies 
g reater than or equal to 262 kev have a very small 
probability of producing electrons. As a rough appro xima-
ti.. on, 8 
Probability of photoelectric interaction ~ 
con st. x zn 
E3 
k 
where n varies from 3, for gamma rays of low energy, to 
5, for high energy rays. The photoelectric effect is 
important mostly at the lowe r energies for which the 
electrons are unable to produce light in the water by 
th e Cerenkov effect. 
In the pair production process, a gamma ray photon 
with energy in excess of 1.02 Mev may be annihilat e d 
Fig . 3 Mass Absorp0ior. Coeffic i ents for Wat er a s a Fur.ction 
of Photon Energy 
1 . 0 ----.. .......- ---------------------------,-----------, 
Wa ter 
E: 
t.J 
~ 
E: 
(_) ,,,,f:( = ? + ~.t" + o,;,.. 
------- 0 . 1 / ,,;? /J /J 
I 
.? 
r' 
Total = 
?rl 
u 
?-l 
c....; 
c....; 
0 
0 
0 ~ 
s::: 
0 
?rl 
.? 
o, 0 . 01 ~ 
H 
0..)   
,0 
<i:: /~:: 
(,] ~ 
cu 
~ /? I JP ~ 
0 . 001 ..__ _______ ...___._ _______. ...__ __. ...__ ___ _._ ________ __J 
0 . 01 0 . 1 1 10 100 
Photon Energy - Mev 
1--4 
w 
14 
with the subsequent formation of a positron - electron 
pair . Since the energy equivalent of the total mass 
of an electron and a pos itron is 1.02 Mev, this is the 
minimum energy necessa r y f or the production of the pair 
of particles. Any energy of the gamma rays in exces s of 
1.02 Mev appears as kinetic energy of the electron and 
positron. 
In water, positive or negative electrons having 
energies greater than 260 kev can produce light by the 
Cerenkov effect. Thus, the gamma rays which are ab le to 
produce these pairs should have an energy greater than or 
equal to 1.54 Mev. In general, it is possible to write8 
Probability of pair production ~ const. x z2 (E-1.02) 
which states that the extent of pair production increases 
with the atomic number of the absorber material and with 
increasing photon energy greater than 1.02 Mev. As seen 
from Figure 3 and Table II, the probability of pair pro-
duction for gamma rays in water is very weak for energies 
up to 6 Mev. Furthermore, the number of gamma rays avail-
able in the reactor with energies greater than 6 Mevis 
very small (see Figure 43), 
For the gamma energies present in thereactor the 
Compton effect is the most important since the Compton 
cross-section for water is dominant in comparison to 
the two preceding effects. In the Compton process the 
photon may be thought of as colliding with an electron 
15 
gy 
i de r ed free ( e . g . 
the bindin g ener
whic, is usually 
cons
 part of the ener
gy 
n ,
is n~g l ccted) . In th e co
ll i sio
n and 
oton is transfe rre
d to th e el e ctro
of the incid ent p
h
itial 
is scattered f rom 
it s in
at th~ same time 
the photon 
n scatt e rin g each
 electron may 
d ire ction . Since in Com
p to
e , its magnitude d
ep e nds on the 
fre
be conside red to 
b e 
8 
er. As a rough ap
proximation 
 absorb ' 
atomic numb e r of 
the
st . x -z ~ can
robability of Com
pton interaction E 
P
n e l ec -
 of a gamma ray ph
oton producin g a
The probability ec t 
 emitting light by
 th e Cerenkov eff
tron capable of
of the incident ga
mma ray and at 
 
depends on the en
ergy
rgy of the scatter
ed electron; 
 same time on the
 ene
the
 can produce an e
lect ron 
the minimum photon
 energy which
v light being 0.40
7 Mev.35 
g Cerenko
capable of emittin
dioactive decay o
f th e Al- 28 
beta rays from the
 ra
The 
re accompanied by 
a source o f 
and the fission p
roducts a
s e condary 
n called bremsstra
hlun g , which is 
g amma radiatio
leration of the be
ta 
m th e de ce
radiation resultin
g fro
 of the material 
ticles in the atom
ic electric field
par
ion . The amount o
f 
beta emiss
adjacent to the p
oint of 
g increases with 
the 
remsstrahlun
e n e rgy radiated a
s b
he electrons are 
 number of the ma
t e rial in wh ich t
atomic
n upper limit for 
bremsstrahlun g 
that a
b rought to rest so
 
that 
a reactor is obtai
ned by assuming 
production in uranium. 
ly stopped by the 
th e beta particles
 are complete
the upp e r limit 
on this assumption
, one f inds that 
Based 
16 
 
n o f bremsstrahlun
g energy is l ess
of t,1e con tribu t io
 released fr om f is
sion 
o tal gamma energy
than 15% o f t he t
13 idly 
ission . The per
centage falls rap
p r oducts pe r f
material has an e
ffective 
t o a bout 1% if the be
ta s topping 
13 Therefore, the effe
ct is 
Z of 13, e . g . alumin
um.
 
ffective Z of th e 
b e ta stopping
clearly negligible
 if the e
y the 
small . The total 
energy radiated b
mat e ria l i s 
l considerably hig
her 
cess is in genera
bremsstrahlung pr
o
t in the visible 
an that by the Ce
renkov process bu
th
 the bremsstrahlun
g is 
the contribution f
rom
reg ion  
l. 3 
tion
al Moreover, a
ny Cerenkov radia
significantly sm
y negligible, bein
g 
o duced by bremsst
rahlung i s clearl
p r
or contribu-
 a second order effec
t of an a lready min
only
t ion. 
CHAPTER III 
EXPERIMENTAL DESIGN 
14 
rief Descrie!_ion o
f the Reactor
A. B
tor, hereafter re f
er re d 
yland Reac
The University of
 Mar
reactor 
R, is a 10 kilowa
tt swimmin g pool 
to as th e UM
flected by g raphi
te . 
water and re
modera ted b y ordi
nary 
ed uranium (93.5 
he fue l is an allo
y of f ully-enrich
T m in 
remainder being U-
238) and aluminu
percent U-235, th
e 
ates . Each plate 
i s 
the form of flat, 
aluminum clad pl
 inches i s the 
ially a sandwich; 
the cente r 0.026
essent
 a layer of 
-aluminum alloy, 
the outer side is
uranium ide 
.027 inches thick 
bonde d to each s
aluminum cladding
 0
o purposes; it pr
e -
he cladding serves
 tw
o f the center . T g in the 
ation of the pool 
and air by sealin
v ents contamin
ents corrosion of 
 products and it p
rev
radioactive fissio
n
iments except the
 
anium by the wate
r. All the exper
the ur er measure-
ealing with spectr
ographic and filt
f inal series d n in 
.ducted on the orig
inal core as show
ments are con
nsists of 16 fuel l reactor core co
Figure 4. The or
ig ina
es 
ree 6 plate assemb
li , 
th
assemblies in a 4 
x 4 array; 
ies and one 9 plat
e assembly. The 
lve 10 plate assem
bl
twe  
odate the three co
ntrol rods
six plate assembl
ies accomm
fety rods and on e 
is 
hich two are boron
 carbide shim-sa
of w
od . Each f uel ele
ment 
tainless steel reg
ulating r
a s ounded 
d bottom and is su
rr
as sembly is open 
at the top an
17 
18 
Flc . 4 I nitlal R~Jc:or Core G ometry , #1 
f1?01.t fac e 
(l) (l) 
0 0 
crj crj 
'H 4--1 
.? .? 
Cf) ?n 
(l) lU 
(l) 
Lev 1 Saf ty Startup 
Cha mber Chamber 
Thermal Column 
O Fuel El mc1Jt 
~ Graphite Refl ector 
[[) Shim Saf ty Rod 
[[I R gulatlng Rud 
~ Neutron Sourc C..: 
19 
f aluminum which i
s 0.064 
e l ement container
 o
by a f uel 
ough the core by g up thr
i nches th ick . Wa
ter flowin
ch 
passes between the
 fuel plates whi
natural conv ectio
n 
ving the heat prod
uced 
art, remo
a re 0.182 inches 
ap
core loading on 
g operation. Fig
ure 5 shows the 
durin
 is conducted. T
wo 
ch the final expe
rimental s eries
wh i es 
perimental sample 
hol
pec ia l fuel eleme
nts containing ex
s
are provided as s
hown. 
on three vertical 
sides by 
The core is reflec
ted 
con-
blocks in fuel el
ement 
aluminum canned g
raphite 
side by the graph
ite thermal 
 fourth 
tainers and on th
e
in an aluminum gri
d plate 
 supported 
column. The core
 is
ater surrounding t
he reactor 
. The w
n ear the tank wal
l
f eet, 
the core to a dep
th of about 17.0 
which covers 
tor, coolant, and 
shield. 
reflec
serves as moderat
or, 
includes a heat ex
changer, 
The water circula
tion system 
pical value for th
e water 
lter. A ty
demineralizer and
 fi
rnhos. 
conductivity is 1
.60 micor
 graphite thermal
 
s include a
The experimental 
facilitie
ssing alongside th
e core, and 
n, a through tube 
pa
colum
s 6 and 7. 
two beam tubes as
 shown in Figure
Associated Electro
nic 
 and 
B. Detector, Det
ector Assemb ly
Equipment 
em and to 
r to simplify the 
measurement probl
In orde
n the intended stu
dy, it 
ity i
maintain a certai
n versatil
d from the whole 
referable to study
 the light emitte
seems p
20 
11': - F i.11al R1.. ac to1' C
, or- ?c - Gt:ometr.1 , // "? 
.? 
[/) 
cu 
(]) 
I I I L ~,;a r' l, Sta
C l 'tup i:..t ,. I ?? Cha :,1bc1? 
]i'1 l(:?1 E
? I Crl lLfll, 
[8J GraphLte R.:flc?cto1? 
[I] Shim Safety Rod 
[]] 
~ 
21 
FIGURE 6 
Vfi:RTICJ\L cnoss - SECTION OF Tlrn UNIVERSITY OF 
MARYLAND REACTOH 
coAITEOt. R't::70 
,A C TUATcJP.S 
I ,' 
CONTRO.& 
,eoo ExT. 
1 
11 ' 
r. ,; 
i 
? , 
I 
v 
" .. .? .,,  J,;;# I 
J i 
(p ._ ,:, .. I 
L ---- L- 1 ' ?1/,,,., ---
-- - 7 
-J 
- ------ ,?O ' ,,L,,, ? /? -- --
22 
FIG. 7 TOP VIEW OP TH,-: UT\!IVlm,SITY OF 
MARYLAND REA CTOH COR1?: 
23 
cor e . The interpretation o f the measu r e men ts carried out 
on the light p r odu c ed in the c or e indeed s eems comple x 
c:.i ecau se of t he abs orption and at t enuat ion o f th e light 
through the large de pth of wat e r and the n umerous r e -
flect i ons on th e aluminum wh ich comp o se s the st r uctur al 
components i n side t he t ank and the fu e l e l ements . Mor e -
ov e r , t his met h od does not a llow a simp le analys is o f the 
cont r ibution o f th e di f f erent radiation s on the emission 
o f t he light . Howev er, it do es not require ul tra -
sens it ive a ppa ratu s sinc e the light in tensity is quit e 
strong f or most measuremen ts . In addition, protect ion 
of personn e l f rom e ither gamma ray s or neutrons is not 
requ ired. The apparat us is easily mounted an d d is -
as s emble d and no problem a ri se s as to activation o f 
mat e rials. Finally, measurements made on the whole core 
a r e r elat ive ly in.dependent o f geome try and con trol rod 
con figuration. 
Shown in Figure 8 is the pho t omultiplier tub e wh ich 
i s mounte d ins i de a cylindrical housing containin g t h e 
v oltag e divider network. A 20 inch c y lindrical aluminum 
t ube , which fits over the photomultiplier and i s attached 
to the main housing serve s as a light collimator. Th e 
entire a s s embly consisting of photomultiplie r tu be, 
h ousing and collimator is sus pended at the top o f t he 
p ool d i rectly over the core b y me ans of a guide bar 
which i s clamped to the edg e o f the tank as il lustrat ed 
Y 
 PHOTOMULTIPLIER 
DSTECTOR ASSEMBL
FIG . 8
~ 
25 
 th  h otomultipl ier
 
