* I , , * I

NASA TECHNICAL MEMORANDUM

I .

A N E N V I R O N M E N T A L M O D E L F O R V A N A L L E N B E L T P R O T O N S

N.4S4 TM X-53351

October 21, 1965 4

By William T. Roberts Aero-Astrodynamics Laboratory

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George C. M m s h d l l Spdce Flight Center, Han~suille, Alubdmd

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NASA - GEORGE C. MARSHALL SPACE FLIGHT CENTER

TECHNICAL MEMORANDUM X-53351

AN ENVIRONMENTAL MODEL FOR VAN ALLEN BELT PROTONS

William T. Roberts

ABSTRACT

,.,'2/2 c: The ma jo r i ty of t he manned and unmanned missions i n space f o r a t

l e a s t the next ten years w i l l be composed mainly of e a r t h o r b i t i n g s a t e l l i t e s and space s t a t i o n s . Although the re a r e many environmental a s p e c t s of space which m u s t be explored and e labora ted upon before the success fu l launching of such missions, few a r e s o c r i t i c a l as the r a d i a t i o n environment which w i l l be encountered.

The r a d i a t i o n environment for e a r t h o r b i t i n g v e h i c l e s w i l l c o n s i s t p r imar i ly of (1) Van Allen p a r t i c l e s , ( 2 ) s o l a r f l a r e p a r t i c l e s , and ( 3 ) g a l a c t i c cosmic p a r t i c l e s . Of these t h r e e , the Van Allen b e l t p a r t i c l e s p re sen t t h e g r e a t e s t hazard.

This r e p o r t summarizes the knowledge of t he energy spectrum and d i s t r i b u t i o n of the Van Allen proton b e l t as it i s known today. A computer program has been developed f o r c a l c u l a t i n g Van Allen p a r t i c l e s i n c i d e n t upon veh ic l e s i n e a r t h o r b i t s . Based upon the 1963 FLUX program of McIlwain, encounter as many as 1.1 x l o 8 protons/cm2/orbi t wi th 40 Mev - - < F < 110 MeV. Mev may be as high as 2.2 x l o7 protons/cm'/sec.

we f i n d t h a t a veh ic l e i n a h ighly e l l i p t i c o r b i t may

I n the magnetic equa to r i a l plane, the f l u x of protons wi th E - > .5

NASA - GEORGE C. MARSHALL SPACE FLIGHT CENTER

TECHNICAL MEMORANDUM X - 5 3 3 5 1

October 21, 1965

AN ENVIRONMENTAL MODEL FOR VAN ALLEN BELT PROTONS

BY

W i l l i a m T. ?.cherts

SPACE ENVIRONMENT GROUP AEROSPACE ENVIRONMENT OFFICE AERO-ASTRODYNAMI CS LABORATORY

TECHNICAL MEMORANDUM X-53351

AN ENVIRONMENTAL MODEL FOR VAN ALLEN BELT PROTONS

SUMMARY

The ma jo r i ty of the manned and unmanned missions i n space f o r a t l e a s t the next t en years w i l l be composed mainly of e a r t h o r b i t i n g s a t e l l i t e s and space s t a t i o n s . Although the re a r e many environmental a spec t s of space which must be explored and e labora ted upon before the success fu l launching of such-miss ions , few a r e s o c r i t i c a l as t h e r a d i a t i o n environment which w i l l be encountered.

The r a d i a t i o n environment f o r e a r t h o r b i t i n g veh ic l e s w i l l c o n s i s t p r imar i ly of (1) Van Al len p a r t i c l e s , ( 2 ) s o l a r f l a r e p a r t i c l e s , and (3) g a l a c t i c cosmic par t ic les . Of these t h r e e , the Van Al len b e l t par t ic les p r e s e n t the g r e a t e s t hazard.

This r e p o r t summarizes.the knowledge of t he energy spectrum and d i s t r i b u t i o n of t he Van Al len proton b e l t as i t is known today. A computer program has been developed f o r c a l c u l a t i n g Van Allen p a r t i c l e s i n c i d e n t upon veh ic l e s i n e a r t h o r b i t s . Based upon the 1963 FLUX program of McIlwain, we f i n d t h a t a veh ic l e i n a h ighly e l l i p t i c o r b i t may encounter as many as 1.1 x lo8 protons/cm‘/orbit wi th 40 Mev 5 F _> 110 MeV. Mev may be as h igh as 2.2 x l o 7 protons/cm’/sec.

