Identification of the hydrogen maser design parameters include the shape of the bulk, q (quality parameter), tuning factors, materials to be used, and operational temperature to offset the wall shift. Expressions for the statistic error on the measured frequency were derived. Localized variations in the concentration of excited atoms were studied and how the shape of the container (the ratio of surface to volume in particular) affects their behavior

Cervenka, P. O.

English

NASA Technical Reports Server

DETAILED DESIGN 
OF A 
VARIABLE VOLUME HYDROGEN MASER 
PETER 0, CERVENW 
REPRODUCED BY. C 
U S  Department of Commerce 
National Technical Information Service 
Springf~eld, V ~ r g ~ n ~ a  22161 
https://ntrs.nasa.gov/search.jsp?R=19840012773 2020-03-20T23:52:28+00:00Z
i TABLE OF CONTENTS 
PAGE 
EI Frquency  E r r o r  
TV Systematic Freyt.teilc-)- E r r o r  
V Filling F2ctor 20 
INTR0'3UCTf ON - REV I E'il OF PERTI:.IErjT I4ASER EQUATI0;IS --
;::?-a a hydi-ogsn a t o n  apprczc52s t i l e  ::a? Is o f  t h e  m3ser btr15, the 
o. /er lzp o f  the e lx ' i i -on  clouds o f  t k e  a tom 2nd t h e  :;a71 cause the a t ~ m  
t o  rev2i-se i t s  v e l o c i t y  2nd .m\re a>iay. The \cave f t i n c i i ~ n  ovei-?(;p i s  
i i ~ i r 2 ~ i ? d  znd 60 15 the ~ n e r ~ y [ l ] .  Thc ~ e t  p h ~ s e  s h i f t  t h u s  ci.::cted i s  
'1 
1 g iven by $ = 5 / hE(t)dt \;i;zrs ~t i s  "Lz du;zticn o f  the c o l l i s i o n ,  (1.1) 
A t  
C A E  "L2  charige i n  hypei-i-inz &iiercjr. Thc c o i - i - z s p n d i n g  s i ~ i f t  Sn the z,ser 
1- @ 
cL-.-ac.,?_ -- - i i ~~+:.,ncy i s  g j  by ;f = Zx . - . - - -  .,I: 3 I- i s  the c o f l f s f o n  r ~ t e .  
- 
- 
,!A - -manet ic d i p o l e  nozsnt o f  thz  electrron i n  the H z t 3 n  = 9.2549 x 
70-21 ~ r ~ s / ~ a u s s  
Tt = t o t a l  tin? 
V c  = ~ 0 1 ~ r 2  o f  the  6:ser c a v i t y  
Q . = q ~ a l i t y  f s c to i -  o f  t he  c-v i ty  
f t o t  = t o t a l  f lux o f  H atoms 
I = f l u x  o f  a t o x  i n  the r i g h t  e x c i t e d  s t a t e .  