 7. Wh 
 
en pr oper 
1y a d" S 
t edJU , e p
in Figure
ater in order 
to min i mize 
on tac t with t h
e w
is in optical 
c
ctor assembly 
. The l ocat i o
n of the dete
reflection l os
s es
y ma rking 
ries i s insured
 b
hroughout the 
experiment se
t e 
f t he guide ba
r. Dur ing t h
ct plac ement o
the tank f or e
xa  
e Cerenkov spe
c trum is
nal series of 
experiments th
fi ilters which p
r ovide 
erferenc e type
 f
observed throu
gh int
specific spect
ra l bands. 
ient means of 
isolating 
a c onv en
nce filters po
ssess narrow 
erfere
Transmi ss ion t
ype int  spectral 
ently transmit 
light of high
Pas s bands and
 consequ
ghly r efl ec t in
g 
er consists of
 two hi
ilt
purity. Each 
f
th an interpo s
i ng fi l m 
ially transmit
ting fi lms wi
bu t part e t wo 
terial. The s e
paration of th
ng ma
of non-ab sorbi osition of the
 pass 
 the wav e lengt
h p
nes
cover films de
termi
ch the f ilter e light whi
d and hence th
e color of th
ban top 
 in each case 
are mounte d a
 filters
will transmit.
 The tomultiplier 
ich fits snugly
 over the pho
of a metal shi
eld wh
he core a s in 
embly is mount
ed over t
and the entire
 ass
 measurements.
 
earlier h optically 
strates the par
ameters whic
Fi gure 9 illu
namely, the waveleng
th 
ence filters, terfer
characterize in s-
e pass band, the tra
n
osition, of the
 peak of th
p "- ' the pass band and the h
alf-
 the peak of
 
mittance , T, at re ssing 
width is conve
nient for exp
Width HW. The
 half-
a l wid th 
efined as the 
spectr
ilt er selectiv
ity. It is d
f  transm.ittance
 is 
band at the le
vel where the
of the pass 
26 
Fig . 9 Pass Band Characteri stics of 
Interference Fi l t ers 
60r -------~----.----r-- --r----
~ = Wa ve l ength of peak 
T = Transmittance of peak 
HW = Half- Width 
50 
40 T /2 
(I) 
C) 
s::: 
(iJ 
-I-) 30 
-I-) T 
-rl 
[; 
(/) HW 
s::: 
cu 
~ 
E--i 
~~ 
20 
10 
+200 + 00 
0 
- 00 -200 0 
wavelength - (A) 
27 
e h 1 r 1 peak tr.,. n 
smi ttance. 
on l I t 1c < stage 
 is a DuMon
t 6292, 10 
er
Tl photomultip
li
t  th o d e h
 av1?. n o a 
 d - on pho oca
0 
evice ~,11.?th 
a c1.?rcular en 
d visible reg
ion 
v 
t lies main
l y in the 
spec tral re
sponse tha h spectral
 
0 
0 
 500 A as sho
wn in t
A+
? 0 th ximum at 440its ma des are s u pp
lied 
wi . 15
 
10 The 10
 dyno
igure 
nse curve o
f F
ode l 40 -2 ) . respo M
 power supp
ly (RIDL, 
y a highly 
s t ab ilized output 
b  to full lo
ad, the 
ent increas
e from zero
 curr 0.0 1% and f o
r 
For a n 
supply varie
s l ess tha
er 
Voltage of 
the p ow t put 
95 to 125 vo
lts the ou
age from 
 o f line vo
lt
the oucput a c hange ion of 
0.01% . The t
ime variat
than g h 
chan ge s les
s 
day. Th e n
eed f or h i
lso a bout 0.0
1% per 
oto-
Voltag e is 
a
e gain o f a
 ph
 from the f
act that th
on arises ll voltage . regulati  overa
h a high po
wer of the
wit ill 
mult i pl i er 
varies ally operat e
d w
multiplier 
as norm
output of a
 10 stage 
The ge . Theref
ore, a 
p ower o f th
e volta
enth n 
Vary with t
h e t t e
oltage will 
produc e a 
e in ove ral
l v
on e Percent
 chang
he gain. 
Percent cha
nge in t etwork whic
h 
the voltage
 divider n
Figur e 11 s
hows 
ply volt age
. 
ed sup
 dyoode wit
h the desir  
Provide s e a
ch e
tely 75 volt
s per stag
xima
 is operate
d at a ppro en 
The tube  volts main ta
ined be twe
of 900
ve potentia
l 
With a nega
ti
ed between 
the 
ts is appli
e and groun
d; 150 vol
thod (900 ca
The operatin
g voltage 
 dynode. 
c athode and
 first such as to 
he photomul
tiplier is 
Vo lts) chos
en for t
ed throug h 
all 
o be record
signal larg
e enough t
Yi eld a eady- state 
and 
startup, stely 
ex:pe . tal phases, 
am ' 
n .. n
 