I n the magnetic equa to r i a l plane, the f l u x of protons w i t h E 2 .5

I. INTRODUCTION

Before 1958 the Van Allen r a d i a t i o n zones were not known t o e x i s t , and t h e only forms of r a d i a t i o n expected ou t s ide of t he e a r t h ’ s atmosphere were the low f l u x , high energy, cosmic rays and occasional s o l a r f l a r e s . Although l i t t l e information was ava i l ab le about s o l a r f l a r e s , they were known t o be composed of high energy p a r t i c l e s and t o c o r r e l a t e temporally w i t h g i g a n t i c e rupt ions on the photospheric s u r f a c e of t he sun.

The f i r s t American s a t e l l i t e , Explorer I, c a r r i e d a Geiger counter f o r t h e purpose of ob ta in ing fu r the r information on the f l u x of cosmic r a y p a r t i c l e s . The experiment worked wel l u n t i l the s a t e l l i t e reached about a thousand ki lometers a l t i t u d e , a t which po in t the counting r a t e suddenly decreased. The experimenters (Van Allen, McIlwain, Ludwig, and Ray) were susp ic ious of what was happening, bu t did not pub l i c i ze t h e i r

susp ic ions u n t i l a f t e r some Explorer 111 da ta were examined. same phenomenon was observed on Explorer 111, Van Allen announced (Ref. 38) t h a t t h e apparent decrease i n the Geiger counter was due t o s a t u r a t i o n by a h igh f l u x of p a r t i c l e s .

When the

These p a r t i c l e s , which a r e trapped by the magnetic f i e l d of t he e a r t h , p resent a r a d i a t i o n problem which must be overcome before extended e a r t h o r b i t a l missions of manned spacec ra f t can be performed. I n a d d i t i o n , the environment t o which unmanned s a t e l l i t e s are exposed may decrease the l i f e t i m e of on-board experiments, power supply, t e lemet ry , e t c . Thus, extensive environmental s t u d i e s of the r a d i a t i o n zones should be conducted before the development of s o p h i s t i c a t e d long- l i f e t ime s a t e l l i t e s .

This r e p o r t sunnnarizes the known f a c t s and sugges ts a poss ib l e environmental model f o r Van Allen b e l t protons.

11. MOTION OF CHARGE PARTICLES I N THE MAGNETOSPHERE

The motion of charged p a r t i c l e s trapped i n the ea r th ’ s v i c i n i t y by the geomagnetic f i e l d is inf luenced by t h i s f i e l d . Pe r tu rba t ions caused by an e l e c t r i c f i e l d imposed by the e a r t h ’ s e q u a t o r i a l r i n g c u r r e n t a l s o a f f e c t the o r b i t a l motions of these charged p a r t i c l e s .

I We may consider a charged p a r t i c l e moving i n t h i s magnetosphere+ as + being subjected t o the geomagnetic f i e l d , B y and a v a r i a b l e f i e l d , E, due t o the high a l t i t u d e (-6Re) r i n g cur ren t . (% = geocen t r i c e a r t h r a d i i ) . The f o r c e , 3, exe r t ed on t h e pa r t i c l e moving wi th v e l o c i t y , v , i s 3

+ + + - + F = q (E + v X B ) ,

where q is the t o t a l charge of the p a r t i c l e . t he e f f e c t s of the g e o m a g n e t i c f i e l d on the p a r t i c l e . normal t o the plane formed by v and 3; thus , the pa r t i c l e is induced, assuming t h a t no o ther forces a re p resen t , t o move i n a c i r c l e w i t h no loss i n k i n e t i c v e l o c i t y .

