Fortran routine for Relay I trapped proton distribution measurement

Fillius, R. W.

English

NASA Technical Reports Server

f September 1, 1966 I 
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, /V&.5& * / / ‘L  * .  
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A Computer Routine f o r  Relay I Trapped Proton Dis t r ibu t ions  
c R. Walker F i l l i u s  f 
6 
I Universi ty  of Cal i forn ia  a t  San Diego, La  J o l l a ,  Cal i forn ia  
1. Introduct ion 
This note is  t o  descr ibe t h e  Fortran rout ine FGLAY I f o r  s c i e n t i s t s  
who d e s i r e  easy computerized access t o  t h e  trapped proton d i s t r i b u t i o n s  
measured by s a t e l l i t e  Relay I. 
that the  vas t  quan t i t i e s  of da t a  gathered by satel l i tes  are o f t en  d i f -  
It has been pointed 0v.t by McIlwain [1963] 
f i c u l t  or inconvenient t o  use i n  conventional pr in ted  form, and t h a t  a 
s u i t a b l e  computer program i s  an appropriate means t o  communicate these  
data. A program has been wr i t t en  t o  t ransmi t  Relay I r e s u l t s  i n  a fashion 
similar t o  McIlwain’s program for Explorer XV, al though t h e  computation 
procedure i s  not t he  same. This program has been run i n  both Fortran I V  
and Fortran 63, wi th  differences i n  con t ro l  cards and i n  t h e  names of 
l i b r a r y  f’unctions being the  only concerns of the  general  user.  
been deposited i n  t h e  National Space Science Data Center, and dupl ica te  
It has 
decks may be obtained by wr i t ing  
National Space Science Data Center 
Goddard Space F l ight  Center 
Greenbelt, Maryland 20771 
2. Instrumentation 
The instrumentation of Relay I has been described i n  o ther  repor t s  * 
[ F i l l i u s ,  1963; F i l l i u s  and McIlwain, 1963; McIlwain e t  al.,  19641. 
is a surmnary of t h e  o r b i t  and de tec tors  f o r  convenient reference.  
Table I 
# 
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. 
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c - 2- 
Table I 
Relay I Orbit and Instrumentation 
Launch: 
Inc l ina t ion :  
Perigee : 
Apogee : 
Anomalist i c  Period : 
Spin Rate: 
Sensor: 
Geometric Factor: 
Shielding : 
Proton Range: 
Sensor: 
Geometric Factor: 
Shielding: 
Proton Ranges : 
Relay I S a t e l l i t e  
12/14/62 
, 4 7 . 5 O  
1300 loll 
7500 loll 
185 min. 
2.7 rps 
Detector A 
0.9 cm sphere of p l a s t i c  s c i n t i l l a t o r  
0.33 cm omnidirectional 
1 .3  gm cm 
> 33.5 MeV 
2 
A1 over one hemisphere 
Detector B 
S i l i con  surface b a r r i e r  diode w i t h  deple t ion  
-2 depth 25 mg cm 
2 0.0136 cm ster d i r e c t i o n a l  * 
1.115 mg cm -2 
over look cone 
(air  equivalent)  N i  l i g h t  sh i e ld  
1.1 t o  14  MeV 
1.6 t o  7.1 MeV 
2.25 t o  4.7 MeV 
I 
. .  
Sensors: 
Geometric Factor: 
Proton Ranges: 
Sensor: 
Geometric Factor: 
- 3- 
Table I (cont . )  
Detector C 
Two s i l i c o n  L i  d r i f t  diodes w i t h  ac t ive  depths 
of 107 and 132 mg em2, operated i n  coincidence 
2 0.22 cm ster d i r e c t i o n a l  * 
18.2 t o  25 MeV 
25 t o  35 MeV 
35 t o  63 MeV 
Detector D 
0.25 cm cyl inder  of p l a s t i c  s c i n t i l l a t o r  
0.0027 cm s ter  d i r ec t iona l  * 2 
Proton Range: > 5.2 MeV 
* The d i r e c t i o n a l  de tec tors  are mounted perpendicular t o  the  satel l i te  
sp in  ax i s  and are gated by a magnetometer t o  record da ta  only when they 
point  within - 10' of t h e  plane perpendicular t o  t h e  l o c a l  magnetic f i e l d  + 
vector.  Thus they measure j the f l u x  of l o c a l l y  mirroring p a r t i c l e s .  
I' 
3. Data Reduction Procedure 
Data reduction w a s  ca r r i ed  out by a procedure o r ig ina l ly  used by 
McIlwain f o r  Explorer XV. The counting rates from each de tec tor  were 
in te rpola ted  i n  time t o  every crossing of se lec ted  magnetic s h e l l s  
(L = 1.5, 1.6, 1.7, e t c . ) .  
f o r  each L shell using t h e  function 