men
28 
Fig . 10 Photomultiplier Sp ectral Sensitivi ty 
~ Range of 
I - Maximum Value 
0 . 75 
.,.--.... 
._~__. , 
Cf) 
:>:, 0 . 50 
-P 
?rl 
:> 
?rl 
-P 
?rl 
(/) 
C: 
Q) 
Cf) 
Cl) 
:> 
?rl 
p 
Ctl 
,- 1 
Q) 
rr: 0 . 25 
2000 3000 4000 5000 6 000 7000 
0 
Wavelength - (A) 
29 
Fii::; . ll Photomult lpli er Bl eed r Network 
J_ 
--
RL 
Ru 
(Anod ) 
___ _J 
D- 10 
R 10 
--- D- 9 
R9 
r- -- D- 8 
Ra 
--- D-7 
R7 
--- D- 6 
R6 < 
~- -:- - D- 5 
Rs 
- -- D-4 
R4 
R 1 = 100k - -- D- 3 
R 2 - Rn = 51k 
R1 = 100k R3 5r D- 2 R2 
R1 r
------ D-1 
T D-14 (Phot ocathode ) 
-H . V . 
30 
sh1.-1 tdowr1 while st i ll main tain in g linearity b e t we en t h e 
inc i ~nt r a diation and th e photoe lectric current. Th e 
de t e ctor beg i ns to r espon d sati s f actorily at a p owe r 
lev e l o f approx i mately 100 watt s . The problem tha t 
a rises durin g th e experimental runs is that the b a ck -
g round light may b e as i n ten se as the Cerenkov radia -
t i on . It is obviously desirable to cut room light ing 
to a minimum during all experimental phases. There -
f ore , all operations are condu cte d at night with a l l 
r o om lighting extinguished. Fi gure 12 is a t ypical 
characterist ic curve for the DuMont 629 2 photomultip l i e r 
r e lating the current amplification to the interstage 
15 
voltage . The output signal across the load r esis tor, 
RL' is fed to one of two channels of a Mark II Brush 
recorder having an input impedanc e of 5 megohms and a 
ma x imum sensitivity of 10 millivolts. The a rran gement 
o f these components is shown in the block diagram of 
Figure 13. A special output connector on th e lin ear power 
level channel of the reactor control console permits 
monitorin g o f the reactor powe r level when conn ected to 
the second channe l o f the Brush r e corder . The signal 
r e ceived by th e linear p ower level channel is derived 
fr om a neutron sensitive ion ization chamber l ocated ov e r 
th e therma l column b ehind the reactor core. This chamb e r 
produces a signal whos e intens ity is proportional to the 
power of the reactor. 
3 1 
. Fig . 12 Average Photomultip lier Characteristic 
0 
??/ 
? 
ctl 
C) 
?rl 
rH DuMon t 6292 
?rl 
rl 
0. 
F. 
,:; 
p 
( ' 
iv 
~ 1& 
,=:; 
0 
Voltage between cathode a~d 
dynode #1 = 2 X volta ge 
per stage 
2 
10 
25 75 125 175 
?voltage p e r Stage - Vol t s 
F2-_; . L -; Srst:.::::-:-: 31 '-'c l?: I) _:_ a t:;~?a::! 
_____ .. 
. Ph be~ -I -
DuMont 6292 
Power Supply 
RIDL 140-2 
1'1 Dual Channel 
Linear Recorder 
Brush, Mark II 
Linear Power 112 
Recorder 
L&N Model H 
Power Supply 
Tullamore 
Vacuum Tube 
Iron Chamber 1 Electrometer 
Westinghouse Tullamore !!5 
WL-6377 
w 
N 
33 
As a test sourc2, a con1.1ercial panelescent l amp rnanu -
factured 0y Sylva ?a is coupe to the detect or hous i n u so 
0 
as to form a completely ligl t - tig - asserno l y . In the pro -
c edure for measuring the s i g, l - to - 1oise ratioj the voltage 
across the photo 1 ltipl i is f irst set at 900 volts and 
t he dark current signal is me sued . The panelescent lamp 
is then turned on ad allow o st jil i ze for one minute 
before r e cordin g th e i gna l . 1e r tio of signals with and 
Without the lamp yiel s thE:: es r e 3ignal-to-noise r atio. 
This procedure is carried ou imm e iately b efore an d fol low-
in g an experimental run i ore o i.nsure t hat signi fican t 
changes in photom il iplier cl r c er i.stics have not t aken 
Plac e durin g the exper i me .t or et e en succeeding exper i -
men ts. Illustrat ed i 1 Fig 1r 14 is ch e spectral ener gy 
distributionl6 of a t yp ical Sylvania panelescent lamp. 
The spec tral emission curve is se en t o be continuous wi th 
0 
it s maximum value at a b out 5100 A . In order to ach i eve a 
Signal approximately equal to th obtained during an 
exper i mental run without c cngi gt e detector supply volt -
age, it is necess ary to ma k he la1p . Maintenanc e o f light 
0 utput of the panelesc nt la p unc er normal operating 
cond 100 P or the first 100 hours itions is rated at r c ent 
op rati g t i me of the lamp is 
o f bu rning time . Si ce t e 
Sign ? f ? t hi? s number , no changes are expected 
l. 1.cantly less than 
and 1 j_ 1 nsity of th e light source. non e are obs e r ved in t 7 
34 
ig . 14 Spectral Ener gy Di s tributio
n 
F
8 f ?7p ic2 l Sylvania Pane l e sc en t 
L a11'tp .::; a t oO Cp 3 . 
~ 
..? 
?,-/ ,--
!,') OU 
...... 
Q) 
..? 
,'-< 
H 
Q) 
> 
?rl 
..? 4 0 
(\j 
rl 
!J) 
0:: 
20 
r 
5U0C 6000 7000 
0 
?11 a -, ?. ~- '::::,. ; c: :1 - ( A ) 
CHAPTER IV 
SPECTROGRAPHIC STUDY OF THE LIGHT 
The object o f this study is to qualitatively determine 
the relative spectral distribution o f the Cerenkov light 
as seen t hrou gh approximately 16 fee t of water and to 
compare this r esul t with calculations in Appendix A. 
For a quick identifi cation by comparison spectra a 
quartz mercury arc is a u seful source because it f urnishes 
a limited number of i n t ense lines we ll distributed 
throughout the visib l e an d ultra-viole t region s 0e tween 
0 0 
23 00 A and 6300 A as seen in Table III. The measuring 
dev ice is a small Hilger quar tz spectrograph shown in 
0 
F i gure 15 with a spectral ran g e between 1850 A and 
0 
80 00 A. A unilaterally adju stab le slit with a calibrated 
vernier allows the slit width to be varied over a wide 
range . The length of the slit can be varied by means of 
a reducing wedge. The plateholder slide is operated b y a 
rack and pinion motion that rai ses or l owers the plate-
holder carrier over a range of 6 .5 cm . The plat e size 
u s ed for this spectrograph is 4 - 1/4 x 3 - 1/4 inch e s. 
The plateholder carrier mounting is hinged at the center 
so that it may be turned throu gh a small angle ao out a 
v ertical axis . Actual settings are read by counting 
th e number of complete revolu ions of the tilt screw 
f rom the minimum tilt position. 
Prior to any measu rement of the Ce r enkov spectrum, 
35 
36 
TABLE III 
Group s o f Mercury Lines Useful fo r Wavelength 
Identi ficat ion17 
0 Approxima t e 
Group Color Wave l en g ths ( A) Intens i t y 
l Re d 6234 10 
6152 20 
2 Ye llow 5790 50 
5770 50 
3 Gr e en Sl:. 61 100 
Li- Blu e L,359 - t'.i-3t\8 20 
5 Viol e t L,07 8 8 
L:.047 10 
6 Ultra v i ol e t 3663 - 3654 - 3650 70 
7 Ul traviole t 33L,2 10 
8 Ultraviole t 3132 - 3126 40 
9 Ultra v i ole t 3026 - 302 2 30 
10 Ultraviole t 2967 10 
11 Ul traviole t 2893 10 
12 Ultraviol e t 28 0L, 20 
13 Ultravio let 2753 10 
14 Ultraviole t 2652 8 
15 Ult r aviolet 2537 30 
16 Ult raviolet 2L~82 5 
17 Ul trav io let 2399 - 23 78 3 
V 
37 
38 
a ser i es of tes t spectra f or the mercury arc are photo-
g raphed correspondin g t o variation s in slit width , 
coll i mator se ttin g and tilt. Slit openin g s vary f rom 
ab ou t 100 microns to full clo sure. During these ex -
p o sure s the full length of the slit is il l um i nat e d . 
The nominal optimum settings finally chos en which 
g ive the sharpest line images throughout the entire 
ran ge are : 
Slit setting: 8 
Focus of coll imat in g lens: 9 
Tilt setting : - 7 . 5 (-22.5 is the 
?arbitrary value de -
noting minimum tilt 
position) 
Photographic plate 
exposure time: 3 sec onds 
The foregoing measurements are performed using Eastman 
Kodak , Type -l 03 a- 0 , medium contrast photo h 1g 8r  ap  i? c p-lat es 
O 0 
having a s ensitivity range betwe en 2000 A and 5500 A as 
shown i n Figure 16. Use of an emulsion of medium con -
trast g ives a response which differentiates b etween weak 
and strong spectrum lin e s. 
Measurement of the Cerenkov spectrum is performed 
by posit ioning the spectrograph on a support bar so that 
the collimator barrel looks directly down at the glory hole 
in the center of the r eactor core (core con f i guration #2) . 
Although spectrograms are taken while the reactor is at ful l 
power (10 kw), the light emitted from the core is 
relat ively weak as compared t o the mercury arc. 
~ . C:?:.:' - -~ -L _ , _--; a- -? i 
H'" .C.), !_), -, ,-<~- "\'"aI ~7  s --?..., : -- - 2'-- -~L- -'. - '-~--.-;;  ~ ( r ,_() 1C..d-: ,._) ~) Ct,~~\)~ Cop i C ::-1
.l. -
Density = 0 . 6 a bove grcss fog 
} 
~-: 
~) 
, __J 
> 
-- -l 
~ 
?.-,l  
i/.!))  1 . ,J 
(,.,' ) 
1----4 
0 . 0 
6000 
000 000 000 
soou 
Wa velen~ t h - (K ) 
w 
ID 
40 
Consequently, thre e exposures fo r 2, 5, and 20 minutes 
a r e I, adc and the exposure f i nal ly chos en to obtain 
a density permittin g a correct interpretation is 20 
minutes . All exposu res are taken during t he fi rst 
30 minutes at full power. 
The mercury arc spectrum and the Cerenkov spec rum 
are photographed close together on the same plate in 
order to minimize lateral di splac ement of the plate . 
Af t e r process ing, the plate is moun ted on a Le eds an d 
No rthrup recording densitometer and s canned. The re -
corded trace of the spectrogram r epresents the dens ity 
of blackening of the spectroscopic plate as a function 
of wavelength. Known lines of the mercury arc sp e ctrum 
are identified at intervals ac ross the spectrogram. 
This al lows one to plot a di s persion curve for the 
photographic plate as shown in Figure 17, e.g. known 
wavelengths of the mercury arc spectrum vs. the number 
of chart divisions from the beginning o f the recorded 
trace corresponding to the edge of the photographic 
plate. Applying the information in Figure 17 to the 
recorded trace of the Cerenkov spectrum together with a 
correction for the spectral sen sitivity of the plate, 
results in the Cerenkov spectral distribut ion as shown 
in Figure 18. As expected the measured curve reveals 
the existence of a continuous spectrum with no line 
structure or bands of absorption. A comparison between 
the measured curve (#1) and the calculated curve (#2) 
l~~__; . _.._{ ivI~:?c:.~2.?'"'. ~.\!?c S1-'2c 4 __, 2. ;~~.:: Cc.J..il'1?a.t ~\._ ? Cl..2.? 
60cc 
5000 
O._<_i:_;. . 
I 
..c 
.? 4000 
bl) 
h 
(1) 
rl 
(1) 
> 
co 
~ 
3000 
2000 
0 40 80 120 160 200 240 
umbe r of Chart Di visi ons from Plat e Edge 
~ 
~ 
42 
Flc; . 18 Cerenkov Sp ec tr ?a l Dlst1?loutlo1. 
l . ' 
0 
-
I I I\. max - 3960A 0 
I - - - I\. - 11 ~IOOA max -
I I Reactor operatin 
I time, T = 20 min . 
/I' 
? I _, I Eff cct lve wat er 
I ~ d 'Pth , X = 16 ft . 
I 
I I J 
I 
I I I I 
' /, ~ I I I \ 
; i 
! 
I I \ 
., I 
_':J 
' I I \ # 2 Ca le . 
,r; 
I I / \ #1 Meas . 
() . 2:,; I I I )( 
I I \ 
I I \ 
I I "' 
/ I I 
?vu 1 -;o ), . _// ( 1(1 I 500t) 0000 7000 
0 
:?;~ ,. ~; -- (A) 
43 
in Figure 18 f or an operating tie of 20 minutes shows 
f air agreement if one considers the assumptions and 
possible experimental errors, namely , lack of da ta and 
significant variations in absorption coefficients f or 
dis tilled water throughout the ent ire spectral reg ion 
und e r consideration and more particularly the region 
0 
below 4000 A. Furthermore , the presenc e o f dissolve d 
salts or o f organic matter in water affect s the 
transmission so that it is not safe to assume a 
value for the absorption coefficient of any given 
sample of water at any wavelength. The calculated 
s pectral distribution assumes the Cerenkov source t o 
be located 16 feet below the pool surface but because 
the Cerenkov source is really an extended one, the 
dis tance from source to detector is poorly defined 
and leads to an uncertainty. Low values are also 
expected in the distribution because o f the calcu-
lation method used in this report, e.g. no account 
has been taken of the scattered photons after the 
fi rst Compton collision. This is compensated to some 
extent, however, by neglecting to account for any 
self - absorption of the gamma radiation. Finally, the 
Ce renkov spectral distribution and intensity is changing 
with time which means that the effective exposure time 
is lengthened. However, negligib le changes in the 
spectral distribution are expected for the exposure 
time u sed. 
CHAPTE V 
ANALYSIS OF THE LIGHT I NTENSITY AS A FUNCTION 
OF REACTOR POWER 
A. Introduction 
To ana l yze the gamma emission rates of a reactor 
capable of producing Cerenkov radiation, it is n ec es s ary 
to examine the reactor operation cycles. Reactor opera-
tion may be divided into four phases with respect to 
power as shown in Figure 19. Phase one i s the reactor 
state before startup where the power .of the reactor is 
extremely low and is attributed mainly to the source 
multiplication and the delayed neutrons from previous 
operations. Phase two is the r eactor startup period 
wh e rein the reactor rises to full power criticality . 
Thi s is accomplished by adding reactivity to the 
system (e . g. removal of the shim and regulating rods). 
The interval designated as phase three is a period of 
constant power. Finally, phase four is the reactor 
shutdown period wherein the shim and regulatlng rods 
, 
are inserted back into the core . The power curve f or 
this latter interval is exponent ial in shape due to 
the gradual release of delayed neutrons . If delayed 
neutrons were not present, the power would drop as 
a function of rod movement to effectively zero power. 
During all phases fission products are being 
44 
45 
~ 
? I 
I 
') 
, -, 
Ir, 
,;:! 
?.d 
,~I 
) 
} 
rL, 
,-,, 
I' 
- ) I 
;-'---, I .- , 
I 
,? I 
) 
p::; 
, -, -- -- -- --
-- ___________________________________ _, 
..1 MOd 
46 
pro"-: ced at a rate which is proportional to the power 
or the average neutron flux. The t otal number of 
fissions in a reactor is 0I:fV where 0 is the average 
h ermal neutron flux, I:f is the macroscopic fission 
cross - section and V is the core volume . Each fission 
is a ccompanied by a number o f prompt gamma s and also 
a number of fission products . The fis sion product s 
late r decay and emit gammas in accord with each 
product 's individual de c ay scheme. Therefore, any 
time a finite p owe r level i s observed in a r eactor , 
fission products are being produced. If a steady 
power is reached rapidly and maintained for a c on-
siderable time compared to st_artup and shut down 
q uickly, the time o f f i ss ion product product ion may 
be safe ly approximated to be the time of full power 
operat ion o r phase three. 
The f ission product gamma production will have a 
ouildup, saturation (provide d the reactor h as been 
operated for sufficient time) and decay characterist ic s 
similar to isotope activation oy neutron capture. By 
measuring the response of the photomultiplier as a 
f unction of time, it is poss iule , in principle , to 
determine the relative fission product gamma ray pro-
duc t ion. If one assumes that the accumulation o f 
f i ss ion products during rise to f ull power is negl i-
gible, the fission product gamma buildup during ste ady 
state reactor ope ration may b e approximated by normalizing 
47 
cu r ves of the Cerenkov light signal at the point fu ll 
s t eady power is achiev ed . Similarly, the gamma dec ay 
after shutdown may be approximated oy normalizing the 
Ce r enkov light signal at the point where the reactor 
is s hut down by rapid in ser tion of the control rods . 
Two factors which complicate the analysis, namely , the 
act i vation of the aluminum and its su b s equ ent decay 
emitt ing both betas and gammas capable o f producing 
Ce renkov light, and the delayed neutron contribution 
to the light signal immediately following shutdown, 
are cons ider e d in further detail in the analysis o f 
the data . 
B. Signal Re sponse 
1. Theoretical 
Amon g the gamma rays emitted by the reactor, it is 
convenient to classify them into two categories: 
(a) those which are emitted instantaneously and 
whose number is proportional t o the power of the reactor 
(b) those which are emitted in the course o f radio-
active product decay and whose number depends upon the 
integrated flux received by these products and the ir 
decay rates. 
Referring to group (a), this is the case of the gamma 
r ays emitted by the fissioning of t he uranium, the 
inelastic collisions, and the radia t i ve captures. They 
di sappear when the reactor i s shutdown. For group (b), 
t h ese are the gamma rays emitted by the fission products 
48 
and by induced radioactivity in the core and structural 
1 ate rials and which ?have half lives rang ing from seconds 
t o years . 
For the subsequent analysis , it is convenient to 
efine the f ollowing terms: 
V - the elec trical signal produced by the compen-
0 
sated ion chamber 
Vt - the electrical signal produced by the photo-
mu ltiplier tube detecting the light emitted in the wate r 
in and around the reactor core . 
VP - the electrical signal proportional to the number 
of prompt fission gamma rays produced in he reactor and 
resulting in the fast electrons emitting the Cerenkov 
light in the water 
V ? - the electrical signal proportional to the numoer 
C 
of gamma rays produced by t he radiative capture of the 