We w i l l he re consider+only The f o r c e , F, is

I f w e consider the po r t ion of ?normal t o the magnetic f i e l d as vI, we may say tha t

mvi2

r - - - q”L BY

2

where r is the Larmor r a d i u s , t h e r ad ius of t h e c i r c l e i n which the p a r t i c l e moves, o r

The Larmor frequency, w, is then

The par t ic le is now i n space moving i n a c i r c l e which is dependent upon the magnetic f i e l d s t r e n g t h , t h e p a r t i c l e ' s charge, mass, and v e l o c i t y normal t o t h e magnetic f i e l d . When the p a r t i c l e begins t o o r b i t , t h e c e n t e r of t he o r b i t is located on a p a r t i c u l a r " l i n e of force" of t he magnetic f i e l d . This s p e c i f i c l i n e of fo rce then remains the cen te r of g y r a t i o n o r "guiding center" of the p a r t i c l e , un less t h e p a r t i c l e i s subjec ted t o some ex te rna l fo rce . The o r b i t of p a r t i c l e s trapped i n t h e geomagnetic f i e l d is subjec ted t o pe r tu rba t ions caused by the presence of t h e r i n g cu r ren t , as we l l as inhomogeneities and slow v a r i a t i o n s of t he f i e l d i t s e l f .

The component of v e l o c i t y , v I 1 , which is p a r a l l e l t o t he magnetic f i e l d must a l s o be considered. causes the p a r t i c l e t o o s c i l l a t e between "mirror points" i n the nor thern and southern hemispheres. The p a r t i c l e s are r e f l e c t e d a t t hese po in t s of equal magnetic f i e l d s t r eng th . equator of t he e a r t h , i t is a t the po in t of minimum f i e l d s t r e n g t h on t h a t l i n e of force . As i t moves e i t h e r n o r t h o r sou th a long that l i n e of fo rce , i t encounters a s t ronger f i e l d which i n t u r n exerts a fo rce , F , , , on the par t ic le , which is opposed t o v , , .

This component of t h e p a r t i c l e ' s v e l o c i t y

When the p a r t i c l e is a t the magnetic

This f o r c e is -dependent upon t h e magnetic moment, p, of t h e par t ic le ,

where

or

3

F i n a l l y , the r e t a rd ing fo rce on a p a r t i c l e moving along a l i n e of fo rce i n t o a region of more in t ense magnetic f i e l d is given by

where the (VB) d5notes the g r a d i e n t of the magnetic f i e l d which is i n t h e d i r e c t i o n of B. It should be remembered t h a t t h i s same fo rce is exer ted on a p a r t i c l e leaving a reg ion of more in t ense magnetic f i e l d , i n which case i t is then an a c c e l e r a t i n g fo rce .

These p a r t i c l e s w i l l be subjec ted t o d r i f t i n g motions due t o e x t e r n a l fo rces exerted by e l e c t r i c f i e l d s , the g r a v i t a t i o n a l f i e l d , and inhomo- g e n e i t i e s i n the geomagnetic f i e l d . We w i l l cover these very b r i e f l y .

-+ I f the p a r t i c l e moves i n the presence of an e l e c t r i c f i e l d , .E, w i t h

a component perpendicular t o B’ then a new v e l o c i t y , $, is def ined such t h a t

+ -3 2x2 v = w + - .

B 2

+ --f Since E and B a r e assumed cons tan t ,

The d r t ve loc i ty then r e Z X i?

ilts from the - t h e d r i f t ve loc i ty , wd, may be found by B2

e m . I n t h e r words,

I n the same re spec t , the g r a v i t 3 t i o n a l f o r c e on a p a r t i c l e having a component mgl perpendicular to B y i e l d s a d r i f t v e l o c i t y

4

The v a r i a t i o n s i n the magnetic f i e l d which the p a r t i c l e encounters w i l l ' a l s o cause a t h i r d d r i f t v e l o c i t y which takes the form,

where R is the r ad ius of curvature of the geomagnetic l i n e of force .

111. MAGNETOSPHERE

Since p a r t i c l e s a r e trapped i n the geomagnetic f i e l d , perhaps some e l a b o r a t i o n on the e a r t h ' s magnetosphere is necessary. magnetic f i e l d forms a d e f i n i t e "magnetic pocket" around us which has become known as the magnetosphere. The boundary of t he magnetosphere is determined by the s o l a r wind which "blows" r a d i a l l y outward from the sun. A t a c e r t a i n po in t above the e a r t h , the geomagnetic f i e l d s t r e n g t h equals t he k i n e t i c energy of t h e s o l a r wind. I n t h a t reg ion , t h e r e is a t u r b u l e n t , chao t i c , intermingl ing of magnetic l i n e s of fo rce and e n e r g e t i c p a r t i c l e s , n e i t h e r of which is dominant. as the magnetospheri'c boundary or t r a n s i t i o n zone. I n the magnetosphere, t h e geomagnetic f i e l d con t ro l s , while ou t s ide the magnetosphere, the s o l a r wind i s t h e dominant energy mechanism.