Far naser operatfon, cne nust haye q < .772. 
In ord2r t o  tune the n3ser accurct2ly, the r a t i o  of the high flux t o  7 ~ w  
J= 11 u x  I-zs~nance 1  ine ;iiiths n ! ,~s t  b? a s  large as possib1.e. The theoretical 
3ne also definzs I - Y e  1 
-- - 
Q-= Vb '1 
iihenever a change of t h z  bulb v0iua2 i s  involved, i t  i s  found useful t o  
t a lk  about a quantity B dcfinsd 2s B = 
'I - 
The. ( 4 )  and ( - )  subscripts i n  the volur;ie V i-zi'er to the la lye (open) a d  
small (closed) configurations, respectively. In the varizble volume hyd,-ogen 
m s e r  shown s c h e ~ 3 t i c a l l y  i n  Figure 1 ,  there i s  a freg;c;ency s h i f t  dlis t o  t 3e  
chznze i n  the volune. It i s  our b 0 p ~  t o  &s ign the systsn so tha t  t h i s  s h i f t  
will  be less  than one p a r t  i n  10'~. 
CHAPTER 1-1 
IDEidTIFICATION OF DESIGN PARAMETERS 
The design parameters are:  
(1) S h a ~ e  o f  the  Bulb: The bulb wi l l  be inade u p  of t:.;o par t s :  
cne fixed and the  other  var iable .  The f ixed p a r t  i s  going to  be cy l i nd r i ca l .  
I t  wil l  have an opening i n to  a var iable  volune t h a t  wi l l  be a truncated cone. 
- ( 2 )  q o r  Q u a l i t y  Parameter: I h i s  \.rill determine whether or note m s e r  
act ion wi l l  occur. 
(3) Tuning Factors: R: f lux tuning f zc to r  
0: var iab le  volurre tuning f ac to r  
(4)  Material t o  be Used: FEP Teflon has been exmined (see  n 3 x t  
sect ion)  and found q u i t e  sui t a j l e .  
(5) Operational Temperature t o  Off-Set t he  Ilall S h i f t :  This teiiipzr- 
a tu r e  i s  believed t o  be approximately lOOOC and wi l l  have t o  be invest igated 
exper im~ntal  1y once t h e  maser i s  b u i  7 t. 
Study of Teflon a s  !{all Material 
'A2 have used a 1 square foot  p iece  of  Teflon i n  order  t o  study i t s  
vacuuin behavior and s u i t a b i l i t y  fo r  use a s  wall r a t e r i a l  f o r  t he  n s w  maser 
design. 
The sample was crumpled t o  simulate operational  condit ions and placed 
i n  a v~cuum ~i-ranifold. \,!hen t he  20 L/sec Noble Vacron purnp a d  sample :.;ere 
heated t o  1 1 7 ' ~ ~  the  pressure reached 8 x lo-' Torr  a f t e r  th ree  days. 
The punp and  sanple were then t rans f2r red  t o  an environczntal chzz5er 
~ h 2 r - s  t h 2  teizp2rztui-e was maintained a t  125" f o r  one day. The t e ~ p e r a t u r e  
nas t h ~ n  raised t o  131 '~  fo r  another day. A t  approxinately t h i s  t e ~ p s r a t u r e ,  
FEP Teflon i s  known t o  change phase. 
I 
I The tomperatul-e was then grzCual7y decreased t o  1 2 6 ' ~  for one day. The  
1 
a n n e a l i n g  process took six days a t  which s t a g e  the pressure was 1.8 x 10-j1 
Torr a t  room temperature. When opened,  t h e  sample  had  n o t  changed i t s  
physical shape o r  d i m m s i ~ n s  and was judged  s u i t a b l e  fo r  use in  the ne:J xascr .  