n eutrons by the aluminum cladding, structural materials 
and the water moderator and causing the electrons to emit 
the Ce renkov light in the water 
Al 
Va - the electrical signal proportional to the numb er 
of beta particles and gamma rays created through the acti-
vation of the aluminum cladding and structural mat e rials 
Vf - the electrical signal proportional to the numue r 
o f g amma rays emitted in the process of fission product 
dec a y 
Al 
Vt - the sum of four terms: Vt = VP+ Ve+ Va + Vf 
49 
Du. ing an increase in t he reactor power, the terms 
Ve increase expon entially wi t h the same p e r i od 
as cha t correspondi ng to th e increase in th2rrnal neutron 
flux dens ity t h rou ghout the r e actor . The signal v!1 
varies in a less apparent manne r. Unde r the influ enc e 
of the n eutron flu x irradiating the c ladding and structural 
materials, the aluminum is activated and d isintegrates by 
emitting beta part ic les hav ing a max imum energy o f 2.86 
Mev and gamma rays of 1.80 Mev which are able to pr oduc e 
fast e lectrons . 
Bec ause of the complexity of the signal Vf, the 
following analysis is performed by assuming that the 
contribution of Vf  to the total signal, Vt is negligible 
initially. Such an .assumption is justified becaus e it 
is found emp irically that the fission product buildup is 
relatively slow. 
If one assumes as a f irs t approximation that each 
disintegration of the activated aluminum yields a beta 
particle capable of producing light, then 
(5) 
where N = the number of Al-28 nuclei 
ta= macroscopic cross - section of Al-27 for thermal 
neutrons 
\ = decay constant of Al -28 
? = thermal neutron flux 
V = volume of aluminum in the core 
so 
Hence 
( 6) 
Th e n umber of beta particles created per second i s 
e qua l t o 
(7) 
wh e r e N ' = AN . During an excursion o f the r eactor , t he 
eutron f lux varies a ccording t o the expression 
(8) 
? b e ing the initial valu e of the flux and a= -1 0 , where (~ 
u; is the r eactor period define d as the time r equired for 
the neutron f lux t o change by a factor e = 2.718 . The 
expression in equation (7) t hen becomes 
N' = VL A0 e-AtJ (ec a+ A)tdt a o (9) 
Int egrating equation (9) yields the following 
N ' = v~6  Ad ee  a - A
(a
t + - A- )t - ] 
Po [ a+ t + c 1 (10) 
The integration constant c1 is evaluated by i mposing the 
initial condition at t = 0, namely 
N' = VLa  0o  ( 11) 
., 
51 
enc e 
a 
>-.( a + >-.) ( 12) 
Substituting the expression for c1 into equation (10) 
a nd simplifyi ng g ives 
(13) 
For luminum A = 4.95 x 10 - J sec- l and th e above 
expres sion rapidly approaches 
(14) 
Therefore 
. a t 
Ke ? (15) 
where le is a proportionality constant. For a reactor 
excursion on a period: 
Vt(t) = Keat ( 16) 
The signal produced by the photomultiplier and con-
sequently the number of photons produced by the 
Cerenkov effect increases exponentially as a function of 
time with a period equal to that of the reactor. The 
s ignal produced by an ionization chamber indicates 
thermal neutrons just as the photomultiplier detects the 
light intensity produced by the Cerenkov effect. I n 
both cases the signal is exponential and has the same 
I 
1 52 
period . 
When the r e actor i s stabilized at a power P, the 
0 
term AV la   rapidly arrives at a state of equilibr ium while 
the signal Vf due to the fission product gamma rays 
continues to increase slowly as a function o f the inte grated 
f lux received by the uranium fuel. The term Vt, conse-
quently , depends upon the previous history of the reactor 
so t hat Vt is not strictly proportional to the power o f 
the reactor. The proportionality between the signa l Vt 
and the power of the reactor is, therefore, valid only 
during an excursion of the r eactor. In effect, the number 
of fission product gamma rays does not appreciably in-
crease i n time during a rise in power, whereas, on the 
contrary, the number of instantaneous gamma rays increas e 
exponentially. If, after operat ion at a stable powe r 
P for a time t , the reactor
0   is fir0 st shut down for a 
time interval t 1 - t and then the power is 0 i ncreased 
to 2P , the value of the signal Vt de
0 pends upon the time 
i nterval t 1 - t o> corresponding to a decrease in fission 
products formed Juring the previous run, as shown in 
Figure 20. 
When the control rods are dropped, the power decreases 
very rapidly from the v a lue P , correspon
0 ding to a state 
of stable p ower, to a considerably lower power level 
associated with the delayed neutrons. The terms VP and 
v which are proportional to the number of insta
C n taneous 
gamma rays present in the reactor decreases rapidly during 
-, E,. 
g::_ -'- J ~ ,J t.r .... ~ -~ ... : _ l. t., ~ ~- .... _ . li l _ ? .... - - .:L. ?. . EL R
 :~ 
l\'~? ::i 3'.: ~~?-, l:. Rec.etc~? Po~:? 
2Po  ?- - - --
~ 
(l.J 
3: 
0 
0... 
Po~----
I 
I 
Pr ,- - - f- -, 
I 
t o t 1 
Time 
V, 
w 
54 
the time corresponding to t he dro p o f the ro ds. Th e 
s u bsequent de creas e in ga mma ray intensity is mu ch more 
low . This decre ase c orre spon ds to the de cay o f the 
f iss ion product gamma rays, the de cay of the de laye d 
neut r on precursors and the decay activities o f t he 
l u rninum wh ich are formed during t he operation at 
power P ? vAl d e
a c reases exponenti0 ally as a function 
o f time with a period e qual to the half-life of Al-28 
(17) 
where k' is a proport i onality constant. The signal Vf 
corresponding to the fission product gamma decay and 
the de cay of the delayed neutron precursors decreases 
in a more complex manner and will be treated in sub-
sequ en t paragraphs on page 81. 
2. Exp e rimental 
a. Transient - Chapter III describes the experi-
mental setup for the transient tests at the UMR. The 
g eneral procedure is to bring the reactor to criticality 
at a lower power level. This level is usually six to 
sev en decades below full power. The regulating rod is 
ten removed a fixed amount and the reactor is allowed 
to rise to full power (10 kw) at which point the reactor 
is instantaneously shutdown by initiating a manual 
scram . This procedure is repeated each time by with-
drawing the regulating rod somewha~ further each time 
I 
i 
55 
until the reactor p eriod b e c ome s undesirably s hort, 
s y 20 secon ds . Each time t he period is 00served on 
the console p e riod r e corde r and also by timin g the 
movement of the Brush recorder galvanometer de f lec-
t ion ove r a d e cade. Examination of the experimental 
curves f or variations of the s i gnal as a function 
of time justifies equation (1 6). In the course of 
a d i v e r genc e , the curves of Figures 21 through 26 
s how that signal Vt follows the neutron signal 
I recorded by the ion chamber for periods as short as 20 s e conds. For longer per iods the effects of 
Al-28 activation and fission product buildup is 
evident from the steeper slop e of the curves. The 
data a re summarized in Table IV. 
These results are augmented by a series of tests per-
f orme d in a General Atomics TRIGA Mark F reactor designed 
for pulsing. Paramete rs which are measured to determine 
the pulse characteris t ics are the peak power and the 
pul s e width at half maximum. The transient behavior 
of h e reactor is monitored using the same photomultiplier 
tube a s in previous tests on the UMR. The Cerenkov 
d etector is positioned about 18 inches above the surface 
of the pool overlooking the core. A collimator, 
attached to the photomultiplier assembly to minimize 
background light, extends down to within 2 inches of the 
pool surface. The first step in performing the transient 
56 
f<' i , ; . c_! ~ Cc l'."'enkov Signal vs Neutron
 Power 
L v l 
T-c:s t a 
Sl o p e = 1. 00 
10 
t?eutron Power Level - Wa tt s 
57 
Fl c; . 22 Ce renkov Slgnal vs N utron Power 
Le v 1 
Tes t b 
l . 'J 
; ) 
' ) 
r? -i 
(_) 
?-
-{ 
?J 
.-,n 
? r I 
U) 
,__) 
'' 
~; 
lJ Sl o p e = 1. 04 
r-l 
LI 
0 
0 . 1 
Ne utron Powe r Lev e l - Watt s 
58 
Fig . 23 Cerenkov Sicnal vs Neutro11. Povkr 
Level 
Test c 
r,') J_ . o 
p 
() 
;..., 
,; 
eel 
I 
--1 
r_/) 
0 
(]) 
::.. -
G) Slop e - 1.06 
0 . 1 
. 01 ~~------------~-------------'4 
10 10 l rJ 
Neutron Power Level - Wat tJ 
59 
Fl : . 24 Ceru1kov Sl [;i1al v ..: , ;;<..:utrori Po w.---?1? 
Level 
l(J 
,, 1 . 0 
p 
--i 
' J 
I 
,u 
? ,'. l 
U) 
I _J 
:J Slope = 1.07
'  . 
,1) 
0 . 1 
JJ I L..,..----------------'--;:;--------
3 - --------' lfJ 1 0 4 1 0
l!1.. utr ?on Po1Nc1? Level - Watt, ::; 
,o 
Fig . 25 Ce 1?e11kuv Signal vs Neutron Power 
Level 
lU 
Tes t e 
1 . 0 , 
Cf) 
rl 
0 
:.> 
rl 
cu 
s:; 
bf) 
?d 
(/) 
;._.. 
0 
~ 
~: 
(l) Slope -- 1.09 
~ 
lj) 
0 
0 .1 
.011---,..------------.....3. 1~------------' 10 10 104 
Neutron Powe r Level - Watts 
j 
61 
Fig . 26 Cerenkov Signal vs Neutron Power 
Level 
, I 
- J 
Test f 
1 . 0 
(') 
) J 
rl 
") 
. 
~. ~ 
: 
.. l 
'-) 
j 
-
.) 
_.., Slope = 1 .11 
r ) 
() l 
.Cl~-------------~3~ ---------------~ lC t 10 1u~ 
Neutron Powe r Leve l - Watt s 
62 
TABLE IV 
Cerenkov Transient Data 
Tes t w(sec) p = Po % Diff . 
0 
a . 20 1.00 10 0 
b. 29 1.04 10.9 9.0 
C ? 34.8 1.06 11.5 15.0 
d. 44.5 1.07 11. 7 17. 
e. 70 1.09 12.3 23.0 
f . 110 1.11 12.8 28.0 
P = apparent power from Cerenkov 
detector 
P = 10 kw - indicated by linear 
0 level channel 
w = Measured period averaged over 
upper two decades (100 w - 10 kw) 
from linear level neutron channel 
o = Slope of curves in Figures 21 
through 26 
63 
tests i s to c alibrate t e Cerenk ov detector. Th e ioniza-
t i o chamber had b een previous ly calibrated at a known 
ste dy p ower by measuring the chamber cur r en t and obt a in-
in g a calibration constant in amperes pe r megawa tt (MW) 
a n d l in e arly e xtrapolating to higher powers. For the 
trans i ent t e sts a chamber signal lead is connected 
throu gh a galvanometer ampli f ier to a Minneapolis 
o eywell Model 1012 fast r e corder which contains a 
e iland Type Ml650 galvanometer. The ma ximum peak to 
peak deflection of the galvanometer is 8 inches with +2% 
lin e ari t y. The recorder trac e is adjusted by means o f 
t he ga in control on the galvanometer amplifier so as to 
o tin a maximum deflection of 4 inches at 1200 'MW . The 
Ce r enkov detector is connected to the recorder in a 
similar manner through another channel on the galvano-
meter amplifier and the trace again adjusted for a 
maximum deflection of 4 inches at 1200 MW. Because 
of the strong light intensity at 1200 'MW the photo-
multiplier is masked. The amount of masking is optimized 
with the supply voltage to ? the photomultiplier so as to 
o btain a strong signal and still prevent damaging the 
d e t e ctor . Final adjustments result in a maximum signal 
of 2.8 volts at 1200 MW . 
The measurement of width at half - ma ximum is straight 
forward and one of the most accurately measurable parameters . 
I t can be used as a substitute for the period since the 
r elat i on between period and half width is linear, e.g. 
64 
t: 1.2 Fuchs the ore tic a l model r lat ionsh ip between Z' and 
W1 
. . by l9 
12 1. s g i v en 
w112 = 3.5 l (18) 
Te ernp 1. .r1. .ca 1 re 1 at1?. ons h.1 .p i. s 19 
( 19) 
I g e neral, it is more difficult to measure? than w
112 
f r o a complete pulse trace. In order to obtain good 
p e riod data, it is necessary to increase the recorder 
s ensitivity so as to obtain a larger spread durin g the 
initial e x ponential power ris e during a pulse. This 
would be at the expense of Pmax and w1; 2 data since the 
recorder would go off scale. Since w1; 2 is more readily 
measur e d, a plot of Pm ax vs lmay be obtained by meas
ur -
ing the half width w112 and using the relation 
Comparison of the pulse shape as produced 
by the photomultiplier with that produc ed by an uncompensated 
ion chamber shows very good a greement as is evident 
f rom the data given in Figure s 27 and 28. The data in 
Figure 27 represents Cerenkov detector and ion chamber 
outputs recorded simultaneously on a Minneapolis Honeywell 
Visicorder for the same pulse. Within the limits of 
accuracy of these measurements n o differ ence exists be-
tween the two detector systems. In the case of the ion 
c h amber, the question arises as to whether the linear 
65 
Fig . 27 Peak Power vs Pul se Half Wid th 
4
10 r--------------,--------------
\ 
\ 
Cerenkov 
0 0 0 
- - Detec tor 
,.. _.,. -+ I on Chamber 
\ A - C.-6 DOFL data 
~ 
cu 
(]J 
P-... 
1J.__ _- .--__________ ._ ________ . ___ _ 
1 10 let 
PuJ se Width at Half Maximum (w1;2 ) - ms ec 
66 
Fig . 28 Pak Power vs Prompt Period 
4 
10 
\ 
\ 0 - - 0 - 0 Cerenkov de t ecto 
\ + - + - + I on Cha mb r 
t:. - t:,. - 1:,, D0FL data 
3 \ 
-------:x: 
(1j 
E: 
..___. 3 -10 
(]) 
3 
0 
0... 
~ 
'1.) 
0... 
10 1-___________- l-_ _;___ ________ _J 
1 10 10
2 
Prompt Pe riod (t) - msec . 
67 
I extrapo l ation of th e steady state calibration c onstant is strictly true. More specifical l y, a change i n t h e 
! 
i neutron to gamma ratio fr om steady s tate to pulse opera -
! tion could affect the measu red peak power. Furthe rmore , 
high gamma and neut r on radiat ion fi e ld s e xp erienc e d b y 
an ion chamber an d i ts connecting cable s may c aus e 
appreciable signa l pickup due t o momentary breakdown of 
cable insu lator . The se e f fects , if pres ent, a ppear to 
b e neg lig i b l e b a sed on the data a bove. The agreement 
b etween t he da ta of the two sys tems is also evid ence 
in favor o f t he validity of equation ( 16 ) f o r fast 
trans i ent s . 
b. Steady State 
A TRI GA test is perf ormed at a steady state 
powe r level of 50 kw to dete rmine the buildup f r a ction 
o f the ligh t signal. For illustrative purpos e s the 
buildup f rac tion will be defined in the following 
manner. Referring to Figure 29, t he buildup fraction, 
B' is g ive n by: 
%B = b-a (20) 
b 
Aft e r f our minutes operation the buildup f raction in 
th e TRIGA reached lJ.4% which is comparable to the value 
of 14.5% f rom the UMR core. The? UMR valu e should be 
s ome~ha t higher since the startup time f r om sourc e 
l e v e l to powe r in the TRIGA and UMR is - 25 0 s e con d s 
and '"'"'1000 secon d s r e spe ctive ly. There f ore , some f ission 
' 
177,1 ? - I -,~?_    , ., L-? .:.. _t r?ti. -~.:._ \"t:- D\., l_._!:i. 1? .l.t...l. v.C I~ .!.a t i vc 1..~ .!.. ~ \.l Lt F1??,c: .c.u: 
vB = ~ a 
b 
( ! 
.? 
?---l 
,::; Steady- State Heu
~ t ron Signa l fro~ Li nea r Powe r Recorder 
~ 
,--j 
cu 
:'.-I __- -
. ,? f 
?rl 
,.0 
H 
<( 
-I 
(U 
;::; 
t.D 
?---l 
(/J 
> 
0 
~ 
~ b 
QJ 
H a 
(jJ 
0 
Time ?CX')  
69 
Product b ui ldup a nd henc e i ncrease in Cerenkov light 
doe s occur dur ing the rise to power. 
p During a stabilization of a reactor at a power 
t o ' thth e c erenkov si. gnal does not remain proportional 
e Power of the reactor. Its v alue depends upon 
the Previous history of the pile, In particular, 
during 
aper . a stabi? 1?i zation at lower power with a long 
the aft?1 .o n at hi.g h power, the gamma rays emitted by 
prod l.ssion products clearly exceed the gamma rays 
Cerenllkc ed b y f.i ssion and capture , Figure 30 shows the 
a funcotv.  si. gnal v t expressed as the bu?i1  dup fraction as 
at kwio. n 0 f time while the reactor has been stabilized 
ru 10 Thi. s curve repres ents an average of several 
ns at 
ranging 10 kw for core loading #1 for operating times 
from 20 minutes to 4 hours. The signal is 
seen to 
approach a saturati?o n value o f approximately 
160 
signPaelr_c en t 0 f power after 4 hours- In addition the 
minut l.nc reases with a half- time roughly equal to 20 
tion es. Th ese numbers are not unique since the satura-
whichV alue and half-time will depend upon the period 
the to power and the spectral response 
of th reactor goes 
s 
e Photo tube. However, Figure 30 
doe
clear1 multiplier 
func. Y illU S t rate the fission product buildup as a 
t1.on All tests conducted in this series 
of time. 
are t-un 
consid for per1.? 
which 
o d s very near 30 seconds one may 
in note? r typical for startup. A further consideration 
th
l.ng the fission product buildUP is e effect of 
Fig . JO Cerenkov Signal Builciup F r ?a c ti on vs R ac l,01, Op:: ?.:>a ting Ti me 
-,---
0 . 7,----,-------,---,----,----~-.
---.
0 . ' ?-
0 . 5 - Po = 1 0 k w 
-
p:\ 
'--' 
s::: 
0 0 . 4 
'r1 
.? 
CJ 
m 
H 
Ii; 
0 . 3 0.. 
:::, 
'D 
.-1 
?r1 
:::, 
p:\ 
0 . 2 
0 . 1 
0 30 0 90 120 150 180 2 10 240 
-...J 
Re a ctor Opera ting Time (T ) - minutes 
0 
71 
amma ray 
ion in he core. Beca
use high g
Self- abs or
pt t
 with shor
t-lived 
ciated
ene:rg i e s 
o
are genera
lly ass
g-lived 
w energies
 with lon
d lo
Products a
n
self-ab sorp
-
 t o
f greater 
fission Products, 
the effec  for a 
ve buildup
 time
tion is  shorten t
he effecti
to re, one may
 expect 
Therefo
given ctor startu
p time. 
rea de of 
cores, the 
magnitu
Variat? 
 