A least squares f i t  w a s  then made t o  the  da ta  
(CR) = A~ + A~ t + A (B/B~) + A,+ (B/B~$,+ (B/B,)"-~ lne 3 
D 
. .  - 4- 
where 
Bo = .311653 
tha t  L, 
i s  the  value of t h e  magnetic f i e l d  at t h e  equator f o r  
L3 
3 n 5 8 is se lec ted  by t h e  computer o r  by the  programmer f o r  t h e  
bes t  f i t .  
CR i s  t h e  counting rate, 
t i s  numbered i n  days and f rac t ions ,  beginning w i t h  1 on January 1. 1963. 
The coe f f i c i en t s  A1through A a re  punched out  on IBM cards which a l s o  con- 
t a i n  the  L value, t he  range of B covered by the  data,  and 100 times t h e  rms 
average of t h e  residuals .  I n  the  approximation of a good f i t  t h e  l a s t  num- 
b e r  resembles a per  cent e r ror ;  however, it is  not t o  be taken as an e r r o r  
bracket,  s ince counting s t a t i s t i c s  can range by severa l  orders of magnitude 
over t h e  e n t i r e  s h e l l  of force.  It i s  an ind ica tor  of the qua l i ty  of t h e  
da t a  and f i t .  The omnidirectional data from de tec to r  A i s  ca r r i ed  through 
the above procedure and then  is converted t o  d i r e c t i o n a l  f l u x  by computa- 
t i o n  combining t h e  methods of Farley and Sanders [1962] and Roberts [1965]. 
New cards are then punched f o r  the d i r ec t iona l  coe f f i c i en t s .  
RELAY I uses these decks as t h e  input data t o  determine the f l u x  a t  an  
a r b i t r a r y  point  i n  B, L space. 
n 
The rout ine 
4. Coverage 
The decks provided w i t h  RELAY I cover e ight  energy ranges of trapped 
protons over most of the o r b i t  from 1 .2  t o  2.2 e a r t h  radii. 
re turns  values f o r  t he  proton f lux i n  a spec i f ied  range as it stood on 
t h e  date  shown i n  Table 2. 
The rout ine 
- >- 
Deck Number 
1 
2 
3 
4 
5 
6 
7 
8 
Table 2 
Energy Range 
1.1 - 14 MeV 
1.6 - 7.1 
2.25 - 4.7 
> 5.2 
18.2 - 25 
25 - 35 
35 - 63 
> 35 
Reference Date 
1/1/63 
1/1/63 
1/1/63 
7/1/63 
1/1/63 
1/1/63 
1/1/63 
7/1/63 
5. Method of Computation 
On the  f i rs t  c a l l  t o  m Y  I the da ta  decks are read i n  and s tored  
L1, t h e  spec i f ied  t a b l e  i s  
In te rpola t ion  i s  then made t o  
1' i n  t ab l e s .  
searched f o r  fou r  L values bracketing L1. 
On a c a l l  t o  a general  point B 
B1, L1 along the  
radial dis tance,  
a t  t h e  four  g r i d  
from t h e  average 
'/3) where G 
t h ree  paths of constant B, constant B/Bo, and constant 
using a l e a s t  squares parabol ic  f i t  t o  Ine (CR) evaluated 
points.  The flux returned by the program i s  computed 
of these three in te rpola t ions  Cp = ( l / G )  exp (izl ( Ine 
i s  t h e  geometric f ac to r  i n  cm ster. I n  the event that  
3 
2 
a su i t ab le  g r id  does not e x i s t ,  or if  t h e  requested point  l i es  outs ide 
t h e  B limits of the  Relay data,  the program re turns  a negative answer. 
If one o r  more of t h e  interpolat ions cannot be made, t h e  program re turns  
t h e  average of those that can. This f i t t i n g  and averaging procedure serves  
t o  smooth t h e  data. 
Also  returned is  an ind ica tor  of da ta  r e l i a b i l i t y .  This i nd ica to r  
i s  computed s t a r t i n g  with the  average over t h e  fou r  g r id  l i n e s  of t he  
I 
. .  - 6- 
rms average of the res idua ls  t o  the f i t .  An rms average i s  taken between 
t h i s  and t h e  variance of t h e  three  in te rpola t ions ,  and t h e  r e s u l t  i s  ex- 
pressed as a per cent of t he  computed flux. 
100 per cent when t h e  points  are interpolated near o r  extrapolated beyond 
t h e  boundaries of the  coverage. Once again, t h i s  i s  not t he  probable 
e r ro r ,  but only an ind ica tor  of qual i ty .  
This number is  flagged t o  
6. C a l l  Parameters 
The subroutine has a five-parameter c a l l  l ist :  CALL IiELAY I (NA, 
EL, A J ,  R) .  
NA is a f ixed point  number specifying t h e  proton energy range 