Case 1: The K.1S n o i s e  i s  i n d e p z n l e n t  o f  the  l ine -v i id th  s o  t h a t  62FH = 62FL 
62Ftuned+ + 62Ftun2d- = ti2FO (111.17)  
>le o b t a i n  a f t e r  s u b s t i t u t i n g  
which becomes, a f t e r  o n e  d e f i n e s  6F = aFH = 6FL 
Case  2: The Ri4S n o i s e  i s  p r o p o r t i o n a l  t o  t h e  l i n e - w i d t h  
~ s s u i r i i n ~  t h e  l i n e - w i d t h  t o  b e  i n v e r s e l y  p r o p o r t i o n a l  t o  t h e  
c o r r e s p o n d i n g  vol ume, 
and 
62FH- = R-262FL- = 
Finally,defining 6F = 6FL, gives 
CHAPTER IV 
SYSTEI.IATIC FREQUENCY ERROR 
The aim i s  the study of localized variations in the concentration of 
excited a t o m  2nd how th i s  i s  affected by the shape o f  the- container (the 
rase of surface t o  vo71ine in psrticular-). This yields 3 frequei?cy sh i f t  
kthich can be used t o  develop c r i t e r ia  that can be used to design the vzriable 
volune part of t h e  xaser. 
The principal assuxption made i s  to consider t h a t  the ualls  
a c t  a s  a sink on the excited a t o x ,  This effect  i s  direct ly proportional t o  
the !$a11 area snd i s  large corpred t o  any other ccntribution. 
After exhaustive conputer nodeling, i t  i s  found thzt  in order to obtain 
an upper bound on the frequency error,  t h a t  part o f  the external vo lu~e  fsr thest  
av:ay from the fixed v01u:qe contributes the most i f  i t  i s  consider?d to incf utiz 
the sharp tapered part u p  t o  the knee bend in the volune, Refst-ring to Figure 
2,  th i s  would include the region marked (11) up to Cl. The other region considered 
i s  iiiarked ( I )  on the sane figure. The fixed vuluce V o  i s  cc;lh?cte4 t o  the 
var!'ah!e V O ! U ~ P _  via  Cog a C O ~ T I I R ~ G S ~ ~ Q R  part which c o n s i s t s  of a hole. 
This i s  shown scheratically in the following section. 
VARLABLE VOLUNiE EXTERNAL STORAGE BULB 
FIGURE 2 - VARIABLE VOLUJIE EXTERNAL STORAGE BULB 
IV. 1 33iro Region  Model 
WVO REGlON MODEL 
REGION (I) REGION (If) 
L e t  the n ' s  refer t o  t h e  d e n s i t y  o f  e x c i t e d  a t o r s  i n  the r zg ion  undzr  
/ 
c o n s i d e r a t i o n .  The S ' s  refer t o  an equivalent p&ping speed due  t o  inter- 
a c t i o n  wi th  the walls and t h e  f ' s  a r e  c o ~ m i n i c a t i o n  terns. 
. 
A t  equ i l i b r ium,  n = n f m  
i n  re1 z x a t i o n  escape 
and 
Then 
and 
Thus  
(IV.1) 
(IV .2) 
Assuming t h a t  t h e  comnunication terns ( o r  C 3 )  a r e  l a r g e  c o ~ p a r e d  t o  t h e  
S's 
B u t  
and 
(IV -9 )  
After substitution and elimination of terrrs in which are considered 
snall compared to - S ,  the result is: 
C 
If r ( A )  i s  the collision ra te  w i t h  the wall and n(A) i s  the density of 
excited atoms near an elerrent of wall area d4, the wall sh i f t  can be written 
using (1.2) 
r 
where i s  the total nurher of atons in voluq~! V and $ (A)  i s  the zverage 
phase shif t  in area dA. 
Then 
I- 
(IV -11) 
The l a r q e s t  c o n t r i b u t i o n  t o  AVW c o w s  from t h e  s m a l l e s t  volume 
con f igu ra t i on  which we c a l l  V,, 
one has 
i = r eg ions  ( 0 ) ,  ( I ) ,  (11)  
IV.2 F i r s t  Approxi-ation 
Suppose 