.ons betwee
n reactor
l n apriori. 
'which ? 
i
difficult 
to ascerta
l.s 
n 
c. Shutdow the decay c
urves 
t 
h 37 r epre
sen
t 
Figures 31
 throug  operat ion
 a
after a ste
ady state
for h ight t e Cerenk
ov l
T equal to 
20, 30, 
g time 
10 k r a reactor
 operatin  
w fo In
inute s r esp
ectively. 
m
45 6 40
  
 O, 120, 
180 and 2 ate
' pt is made 
to correl
attem
t he nt analysi
s, an 
seque h e report o
f 
sub  int 
th t curves wit
h the data
e 11.?gh decay b  com inatio
n of 
13 aTheir data
 are 
Rna.be and Putnam . 1550 
es after fi
ssion (l-
t'Wo rces; for 
short tim
ou Ridge Natio
nal 
s
ult s of Oak
 
s
xperimenta
l re ecay time s,
 
seconds), 
e nger d
2 7 , 28 whereas
 for lo
aboratory a
re used, d King are L
btained by 
Perkins an
comp s oted decay c
urve
are neglect
ed in 
U
roduct beta
s 
25 e fission 
p  sub-
a.ctop ted .
Th endix A. Ap
ited in Ap
th? ns
 c
.s analysis
 for reaso uct 
l ions of fis
sion prod
of tabulat
stantial nu
mber ing both ex
-
 the litera
ture hav
Par  appear in 20 29 however, a.meters 7 ,l3 , -
cal bases;
mental and
 theoreti
Peri  extensive 
and up-
ost
nab tnam is on
e of ~he m
K ? e and Pu
72 
Fig . 31 Cerenkov Lig ht Decay a s 
a Function of Shutdown Time 
1. 0 
'D 
Q) 
.N,...,  
rl 
cu 
E 
::..., 
0 
.....;_:_:_ , Mea s . 
0 .1 
r-1 
cu 
s::.: 
.,b....O,  
Cf) 
> Rea ctor Operating Time (T) -
0 
~ 20 mir. . 
s::.: 
Q) 
~ 
Q) 
0 
. 0 1 
10 1cr 
Shutdown Tlme ( td ) - Sec . 
73 
Fig . 32 Cerenkov Light Decay a s 
a Function of Shutdown Time 
1. 0 r--------~;::----.-------------, 
--'D---- -
(1) 
N 
?rl 
rl 
cd 
E 
H 
0 
...._~__ .. 
0 . 1 
rl 
cd 
s::: 
bO 
?rl 
Cl} 
Re
> a ctor Opera ting Time ( T) -
0 30 min . 
~ 
~ 
(1) 
H 
(1) 
0 
. o 111o-__2, ------ - --- - - 1-'-o 3----------~10 4 
Shutdown Time ( td ) - Sec . 
74 
Fie . 33 Cerenkov Light Decay a3 
a Function of Shutdown Time 
1 . 0 ,-----------~-----.-------------~ 
Cale . 
0 . 1 
rl 
cu, 
'-D 
?.-J 
Cl) 
Reactor Op c1-ating Time (T) -
it5 min . 
,._, 
]) 
0 
. 0-1>---------------'---------------l 
Shutdown Time ( t ) - Sec . 
d 
75 
Fig . 34 Cerenkov Light Dec a y a s 
a Function of Shutdown Time 
~ . 0---------""""C----.--------------,. 
..--... 
'd 
Q) 
N 
?rl 
rl 
a:l 
E 
>-< 
0 
.._:_:_: .. 
rl 0 . 1 
a:l 
>=: 
bO 
?rl 
Cl) 
> 
0 Reactor Operating Time (T) -
.Y, 
>=: 60 min . 
Q) 
>-< 
CJ 
0 
. 0 1 1--::------------_.__--;3:;------------
--
102 10 
4 
10 
Shutdown Time ( td ) - Sec . 
76 
Fig . 35 C- renkov Light De cay a s 
a Function of Shutdown Time 
7 ,.._ 
~ - V r----------.,...._,c-----,--------------, 
.,,.....,_ 
?o 
".) 
-~~ ?1  
rl 
qj Meas.~ 
E 
;:... 
'.) 
'-----' 
,......, 0 . 1 
qj 
~ 
b(J 
?rl Reacto r Op e rating Tlme (T) -
Cl) 1 20 min . 
> 
0 
~ 
C 
GJ 
iY 
GJ 
0 
.Ol '--------------'--3 --------------14 1a2 10  10
Shutdown Time ( td ) - Sec . 
77 
Fig . 36 C r nkov Llght Decay a s 
a Funct ion of Shutdown Time 
,........ 
~ 
w 
N 
?rl 
rl 
m 
E 
H 
0 
.._h__ , 
0.1 
rl 
m 
h 
~ 
?rl 
Cl) 
> Rea ctor Operating Time (T) -
0 180 min. 
~ 
h 
w 
H 
w 
0 
. Ol-1------------ -------------- --' 
1J 1J 1J 
Shutdown Time ( td) - Sec . 
78 
Fig . 37 Ce r enko v Light De cay a s 
a Function of Shutdown Time 
1 . 0,---------""""'oir;~---.-------------, 
~ 
w 
N 
?rl 
.-1 
ro 
E 
H 
0 
h 
------
.-1 0 . 1 
ro 
h 
~ 
?rl 
~ 
~ 
0 
~ Reactor Op e rating Time ( T) -
C 
w 24 0 min . 
H 
w 
0 
. 0 1.,__,.,_ ___________________________ ,4 
10 10 10 
Shutdown Time ( t d ) - Se c . 
79 
 be us ed a s a 
bas is 
fo d and will
to - date r efer e
nces 
wh ich f ollow. on products 
r the calculat
ions on fiss i
fo ion products, ss
e of energy re
lease from fi
Te rat  
fission, can b
e represented
tion of time a
fter 
a s a ~nc
g expression : 
by tle f ollow
in
-s ev/fiss-sec
 ( 21) 
r(t) = a t0 
nd 
fission in sec
onds and a a
fter 0  time a
Where tis the tn rn the 
 report of Kna
be and Pu
s are constan
ts. In the
energy groups 
covering 
ed into s even
 