desired (see Table 11) 
B is  a f l o a t i n g  point  number specifying t h e  magnetic f i e l d  at 
which t h e  i n t e n s i t y  i s  desired.  
(B < 1) o r  it can be normalized t o  the  equator f o r  t h e  speci-  
f i e d  s h e l l  of force (Bk 1.). 
which way B has been specif ied.  
B can be given i n  gauss 
The routine w i l l  recognize 
EL 
AJ 
R 
is  a f l o a t i n g  point  number which spec i f i e s  the L value a t  
which t h e  i n t e n s i t y  i s  desired.  
i s  a f l o a t i n g  point  number specifying t h e  returned i n t e n s i t y  
-2 -1 -1 i n  un i t s  of protons cm sec s ter  . If measurements 
were not obtained a t  the  point  specif ied,  AJ w i l l  be given 
as -.1. 
is  a f l o a t i n g  point  number giving an ind ica t ion  of da t a  
qual i ty .  Its computation is  explained i n  sec t ion  5 .  
7. Subroutines 
RELAY I uses the following spec ia l  subroutines: INTEFP, DEPUNC, 
JSERIE, EU.IAMDA, and PARFIT. Their funct ions are l i s t e d  b r i e f l y  below: 
R E m Y  I is  the  head subroutine. It i n i t i a l i z e s  t h e  da t a  a r rays  
and feeds INTERP. 
INTEFP d i r e c t s  t he  computing. It c a l l s  subroutines JSERIE, PARF'IT, 
acd R L ,  f o r  subcomputations and produces t h e  average 
in t e rpo la t  ions. 
- .  . 
' ,  - 7- 
* 
JSERIE 
PARFIT 
DEPUNC 
evaluates  the  f i t t i n g  funct ion on t h e  L s h e l l  f o r  a given B. 
obtains  R given B and L. 
computes t h e  l e a s t  square parabol ic  f i t  t o  t h e  values on t h e  
four  L l i n e s  surrounding t h e  requested point.  
decodes t h e  da ta  cards f o r  RELAY I. 
8. Timing 
RELAY I averages about 25 milliseconds per  c a l l  on CDC 3600. 
9. Diagnostic P r in t ing  
The i n t e r v a l  var iab le  KEYPNT i n  RELAY I controls  a pr in tout  option. 
If no i n t e r n a l  pr in tout  i s  observed, leave KEYPNT = 1. If t h e  r e s u l t s  
alone are desired,  set KEYPNT = 2. 
DECK B L TIME FLUX QUALITY 
If KEYF'NT = 3, an extensive pr intout  i s  cal led,  including t h e  t a b l e  of 
coe f f i c i en t s  on t h e  f irst  c a l l .  This option is intended only f o r  t rouble-  
shooting. 
A l i n e  w i l l  be pr in ted  i n  the  format: 
10. Tape Assignments 
The da ta  cards a re  read i n  from LOGICAL UNIT 5. 
Under KEYPNT options 2 and 3, t h e  output i s  pr in ted  on LOGICAL UNIT 6. 
Acknowledgements 
The author is  g r a t e f u l  f o r  the he lpfu l  advice of D r .  Carl E. McIlwain. 
The rout ine t o  convert from B. L. t o  r, h coordinates w a s  wr i t t en  by D r .  Charles 
Roberts of t he  B e l l  Telephone Laboratory. Checkout i n  Fortran I V  w a s  per- 
formed at  the  Western Data Processing Center a t  U.C.L.A., whose cooperation 
is  appreciated.  
and NASA grant  NsG-538. 
This research was supported i n  p a r t  by Relay Grant wr-116 
. .  . '. 
, *  . .  
-8- 
Ref e rem e s 
Farley, T. A. and N. L. Sanders, "Pitch Angle Distributions and Mirror 
Point Densities i n  the Outer Radiation Zone," J. G. R. 
(June, 1962). 
F i l l ius ,  R. W., "Sa te l l i t e  Instruments Using Solid State  Detectors, I' Res. 
Rept. SUI 63-26, Department of Physics and Astronomy, S ta te  University 
of Iowa, Iowa City, Iowa, 1963. 
F i l l i u s ,  R. W., and C. E. McIlwain "Solid-state Detectors f o r  Inner Zone 
Protons, Space Res. 3, 1122-1128, 1963. 
McIlwain, C. E., "The Radiation Belts, Natural and Ar t i f ic ia l"  Science, 
- 142, 353-361 (1963) 
McIlwain, C. E., R. W. F i l l ius ,  J. Valerio, and A. Dav4, "Relay I trapped 
Radiation Measurements, "NASA TN D-2516, December, 1964. 
Roberts, C.S., "On the Relationship between the Unidirectional and Omni- 
direct ional  Flux of Trapped Particles on a Magnetic Line of Force," 
J.G.R. 3, 2517-2527 (June 1, 1965). 
I 


A Computer Routine for Relay I Trapped Proton Distributions

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