Khen t h e  phzse s h i f t  4 i s  cons t an t  o v e r  t h e  r eg ion  (i) 
i 
4 
4 * A  4 + A  q, = + A  
0 1 1  2 2 t o t a l  
:!hen t h e  bu lb  tem?era ture  i s  such t h a t  t o  zerotif a p p r a x i n ~ t i o n  the 
wal I s h i f t  van i shes ,  
(IV . ? 3 )  
(IY .15) 
(IY .16) 
( r v  J7) 
(IV. 18)  
(IV. 19) 
(IV. 20) 
(IV. 21 ) 
After s u b s t i t u t i o n  f o r  t h e  E's i n  term o f  t h e  S ' s  and C's 
(IV. 22) 
Anothzr way o f  w r i t i n g  t h i s  i s  
IV. 3 Second Approxirration (Using the P r o p e r  ;)-
Let us c3a?ute f - a c c u r a t e l y  i n  terns o f  n  , n  2nd n . T h i s  g i v e s  
0 1 2 
Also-by d e f i n i t i o n  of  t h e  average 
(IV ,231 
(IY .24) 
(IY. 25) 
(IV ,263 
(IV .27) 
(IV .28) 
(IV .29) 
B u t  
J J 
- 
A 6  + A $  + A +  = + A  
0 0  1 1  2 2 total 
(IV. 32) 
(IV . 3 3 )  
A t  the n u 1  1, 7 = o  (IV. 3 4 )  
(IV. 34) 
After substitution for the Ek the ~xpression i s  
where 
(IV. 36 )  
Th2 wall s i i f t  error czn be written 
Since = o  and hence 
With reference t o  Figure 4 for the r z z n i n g  o f  sore of the no~znclature, 
(IV. 39) 
l e t  us describe so-e details o f  the co-prrtztions. The vo1 uses labelled V , V 
7 2 
and V are shown in the same Figure 2nd the  corresponding areas will  have the s z r e  
3 
subscript (i .e., A refers t o  the area o f  volune V etc).  
2 2 
S@f-lEPv,/IATIC OF ONE HALF OF THE VARIABLE, VOI-UME 
- - 
FIGURE 4 - SCHEI'JATIC OF ONE HALF O F  THE VARIABLE VOLUME 
So one ob ta ins  
(IV. 40) 
(IV .47) 
(IV .42) 
(IV .43) 
A = r ( R 3 + ~ 4 - a )  +T + ZiR L - i r ~ ~ + Z i i 2  D (IV. 44) 
2 1 3 4 3 4  
F o r  the e q u i v a l e n t  pu-?ing s p ~ z d  we use the expression 
t o 9 e t k r  w i t h  forr-~l a (IV. 33)  obt3-i qed i n  the second a ? p r o x i - ? t i o n ,  
CHAPTER V 
FILLIHG FACTOR 
r ~ c  = V H 
b - < z >  bulb 
V < H L >  cavi ty  
C 
where H = 1 
< z'bulb V (V.2) 
b 
and <Hz> 
cav i ty  
= "*2dv C 
= " ("2 + dV . 
s cav i ty  
For operation i n  the  TE 
 ode [3]: 
01 1 
H z = $)sin (F) (Y .A) 
0 
H r = ( i a  ~d ) J ~ * ( S  cos (;z) - 01 a  
07 
= - (xa -\ J f r) cos b z )  -
S d l  1 07a 
O1 / 
where a = cavi ty  r a d i u s  
d = cavi ty  l e n g t h  
S = 3.8317 ( f i r s t  zero of J ) 
0 1 1 
I f  the cavity squatness i s  described by 
Then 
where p =d so, 2g2+x2 
I t  i s  found that the optimum val ue for  p = 0.450 
- 
a 
when one wri tes  
Then one can define the new factor  U 
Using the formulae p u t  forth in section IV one can obtain the systematic 
frequency s h i f t  (section 10 i n  the program l i s t ed  in Appendix A ) .  Using the two 
new values of q obtained when the variable volume i s  i n  the open and closed 
configurations and subst i tut ing into equation (111.13) gives the s t a t i s t i c a l  
e r ror  for  d i f fe rent  values o f  U (iection 12 of the prugram 1 i s t i ng  - Appendix A ) .  
Such t h a t  
Ye have plot ted the s t a t i s t i c a l  and systematic frequency errors  as a 
function of L , t he  external volune length for g = 2, 3 and 4 for U = 7.5 and 2. 
3 
These p lo ts  are shown i n  Figures 5, 6 and 7. The values of  g = 3 or 4 fo r  U = 1.5 
o r  2 and L n, 10 cn give e r ro r  values tha t  a re  acceptable fo r  the present work. 
3 