Photons are c
lassifi  VII, 
 0.1 and 5.5 Me
v (see Table
th nergy range be
tween
e e n energy which
 
m photo
endix A). Since
 the minimu
App
Comp ton electr
on (Cerenkov 
can produc e a 
0.260 Mev e energy 
.407 Mev and t
he averag
threshold in w
ater) is 0
ev, if we negl
ect this 
p is 0.30 M
of the first g
rou r the 
ergy relea se p
er fission fo
 of en
group the rate by the followi
ng 
 six groups is
 represented 
remaining
nction: 
Piece-wise con
tinuous fu
) 
0070 t- l<t<l0
 sec (22a
0.364
3 (22b) 
9 t -1 <t<
l0
r(t) = 0.82
. os 10
(22c) 
s at a power P
(?) watts 
or the reactor
 that operate
F t power is rep
resented 
the decay of f
ission produc
for time T, 
by: 
l 
80 
P(t,T) ~ K/;? ?r(t + ?)P(?) wat ts (23) 
/ 
where K = 5.12 x 10 -3 fissions per Mev and? is an 
arbitrary time during operation. For the case of constant 
power level operation P(?) = P , and equation (2 3) 
0
b ecomes 
-s . 
]_ 
d? (24) 
where 
+ = + -s r(t ?) ai (t ?) i ( 25) 
Applying equations (22a), (22b), and (22c) to equation 
(24) results in the following expression: 
( 26) 
Integrating equation (26) yields the desired relation, 
n amely 
3 0 30 0 30
P(~~T) ~ 5.12 x 10- { 1.21 [ (t + 10) . -(t + 1) ? ] + 
14.5 [ (t + 10)-o.oa_(t + 103) - o .os] + 15.1 [ ( t + 10)-0.31 
-(t + 31T) -o ? ] } (27) 
A reasonable fit between calculated and measured decay 
curves is possible if a comparison is made for a normaliza-
tion at t = 500 seconds instead of at t = 1 second for the 
following reasons. If one considers the contributions of 
the Al-28 (t 1; 2 = 2.3 minutes ) decay betas and gammas to 
81 
the Cerenkov light, then after approximace y 3.5 half-lives 
mo st wf t e aluminum ha s decayed. In addition, the 
analys~s is co licate to some extent by the emission 
o= d :~yed neutrons . The f ormula for the ga:crma decay 
:ca te due to fission produc sin a reactor applies to a 
~eactor of operating interval T seconds, during wh i ch 
he reac tor power or f ission rate is not zero. Reactor 
shutdown refers to the instant at wh? ch the fi ssion 
rate r ap "dly drops due to control rod insertion , however, 
fi ss ion products con inue to generate delayed neutrons 
aft er shutdown. The delayed neutrons maintain the 
neutr0n flux at a level of the order of 1% of the pr e -
shutdo1;,m flux for time s up to a minute o:c s o, and this 
?.;:eeps t 1 e t?? ssion rate at a similar fraction of the 
cpera~ing power levelo When this occurs, terminating 
t e o~erating time, T, at the point where shutdown 
01 ly ? egins t o occur must obviously be avoided in 
order to oc able t o eva luate and compare the c lcu -
~~ted and measured dee y curves. 
~ormalizing the calculated and measured curves 
a t = 500 sec onds then indeed s eems reason ble as a 
basis fo~ comparisono The normal ized data is shown 
in Figures 31 throug? 37. Figure 38 is a plot of the 
perc ent difference between the calcu lated and measured 
curves vs, O)erating timeo These valu ..:: are calculated 
f or a decay time of 104 seconds at which point a maxi -
mu ~ difference occurs. It can be seen from Figure 38 
j,'Jg . ( ;,:.: 1)1 L'l't:n.. ..? 1 ":, DcLvrecr1 Me-i.i., Lll't.,cl w1c. CaJ cul a t c:d Decay Cu r ve;:; _) U 
!/ ( i 
4 
Dec ay T ime = 10 Second;,,; 
::iO 
\\) 
0 
:...: 
1._) 
~ --- -----
'1) 
~ 20 
~ 
?rl 
r::::i 
~ 
10 
30 oo 90 I. ' )(' 0 i __ v 150 HO 210 240 
Reactc,1? Opecc:, r-in._:; 'l'i,w ( ;11 ) - Mi1 1ul es 
00 
N 
83 
t hat 1e di f -e r ence between the analy ical and empirical 
curves decre se s as the reactor operating time increases. 
The observed differences are comparable to fission product 
ecay s tudies ma de by others . 
Fi l t e r Te sts 
The f i na l series of experiments performed on the 
core a s shown in Figure 5 is suggested by t he ana l ysis 
p rformed in Appendix A. From the curves in Figure 49 
in A~? nd i x A it can be seen that the s pectrum changes 
0 
v ery slightly over the wavelength regi on from 2500 A to 
0 
3400 A during the t? e interval from zero to four hours . 
This suggests the unique possibility of a Cerenkov 
radiation detector which is insensitive to f ission 
product buildup and hence may be used as a power level 
detector. Subsequent measurements identical in 
p roc edure to previous steady state tests except for 
t he use of filters, are performed to verify these 
ssumptions and conclusions. All tests are conduced 
f or an operating time of one hour and a startup period 
of approximately 40 seconds. Experimental results are 
tabulated in Table v. Figure 39 illustra tes the buildup 
a s a f nction of time for each of t he tabulated cases in 
Table v. Two fac s are noted from the results, namely , 
0 
the maximum buildup occurs in the vicinity of 3920 A 
which lends furthe r validity to the Cer enkov spectrum 
calculations in addition to the spectra raphic data. 
Secondly, the minimum buildup observed is 18.3% at 
84 
TABLE V 
Fractional Buildup of Cerenkov Signal After a Reactor 
Operating Time of One Hour 
Wavelength 
ato 0 Fraction.al 
Tmax (A) Tmax (%) Half Width (A) Buildup 
3500 31. 6 235 0.204 
3920 30 110 0.284 
4450 30 80 0.263 
4700 35 90 0.242 
4980 47 120 0.2 24 
5530 44 120 0.183 
No Filter 0.442 .. 
r 
Fig . 3 Buildup Fl'cct:L or1 \?s Reactor Ope2:1ating Ti me (F.:'..lter Tests) 
0 .5 ~---.----~-----r------.-------.-----,-------, 
P0 = 10 kw No Filter 
? I, 
--p----...:.:_) , 
I 
, 
C 0 . 3 ,.._.3920R 
0 
~ 
..? ,.._.4450~ 
0 
crj ;>..?47ooR 
;...; ,.._.49soR 
~ 
0.. ,.._ .. 3500R 
;::::i 0 . 2 
'D ===--======== ,-..?5530~ rl ?--1 
;::::i 
p::i 
0 . 1 
0 10 20 30 0 50 60 
Reac to r Op e rating Time - Minutes 
()tJ 
V1 
86 
0 
5530 A which is essentially the long wav elength limit of 
the transmitted spectrum at the pool su rfac e. In view of 
the fact that the short wavelength limit of the transmitted 
0 
Cerenkov spectrum is approximately 2000 A and the buildup 
0 
fraction appear s to decrease below 3920 A, an investigation 
0 0 
further into the ultra-violet between 3500 A and 2000 A 
suggests that one might expect even l es s buildup; the 
practica l limitation imposed on such an inves t i gat i on is 
the increas ing attenuation of light in this wave l ength 
region. One notes from the spectrographic data in Figure 
18 that the Cerenkov spectrum as seen by a detector at the 
0 
pool surface cuts off at approximately 2000 A whereas 
the true unattenuated spectrum continu~s further into the 
ultra-violet. 
In any interference filter the transmission pattern 
is affected by lack of parallelism in the incident 
light or by the whole beam not being normal t o the 
filter surface. A shift in t he peak respons e to a 
shorter wavelength will resu lt from either deviat ion, 
but the shape of the transmission curve remains almos t 
unchanged up to an angle of incidence of about 20 degree s . 
For the standard Jena filters, an angle of incidence of 
0 
10 degrees results in about a 20 A displacement of\m ax 
0 
and about a 30 A displacement f or a 20 degre e tilt . 
In view of the minimal shift in peak respons e up to a 
20 degree tilt and the fact that a light collimator 
87 
s used, any errors due to lack of parallelism of the 
incident light is considered neg ligible. 
Up until now, no mention has been made of any 
p o sible variations in the Cerenkov spectrum due to 
temperature effects or dispersion. Referring to 
Table I, less than a 2% change in the index of re-
fraction occurs over a wavelength reg ion extending 
0 0 
from 3034 A to 64-38 A for a temperature of 20 ?C. 
Moreover, the negative temperature coefficient of 
n equal to - 1.00 x 10-4 per ?C results in less than a 
2% chang e over a temperature range 20 to 60?C for the 
same wav elength region. Consequently, no observable 
effects are expected in the measured data. 
It should also be noted that gamma ray activities 
from previous operation at pm1er levels in excess of 
1 kw produce a residual Cerenkov light signal at 
shutdown which lingers for several hours or more. 
Hence, in order to minimize any measurement errors, 
at least one day is allowed to elapse b etween 
rea ctor operation at power l evel s g reater than 1 kw 
and an experimental run. Each startup therefore is 
effectively equivalent to startup with a cold clean 
core. 
CHAPTER VI 
Sffiv -iA~Y 
A r e lative l y s i mple, s i n gl e in s cru 1ent f or th e 
measurement of r eact or power does n ot y e t exist . Th e 
mos t c omr;:ion means of me asu ring power leve l in a reac tor 
i s to ut .:.l ize neutron detec tor s wh ich g ive a d i r e ct 
i nd ication o f the neutron population density . Bo h 
the reactor power and the n eutron flu x are directly 
r elated t o t he n eutron den sity i n the r e ac tor , but 
th e neu tron flux i s als o d ependent on che n eu t ron 
at tenuat ion between the reac t or and the detector . 
Measurement o f the n eu t ron flu x then provide s a 
u seful signa l f or op erat ion a nd con t r o l o f r eac tors . 
Howev e r, b e c a u se t he presently use d n eutron det e ctor s 
are located out s ide th e reac or lat t ic e , they are 
s ensitive to perturbat ions in core l eakage an d shie l -
ing due to control rod confi gura tion and changes i n 
att enuation characteristic s o f the int e rvening material . 
It is p os s ible, in princip l e , to u se the signal 
f rom a Ce r enkov dete ctor f or reactor contro l, bu t 
because th e gamma r a y i n t ensi t y is not s imp l y re l a t e d 
to the reactor power the problem is more complicated. 
For example , a short time a fter reactor shutdown f rom 
long operation a t high p ower the d e layed gamma r ay 
a c t ivity from fission products migh t ob s cure a 
da n gerously rapid incre ase in n eu tron popula t ion . 
88 
89 
Ior~over, even afte r several h our s shutdown , Cerenkov 
measurements might be i n a ccurate du r i ng startu p at low 
power levels be c ause t he sign a l is du e partl y to gamma 
ray a ctiv i tie s from previous oper at ion at high power. 
The a ttempt to use int e r feren c e fi lt e rs as a mean s 
o f opticalLy bia sin g out the fission product contri-
bution to t h e Cerenkov signal met with limited succes s 
i n sofar as the rang e of fil ter wavelengths used and 
the physical situation permi tted, namely, t h e att enua-
tion characteristics of wat e r as a function of wave -
l e n g th. 
In sp ite of these limitations, the g ood agreement 
between t h e Ce renkov detector and th e i on chamber 
r espon se in the transient t e sts has a number of interGs t -
ing and significant i mp lications . The Cerenkov d e tector 
affords an excellent means of monitoring pulsed pool 
rea ctors or the power variat i on during an over - power 
surge, and without exposure to high neu tron and gannna 
fluxes which could destroy normal neutron detectors . 
Furth ermore, since it can be remotely located, the 
Cerenkov detector, by integrating the total light in-
tensity produ c ed by the reactor, is relatively in-
sensitive to core perturbations and shielding. 
The fact that the Cerenkov light decay follows 
the empirical equations for fission product gamma 
decay suggests the possio i lity of using this technique 
90 
for re note monitoring of spen - fue l - element activities 
or i,tur ?s of radioisotopes . A Cerenkov light CQl i-
bration source of well define geometry could be fab ri -
cated and placed in a mater i ? 1 o f high refra ct ive ind2x 
and low abs orpt ion coefficien such as water and used 
as a standard . 
One obvious area open to additional inves i gat ion 
is the measurement of the Cerenkov light further in to the 
ultra-violet region to determine with c e r tainty whe ther 
or not a region exists which essential ly is unaffected 
by fission product contributions . In line wit~ th is 
discus sion, mention might be made of t he fac t that 
pressurized water systems ( e . g . power r eactors) ope r ating 
at higher temperatures than those encountered in research 
type reactors have an inherent fission product biasing 
factor, although small. This factor occurs as a resu t 
of the negative temperature c oefficient of index of 
refraction. Thus, at temperatures in the neighborhood of, 
say, 280?C the effective threshold f or t he production of 
Cerenkov light is approximat e ly O. 3L~O Mev; the mini um 
gamma ray energy for the produ c tion of a Compton e lec t ron 
having this energy being 0. 55 1ev. Althou g this has 
the effect of reducing the light signal from both the 
fission product and 11 prompt 11 gamma radiations, it is 
more pronounced in the case of the fission products 
because o f the fact that v ery few iission products have 
91 
reater than 3 l J energ ies g ev T.?\7 .e reas t h e 11prornpt 11 
garnm2 !:;l:)2Ctrurn extends beyo d this up to about 7 
Me v . 7 '7~ 0 
Since the inst antaneou s g ammas follow the react or 
power , a gamma detector biase d around 3 Mev affords 
a means of eliminating fiss ion product gamma rays 
and thus obtaining a ' 1purer 1 signal proportional to 
power. Using a Cerenkov detector, one could take 
advantage of the index of refract ion of the medium 
to s e t the energy bias . In thi s connection gaseous 
media appear to have t he greatest potential since th e 
r efractive indices of gases are so much lower than t hose 
o f sol ids and liquids. Mo r e over, the refractive in dex 
may be varied over a wide r2nge by simply varying the 
pressure. Bor k ows.K .i  an d I( err, Jl 1. .n a pre 1 i?m 1. .nary 
experiment, demonstrated t he effect of biasing out all 
gammas below 3 Mev by using CO2 and SF under high
 