The e a r t h ' s

This reg ion is known

The inner boundary of t he t r a n s i t i o n zone, which is c a l l e d the magnetopause, occurs a t about 10 R e on the sunward s i d e of the e a r t h , wh i l e t he ou te r boundary of t he t r a n s i t i o n zone is i n t h e form of a c o l l i s i o n l e s s shock wave a t about 3-4 Re beyond the magnetopause.

Figure 1 i l l u s t r a t e s the f i e l d s t r e n g t h F, a s we l l as i t s s p a t i a l coord ina te s , 8 , and (J ( a l s o s e e Reference 3 4 ) . A s would be expected, t h e shock wave ou te r boundary i s most c l e a r l y seen by a smoothing ou t of F, w i t h the d i r e c t i o n components s t i l l v a r i a b l e , though l e s s so .

The magnetopause extends around the e a r t h in the apparent form of a n elongated teardrop wi th the t a i l po in t ing d i r e c t l y away from the sun. The shock wave, however, appears as a shroud and shows no tendency toward convergence. Figure 2 i l l u s t r a t e s the r ecen t i n t e r p r e t a t i o n of the IMP-I d a t a .

5

0 cu 0 d

0 0 0 0 m o m + I

A

v) 0 E E 0 m Y

I L L

CD

0 cu

Q) [L

0) V c 0 v)

Y

c .- 5 0 V

c Q) 0 0 Q) W

.- L c

0

6

W

W I P, v)

z W U = L 0

a

e

7

The n e u t r a l s h e e t extending toward the magnetic " t a i l " is an a r e a i n which a magnetic n e u t r a l s u r f a c e e x i s t s . conta in an excess of p a r t i c l e s s o t h a t i t was prev ious ly thought t o be a t h i r d r a d i a t i o n zone. A t p re sen t , however, the f e e l i n g is t h a t these excess p a r t i c l e s a r e necessary s o t h a t t h e i r combined magnetic moments may balance the geomagnetic f i e l d . reg ion could be the source of t he h igh energy a u r o r a l p a r t i c l e s . Per turba t ions occurr ing i n the f i e l d would produce a plasma pinch e f f e c t which could a c c e l e r a t e the low energy p a r t i c l e s i n the n e u t r a l s h e e t t o very high v e l o c i t i e s .

This reg ion appears t o

It has been suggested t h a t t h i s

The conf igura t ion of "ea r th , r a d i a t i o n b e l t , and magnetosphere" is very much l i k e t h a t of a t y p i c a l comet wi th the e a r t h r ep resen t ing the nucleus, t he Van Al len b e l t s r ep resen t ing the coma, and the magnetosphere represent ing the comet's t a i l .

The IMP-I da t a show no i n d i c a t i o n of convergence of the magnetospheric boundary even though t h e , s a t e l l i t e apogee extended out t o 200,000 k i l o - meters . Thus, i t is presumed t h a t the magnetospheric t a i l extends out wel l beyond the o r b i t of t he moon.

I V . THE B-L COORDINATE SYSTEM

Perhaps the b e s t way t o exp la in the B-L coord ina te system f o r t rapped ionized p a r t i c l e s i s t o take a na ive approach. One normally th inks of a magnetic f i e l d i n terms of t he so -ca l l ed " l i n e s of force." Each " l i n e of force" is an i n d i c a t i o n of t he d i r e c t i o n of t he magnetic f i e l d a long i t , and the f i e l d s t r e n g t h is determined by the compactness of t hese l i n e s of force. The fol lowing ske tch (Figure 3) shows t h i s concept f o r a simple d ipole magnetic f i e l d .

I FIGURE 3

I f t h i s d i p o l e is assumed t o be enclosed i n a sphere , then the e a r t h ' s magnetic f i e l d could be roughly approximated i n t h i s way. I f po in t s A and C a re two po in t s along the same l i n e of fo rce , which may be designated as L, the magnetic f i e l d s t r e n g t h , B, is much more i n t e n s e a t C than a t A. I f a coord ina te system is cons t ruc ted based upon t h e f i e l d s t r e n g t h and l i n e s of fo rce , t he r e s u l t i n g system could be used t o s p e c i f y equal po in t s i n any f i e l d .