CHAPTER VI 
ACTUAL D E S I G N  - COUCLUSIOUS 
Referring to  Figure 2 fo r  the  neaning of the various quant i t ies ,  the 
di-rensions fo r  a t r i a l  configuration are  7 i s ted below. 
A .  Fixed Vol unz 
The cavity i s  t o  be rad2 of  aluminum and the bulb will be cylindrical 
w i t h  a radius equal t o  .45 tha t  of the  cavity. The raxinum length of the 
cavity can be about 30" (l imited to the length o f  Pena l  loy sheets comsrcial  fy 
available) and i s  equal to  the length of the bulb. 
g i s  the r a t i o  o f  length t o  radius o f  the cavity. For g = 4 = d - 
a 
d x .45 cavi ty 
a 
bul b ( V I . 7 )  
So a = d x .45 - 33 x 2.54 x .45 = 8.6 crn 
bulb 4 4 
i s  the radius of the  bulb. 
For a nassr s table  t o  one p a r t  i n  lo1'+, the dimnsions fo r  the vari zble 
vol urns can be: 
V = 6250 c c  ( f o r  g = 4 )  q' = .442 
0 
R = 7 c n ;  H = 3  cs; R = 71 cm; R = 13 cm 
2 3 4 
D = .5 cn; 9D = .5 cn 
Bulb :-'ateri a1 : FEP Teflon. 
2, I0 C P R O G R A H  Hi-iI118 DATE:lZ-JAN-77 
2.20 C FOR k VARIABLE V O L *  C O N T A I N I N G  A CUT-OFF  I N  THE 
2*30 C NkRROW PART* 
2 - 4 0  C 
2.50 C THIS  F P O G R A H  ALSO HAS CHANGING ETA FRIHE 
2.60 C FROGRAM HODIFICATION DATE: 17-JAN-77 
8.90 C CTHE F O L L O W I N G  SECTION SETS UF ALL THE DEFAULT VALUES3 
l O * l O  C C T H I S  PART CALCULATES T#LSsfSTEHATIC ERROR3 
16.11 C 
10.20 S L3=IiS L 2 = 2 S i  
10-23 S Vl=PIt(E3"2#iL2-L3)f.3333XR332%H) 
LC, 25 S t f 2 = F I X  (RJ-2$L3-. 3333L38 iF;3-Z+(R4-11) - 2 t f i Z s  ( R 4 - 1 i  > 1 1 
ifi.zo S V3=PIw(LZ-L3jX(R4"2-R3^2) 
16 I 22 5 V n = V O f  VliVZSV3 
3G4Z3 S C1=2XFI*k3$iL2-L3) 
15.35 5 C 2 = P l a + !  ( R 3 - 2 - H 3 - 2  j 
16.40 5 C G = P l x ( R 2 - 2 )  
10.50 5 ~1=~Pl~~3~FSQT(R3n2iHH21+PI~CH332-R222)~ 
10*60 S A2=FSQTi(R4-D-R3)"2fL3-2> 
10.61 S A2=iRS+R4-D>%A2+2%R4PL3 
10+62 5 A Z = A Z f R 4 - 2 - ( R 4 - D j - 2  
10.53 S A2=FI+A2 
10.65 S A3=PI%(2SR4%(~2-L~i+(R44~-R33~)) 
10+70 5 ZZ=(A1+R2fR3)/CO 
ii,.75 S ZX=W1*(AlfA3)XZZ+W2fi;2$(ZZfA2,~'C2) 
10. $":, 5 Z"r'=-CJEYf;4ZX/(S~Fr$'lii) 
L c * E 5  S Z R = M L ~ I > ~ * . Z Z ~ U ~ ~ ( A ~ ~ A ~ ~ A ~ Z Z + C A ~ + A ~ ~ / ' C I  1 
10.95 S ZS=-~JEZb;.*ZR/(8%FI$Vii) 
13.92 f ~ZS-ZY~i0,?5~10.95~IGC?7 
- 1;,95 = SE=ZSt:G 10-98 
- - icl"T SEzrJ 
1 3 . 4 5  S SE=SE/lc42E09 
:id.54: D 3 . i  
11-05 C CCALCULATION OF E7 
11.06 C 
11.10 S VN=R4"2%L2+L3/3x(R3n2+(R4-I~)-2tR3$(fi4-I~)) 
11-12 S VN=FI* (VblfR3-2*H/3) 
1 m- c- 
11.30 S VP=VOfVN Q R ~ G ~ ~ J & %  P>cGr $3- 
11.50 S E=VP/VH POOR QUAFST~ 
11.70 S QA=VF/VO 
11 t40 S EX=O 
L1.95 1 12 
12110 C CCOHFUTE THE STATISTICAL ERROR ON THE FREQUENCY USING 
12t20 C THE HEW VALUE O F  E WITH THE ERROR FORMULA F R O M  HMD013 
12-30 C 
12.40 S EPx.5 
12*50 S C=.213669ES03/EP 
12t52 S C=C/U 
12.60 S OO=C*8/35000; 
12*62 S R=QOLVPi/VO 
12.70 S SO=3-6fiQ+Q"2;1 <-S@)12.72r12.72iR 
12+72 S SO=FAES(SQ) 
12.73 S J=FSOT(SQ) 
lZ*EO S H?i=(l+Q+J)/(I+Q-J) 
12,81 S O=QO%VP/VO 
12t82 S SL!=1-6*RfR-2;1 (-SQ)12t83t12t83iQ 
12+83 S J=FSQT(SRI 
12+84 S RP=(ltGiJ)/(ltQ-J) 
12.85 S G=(F-2*(RPn2tI))/((RF'-1)-2) 
12,90 S H=(R?f-2Sli/((RM-1)^2) 
12.95 S ER=FSRT(GfH)/(B-l) 
12.49 S 'f=Ez 
EINSERT AT THIS LOCATION A SUITABLE PLOTTING PROGRAH3 




Detailed design of a variable volume hydrogen maser

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