6 
pressure to achieve the required index of refrac ion. 
Their detector consisted of a gas filled tuoe and as 
a re su lt was only able to measure the local power 
density and h ence is subject to local perturbations . 
In order to realize the fu l l benefits of a gaseous 
Cerenkov detector and ye t retain simplicity, i t is 
desirable to utilize such a det ector where, first of 
all, a$ much of the core as possible can be viewed in 
orde r to minimize any geometry effects and secondly, 
a minimum amount of equipmen is necessary . The 
92 
obvious choice is a gas cooled r eactor wherein typic al 
coolants su ch as He and co2 are already under hi0h 
pressure rangin g from 500 to 2000 psia . The only 
necessary equipment would be a light sensor judicious ly 
located so as to minimize or eliminate comp l e t e l y any 
gamma rays streaming toward s the viewing window and 
photomultiplier. These would produce Cerenkov radiation 
not properly biased since their refractive indice s are 
high compared to gases. It appears that, for any 
simple and practical scheme, the Cerenkov detector at 
present is limited to water type systems. A water 
system provides a highly transparent medium for t he 
product ion and transmission of Cerenkov light which is 
chemically stable, non-scintillating and acts as it s 
own shie ld. The refractive indices and corresponding 
kinetic energy thresholds for electrons for s ome common 
gases at normal temperature and pressure ( J. T .P.) is 
given in Table VI. Figure 40 shows how t he threshold 
energy for these gases varies with pressure . 
Another appropriate area for further work is the 
extens ion of the detector operating range to possib ly 
four or five decades . Nuclear reactors opera eat 
power levels ranging from milliwatts to megawatt s. 
In order to measure the Cerenkov signal over all or 
most of this range without range switching it is 
necessary for the detector to have a logarithmic 
response . In addition, since the reactor period is a 
93 
TABLE VI 
Threshold Kinetic Energies f or Electrons in Some Common 
1 
Gases at N.T. P . 
Gas n Et(Mev) 
Helium 1 . 000035 61 
Argon 1. 000284- 21 
Air 1.000293 21 
Nitrogen 1. 00029 7 20 
Carbon Dioxide 1 .000450 16 
94 
F l g . 4 U Varia tlon of Thr e:::;holc.:i 
F Eu Ln Ec :t ri go  n ,  o Ef t  aPr ::;c  ; a:  ,sur for? Some Common Ga .Jcf, 
102  .--~-------.-------,------------
-;;---
H !>, 
(]) bl) 
,:: H 
Q) (]) 
.-:: 
0 (]) 
?rl 
.? .? 
(]) rfl 
.-:: (]) 
?rl H 
~ 
 
Air , N
.1 2
and A 
0   
'---' / 
~ 
(' 
Gj 
' 'j 
ri 
0 
..c: 
G} 
(]) 
::.., 
..c: 
8 
1 10 
Absolut, Pressure - a tm 
95 
loga:..-i~'1, ic function , signal s w:1ich are p :::-o;_)ortio .:il to 
reactor period may be used to control the reactor and to 
l imi t the rat e of power level rise to safe values . 
Advantage might ~e taken of the logarithmic rela ionship 
1.;etwecn the gain and applied voltage inherent in 
photomultipliers which has been investigated by S?Heet, 32 
33 3L,_ 
Bell et al and others. ? Contrary to pulse - ypc 
de ector systems whose signal is limited by noise, 
measurement and transmission of a d.c. signal is un -
affec t ed in this manner and may r equire less circuitry. 
APPENDIX A 
The o~ject of his section is to present the rela-
tions necessary to calculat e. :cor any known. in itial 
elect ron en e r g y d istribution the C(::renkov radiation 
spectrum for any medium of knovm refractive index . 
In the case of garrnna rays penetrating a refractive 
substance, it is necessary first to determine the 
initial electron energy distribution . These distri -
butions have been tabulated for a wide range of gamma 
energ ies. 35 , 36 
The electrons may be re lated to a number o f Cerenkov 
light quanta by 
y,, 
{m2 e2 
= 6 >.. N . N /\. 2 (1 -
1 ) dx 
PJ he j 82 n2 ( 1) 
avg la: 
where N . is the number of ligh t quanta in the wavelength 
PJ 
int e rval 6A about>.. genera ed in unit ti1 e by N. 
avg J 
electrons of specified initial energy coming to rest in 
the medium . 
e is the charge of the particle 
his Planck's constant 
c is the speed of light in v acuo 
xis the total range of the particle within 
the medium 
B electrons m ax is the initial veloc ity of the
 
1 
is the limiting velocity f o r the Cerenkov 
11 
effect 
96 
97 
tion (1) may be e
val a t c d 
a
Th in t ~g ral in e
qu
1 ) vs x. 38 F?" f (1 igu
re 
ically from a plo
t o - 82n2 graph
. It is 
 plot made fo r ?w
ater (n = 1. 333)
i:.l is s uch a
dent (see Table I
 
here that n i s wa
v elength indepen ' 
as urned 
is a plot o f elec
tron ran g e as 
Chapter I I) . Fig
ure 42 
-
ectrons in water 
for es tabli sh
a f unction of ene
r gy for el
pecified initial 
ng v a lue s o f x co
rresponding to s
i
35 egration up to eac
h range 
Int
electron energies
.
nt values of s ele
cted 
ssa midpoi
corresponding to 
absci
may be carried ou
t a n d the 
rgy g roups 
initial electron 
ene
on (1). 
tegra l so obta ine
d used in equati
v alues of the in
ed into equat ion 
(1) and N. 
stitut PJ 
Each N. may be su
b
J ner gy group over 
uated for each in
itial electron e
eval
inte rest . From t his
, N , t he 
 of pt 
the wavelength ra
nge
nerat ed in unit t
ime at 
 quanta ge
total number of l
ight
ng 
 be obtained b y s
ummation accordi
a wavelength Aav o
- may
0 
to 
( 2 ) 
 j initial elec tron
 
en over a ll the
where the sum is 
tak
 each wave -
s . The number o 
light quanta at
energy g roup btain 
 plo tted vs wave
length A. avg to o
length may then b
e
e spectral distri
bution . 
th
ssible to 
bulated by Johns 
e t al make it po
Data ta
 distributions wh
en the 
electron energy
calculate initial
 
 36 
s . 
35 ' To obtain th 
n is garmna r ay
incident radiatio
n th e wavelength r unit time i
radian t ener g y em
itted pe
e o f the relation
 
int e rva l 6A a b out
 A u se is mada v g 
Fis . 4 1 Ra .1L;? .. of El ect rons in Wa ter a F / s a unctio In .  o )f   (l-,/-1~1/ 
0 . 
o .4 
n 1. 333 
~ 
", 
'-. \~ O . 3 
' / 
~ 
"-"._'_ _ 0 . 2 
0 . 1 
0 1. 0 2 . 0 3 .0 4 .o 
Range - cm 
1..0 
(X) 
99 
CJ 
'.] 
~ 
-l ') 
~ ,-_, 
?~ 0- 
L 
~ 
r; \ 
\ 
r- ' 
:,J 0 
l['\ 
> 
CJ 
~ 
-
~ 
Cv 
::;: ,?, \ .. 0 C ? e, .--< .. .., \ , \ ., 
\ 
_. , \ ~ 
\ 
') ~ 
-; r:., 
,-J _, 
C) .? 
(J \ -::) 0 
rl ,:j) 
rY') 
~ rl 
~ 
,....,. 
,_ \ 
(I., 
?' 
.u () 
.:,:: 
~J 
,?,.- 1 
~ -< Ir  C ,..., 
; 
I 
I 
I 
I 
C) G C) 0 C) 0 
. .."'\ ?Y) (\J rl 
,,- -;3~["Eti :," ,::-'2. ;);; 1:'3: 
100 
( 3 ) 
the energy in ergs radiated in
 unit time 
wh e re Ek is 
th Planck's 
a t the k wav elength in int e
rval 6A , his 
o. A 
con s tant, and c is tho s peed o
f light in vacu
 E- vs A between wave leng th
s of interest 
plot of K avg 
al to 
produces a curve which bound s 
an area proportion
total Ce renkov radiation energ
y b etwe n thos e 
t he 
g ths. Thus, the total Cerenk
ov radiation ener gy , 
wave len
Et, is given by 
 when 
where Et has the dimensions o
f ergs per second
\'s are expressed in centimet
ers and 
E 
 
E' = k 
(5)
6 \ 
lculations are performed for t
hree cases, namely, 
Ca
p t spectrum, prompt plus 20 min
ute fission product 
prom
prompt plus i~ hour fission pro
duct spectrum. 
s pectrum, and 
e lower 
From e quation (1) on page 2 o
f the main text, th
alue of s that can make Ce renkov radiation limi ting v
, 
coh e rent in a me dium of refra
ctive index 1.333 is 1/1 . 333
or 0.750 . The relation betwe
en particle energy , E, and 
101 
R is 
E = m c 2 - 1 ( 6) 
0 
~, ere m i s tha r es t ma so o f the parcicle . From e qua-
0 
tion ( 6) the limiting value of E for production o f 
Cerenkov radiation electrons in water is 0.260 Mev. 
Figure 43 is a plot of the calculate : gamma 
sp e ctrum in the core of the UMR. for t h e fol l owi ng 
cases: prompt spectrum, prompt+ 20 minute fission 
product spectrum, and prompt + L~ hour fission product 
spectrum. The subsequent calculations assume that 
only the Compton electrons are of consequence in t he 
production of Cerenkov radiation (both pair production 
and photoelectric effect are negligible in comparison). 
Calculation of the fission product gamma spe ctrum is 
based on data reported by Knabe and Pu t n am . In this 
report the photons are classified first into seven 
energy groups covering the energy range between 0.1 
and 5 . 5 Mev. The group limi ts are the same as g iven by 
Perkins and King. 
25 
In addition, group VII o f the 
Perkins and King data is split up into six individual 
sub-groups so that actually twelve energy groups are 
considered. The group limits are listed in Table VII. 
It is found that the average energies of each of the 
twelve groups are effectively constant in time up to 
about l0 6 seconds. The calculation of the fission 
product gamma spec trum presented herein includes all 
102 
Fig . 1-13 Calculat ed UMR Gamma Sp e ctrum 
10 
Promp t Sp ectrum 
--- Prompt + 20 min . 
f . p . Sp e ctrum 
----- Prompt + 4 hour 
1 . 0 f . p . Sp ectrum 
- 0 . 1 ? 0 
.? 
C) 
..c: 
'.J., 
0 .01 
0 . OO J-L_ __- -1._ ____ L._ __- --1-:-----
0 - ::-----:2 ~ :--6 8 10 
Gamma E~ergy - M v 
103 
TABLE VII 
FISSION PRODUCT GAMMA 
ENERGY GROUP DEFINITIONS 
Reported 
 
 Perkins & King Energy 
Range Ave .
12 Groups ev) Energy (Mev) 
Subdivision Groups 
(M
I 0 . 1 - 0 . 4 0
. 30 
1 
II 0 . 4 - 0 . 9 
0 . 63 
2 
III 0.9 - 1.35 
1.10 
3 
IV 1. 35- 1.8 
1. 55 
4 1. 8 - 2 . 2 1. 99 
5 V 
VI 2.2 - 2 . 6 
2 . 38 
6 ies be -
7-12 VI I 
2 . 5 - 5. 5 Var
tween. 3 . 5 
and a bout 
3. 1 
Group VII Subgroups 
VIIa 2 . 6 - 3 . 0 2 . 75 7 
VIIb 3 .0 - 3 . 5 3 .
25 
8 
VIIc 3 .5 - Lj . ? 0
 3 . 70 
9 
VIId 4 .0 - 4 . 5 
L, . 22 
10 4 . 70 
11 VIIe 4 .5 
- 5.0 
5. 25 
12 VII? 5.
0 - 5.5 
1 04 
roup I s in c e t he g a mma en e
rgy wh i ch 
g rou ps e xcept g
260 Mev Comp ton e l e ctron (
Ce r enkov 
can produc e a 0 .
o ld in wat e r) is 0.40 7 Mev
. The approp r ia e ly 
t hresh
t hre 
we ight e d Compton el ectr on 
en e rgy spectra for t he 
ioned are calculated from 
information i n th e 
c ase s ment
 plotted in Figure s l\ t'.; 
r efe r enc e by Johns et al a
nd a re
resent the 
through 46 respectively . 
These curves rep
l energy distribution of C
ompton electrons pro-
initia
t gamma ray sou rces as 
duc e d in water by the impo
rtan
d in Chapter II for a reacto
r power equal to 
mentione
he number of electron s prod
uce d with ene rgies 
10 kw . T
r mined f or d iscrete ph oton
 
in each energy interval is
 de t e
ging from 0.6 Mev to 8.0 M
ev and th e y are 
energies ran
ded together to give the m
ulti-peake d curve s shown 
ad
ssumed in e ch cas e 
in i s
 a
Figures 44 through 46. It 
 homogeneously distribut e d
 
that the entire source is
oughout a volume of water 
so large that only a 
thr
ligib le fraction of the cor
e gamma rays escape 
neg
ou t producing a Compton el
ectron . In addition, 
With
f U-235 are 
beta particles from fission
 product s o
glected as mentioned earli
er in Chapter II. 
ne
il Compton electron 
If f?dE is the fraction of
 reco
 E and E + dE then the area with energies between
d by graphical integration
 of the curve s in 
obtaine
e tota l 
Figures 44 through 46 may 
be identified with th
ch case. 
number of Compton electron
s produced in ea
Fig . 44a Di stribution of Compton Recoil Electron Energ i es 
400 
Prompt Spe ctrum 
--C-J-)- 300 
.? 
-rl 
s::: 
::s 
>, \_ 
H 
co 
H 
.? 
?rl 
.0 200 
H 
.._c_o_ , 
~ 
100 
0 0 . 5 1.0 l. 5 2 . 0 2 . 5 3.0 
El ectron Energy - Mev 
I-' 
0 
Vl 
FL: . 44b Di s tribution of Co:-:1pton Recoil Elcc::~'J:. Ene:?[;~:._? 
'.0 ..-----
:3 r_? .. p1. Sp( et;-?, .. 
--(-/)- 
..j..) 
.,-; 
s:: ,,. 
;:::S 
>, 
H 
co 
H 
..j..) 
?rl 
.0 
H 4 
..._co_,  
I 
' 2 
0 I ~ 
2 . 0 4.o s .o 6.o 7.c 8.o 
Electron E:.e1?_;y - .Mcv 1--' 
0 
0\ 
Fi s . Li~a IJist r?i but;ion or' Comptcir, Recol l Elect ,?c..i. E__ e1-_s'.c' 
]J'_ 
400 Prompt + 20 mi n . f . p . Spect r u~ 
--I-ll- 
..? 
.,-I 300 
s:: 
;:S 
~ 
H 
m 
H 
..? 
.,-I 
.0 200 
H 
...m.....  
I 
~ 
100 
~ t::::::::::::::l 
G 0 . 5 1. 0 1. 5 2 . 0 ') !'.:; 
Electron Energy - Me v 
...... 
0 
" 
Fig . 45b Di stributlun of Comp ton Recoil E J c.:c t r-on E: _eL_ _ : i 
ll 
8 
Promp t + 20 mj_n . f . p . Spect ru?11 
,,......_ 
U) 
.? 
-rl 
C 6 
::! 
~ 
H 
cu 
H 
..,?..,  
.0 
H 
.._c_u, . 
I 
"-
2 ,_ 
0 
2 . 0 3 .0 4 . 0 s.o I I 7 . () . I) 
Electron Energy - Mev 
~ 
0 
00 
Fig . 46a Distribut i on of Compton Recoil El ectron Energies 
500 
400 Prompt + 4 hour f . p . Spectrum -
,......_ 
1:/J 
.? 
-rl 
s:: 
:::s 300 
::>, 
H I 
eel 
H -
.? 
-rl 
,.0 
H 
....e_e_l, 
200 
. 
I 
~ 
100 
0 0 . 5 1. 0 l. 5 2 . 0 2 . 5 3 . 0 
El ec tron Energy - Mev ,... 
0 
\0 
Fig . 46b Distribution of Compt on Recoi l El ectron Energies 
_l v'  
8 Prompt + ~ hour f . p . Sp e c trum 
-O-l 
.? 
or-I 
C L 
::s 
:>, 
Hcu  
H 
.? 
or-I 
'? I, . t 
....c_u_ , 
I 
~ 
2 
0 
2 . 0 3 . :, 4 .0 5 .0 6 .0 7 , 0 :3 .0 
El ectron Energy - Mev 
..:;;. 
111 
is mu s t equal th e numb e r o f g mma rays pro duc e d
 i n 
Th
the s ame time inte rval in t he steady .:;tat e s i n
ce i t 
i s s p e ci f i e d tha t the volume is large enough t
hat 
only a n eg ligible number of gamma rays escape 
be f ore 
Compton interaction. The are a under Figures 4
4 throu gh 
s in 
L:.6 is divid e d into 19 suo - areas and the electro
n
e a ch sub-area are assigned t he abscissa midpoi
nt energy 
value . The fraction wh ich each sub - area is of
 t he total 
multiplied by the tota l nurn~e r of Compton elec
trons , 
g ives N . . The calculations are made for the Cerenkov
 
J 0 0 
r ad ? tion emitted between 2000 A and 8000 A. Figure L,7 
is a p lot of E' vs for a r eactor power of 10 kw 11.avg 
 a n e ffectively infinite volume of water . In 
all cases, 
in
the effects of any self - absorption are neglect
e d because 
of the resulting complexities since the calcul
at ions 
rmed with the idea of only obtaining qual itativ
e 
are perfo
information . It should also be mentioned that
 the me thod 
as de scribed herein may lead to low answers, s
ince no 
account has b een taken of the s cattered gamma 
rays 
possessing energies in exces s of 0. 407 Mev, e .
g. the 
inimum energy which can produce a 0 .260 Mev Com
pton 
m
electron. 
Becaus e of the 17 foot depth of water over he
 
core the spectral distribution of the Cerenkov
 radia-
tion as seen by the photomultiplier tube mus t 
be 
corrected f or the transmission characteristics
 of 
water. The attenuation is expressed in terms 
of the 
Fig. -:1 Calcu::...ated Cer'enko\- Spectra :: Distribution 
~000 --- -.-------,--------.----~---~---
800 L 
0
~ 600 
C) 
Q) 
rfJ 
"[f-) 
bD 
h 
(I) 
00 
Prompt + 4 hour f . p . 
?:J 
Prompt + 20 mi nute f . p . 
/ 4 
200 
Prompt 
o'----------'----------'-------~------'-------'------~ 
2000 3000 4000 5000 6000 7000 8000 
0 
Wavelength - (A) .... 
I-" 
N 
113 
2n ity kin the equation I= 1 exp 
(-kx). I represents 
qu 0 
t with initial 
the intensi ty of a paral lel beam of 
ligh
 depth of x 
intensity I , after pass in g through 
a
0 
 
c en timeters of water. F i gure L1-8 is 
a plot of i vs
A for distilled water . Large variat
ions exist in 
t he reported literature v alues o f k 
vs A over c ertain 
0 
wavelength regions especially be low 
4000 A. Disti lle d 
water , a s used in these studies, is 
very far from a 
 su b stance and the di fferent resu lts
 are attr ibu ted 
pure
basically to differences in the wate
r . The data chosen 
epresent average valu e s and is also here appears to r
the most recent available. L1-0 ,
4 i, 42 , 43 , 4 L1- The trans-
= exp (-kx ) i s 
mission spectrum of water H(A) = I/I 0 
pth of 16 feet and 
calculated for an effective water de
multiplied by each of the Cerenkov r
adiation spectral 
nd-
distribution curves in Figure 47 to 
obtain the correspo
ing spectra shown in Figure 49 as se
en by th e pho to-
multiplier tube. 
114 
Fig . 48 Att e nuati on Coeffici en t of Di s till d 
Wat er vs Wave l eng th 
_l 
10 
Temp . - 20? C 
~ 
I 
E 
C) 
- 2 
lJ 
,--.,. 
..~.__. . 
.j...) 
()) 
?rl 
v 
?rl 
Ci-1 
' H 
QJ 
0 
0 
C 
0 _3 
?r l 
? 10 
~~ 
;:, 
r ? 
'1) 
~ ..) 
.j...) 
<r: 
4
10 - L-------'-----:-~-----'------L-----..:....L--J 
2000 3000 4000 ~000 6000 7000 
Wa ve l ength -(A) 
115 
Ca lc-__iluteJ. C ..;e .. vi_'.::,\? Sp, _::t_, ?..,_; D:. .~ ~:. ?.~ ."i: i. :.,~ 
Tlu"G\.,,;.:)t l t) Feet of Wat e r 
300 l 
I 
Prompt + 11 h1? . f . p . 
/ 
Prompt + 20 mln . 
0 ,-::; f . p . 
0 ' 200 
1) 
?i 
Ul 
~a 
,--< 
..J 
Prompt 
H o 
H 
,,,....._ 
,< 
.,___, 
i:.r:i 
1 ) 
0 
2U00 3000 hooo 5000 00 7000 
0 
WavcJcn,,?t-h - ( /1 1 
SELECTED BIBLIOGRAPHY 
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116 
117 
16 . Private Communication . 
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118 
b e l and R. W. Peel le ) r,. A . Love
 and 
29 . W. Zo
ok, "Ana l ysis of Fis sion Product
 
c;. M. Estabro
 Spectra -Exper imen , " ORNL - 2389 , Gamma Ray
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. Love 
30 . F. C. Maiensche in, R. W. Pe
e lle and T . A
"Energy Spec t rum of Prompt Gamma 
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p. 99-110 , 
the Fis sion of U-235," ORNL-2389
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nics 14, 
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34. P.
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35. H. E
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G. Fo Whitm
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37. R. G
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 1956. 
Contr. 
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d 
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4
175, 1934. 
44. E. O. Hulburt, JoO.S.A., 17
, 15, 1928.