B is r e l a t i v e l y easy t o specify. It is simply t h e f i e l d s t r e n g t h a t any po in t i n ques t ion . But how is L def ined? For s i m p l i c i t y , l e t us d e f i n e L as the r a d i a l d i s t ance t o the l i n e of f o r c e i n ques t ion , measured i n the magnetic equator ia l plane. Thus, i n Figure 3 the L coord ina te f o r po in t A is 2R, where R is the r a d i u s of t he sphere enc los ing t h e magnetic d ipole . The L coord ina te f o r p o i n t C is a l s o 2R, and here one w i l l n o t i c e that poin t C does no t l i e a t 2R r a d i a l d i s t a n c e from the c e n t e r of t he sphere. This discrepancy i s accounted f o r by the d i f f e r e n t va lue of B a t po in t C as compared t o po in t A.

It is i n t e r e s t i n g t o r e a l i z e t h a t many s a t e l l i t e s i n n e a r - c i r c u l a r o r b i t s which c a r r y experiments t o determine the .Van Allen r a d i a t i o n b e l t environment use t h e term L as a n ind ica t ion of t he geomagnetic l a t i t u d e . A s can be seen from Figure 3, t h i s is an accep tab le procedure.

Although t h i s has been a very crude approximation, i t is s u i t a b l e i n terms of the func t ion of t h e B and L coord ina te system. Actua l ly , though B is .as def ined i n the previous d i scuss ion , t he geomagnetic f i e l d is no t adequate ly represented by a d ipo le f i e l d . I n f a c t , a dev ia t ion of 3 per cen t of the ca l cu la t ed f i e l d a t a p o i n t from the a c t u a l f i e l d may r e s u l t i n an e r r o r of move than an order of magnitude between the ca l cu la t ed f l u x and the measured f lux. For t h i s reason , t h e earth's magnetic f i e l d is usua l ly determined from a s p h e r i c a l harmonic expansion, which g ives a n adequate representa t ion of the geomagnetic f i e l d .

The term L is a func t ion of B and the i n t e g r a l i n v a r i a n t , I. I f we denote t h e "mirror points" as M, and M, f o r t he nor thern and sou the rn hemispheres, r e s p e c t i v e l y , and ds as a segment of pa th l eng th along t h e l i n e of f o r c e connecting these "mirror po in t s ,I' then

Mn

v , , ds .

9

This forms a s h e l l a long which p a r t i c l e s a r e constrained t o move. This s h e l l contains p a r t i c l e s w i th a g iven energy spectrum. P a r t i c l e s of h igher energy l e v e l s w i l l have t h e i r "mirror points ' ' a t lower a l t i t u d e s wi th in t h i s s h e l l , assuming equal p i t c h angles . The p i t c h angle , a, may be defined by

I1 a = a r c cos - , v t

where v t i s the p a r t i c l e ' s t o t a l v e l o c i t y and v , , i s t h a t component of v e l o c i t y p a r a l l e l t o t h e magnetic f i e l d i n the geomagnetic e q u a t o r i a l plane.

V. SOURCES OF CHARGED PARTICLES

One of the main problems which remain t o be solved i n expla in ing t h e Van Allen r a d i a t i o n b e l t s is the quest ion of t he source of these h igh energy p a r t i c l e s . The two main sources of p a r t i c l e s appa ren t ly a r e the decay of neutrons caused by cosmic r a y i n t e r a c t i o n s wi th t h e atmosphere, and t h e "leaking in" of s o l a r p a r t i c l e s a t t he poles and d i f f u s i o n through the magnetospheric boundary. The neutron source has been w e l l e s t a b l i s h e d as a con t r ibu to r of p a r t i c l e s i n the inner Van Al l en b e l t .

Cosmic rays a r e inc iden t a t t he e a r t h a t about a rate of 2.5 p a r t i c l e s These par t ic les range i n ene rg ie s from a few Mev t o about l o9 (cm2 s e c ) - l .

Bev. I n the process of s topping these h igh energy p a r t i c l e s , a n average of about seven secondary neutrons are produced p e r cosmic r a y par t ic le . These neutrons then decay i n t o protons and e l e c t r o n s which a r e i n t u r n captured by the geomagnetic . f i e l d .

So la r p a r t i c l e s are suspected of en te r ing t h e magnetosphere a t the po la r regions, where t h e l i n e s of fo rce o f f e r the l e a s t r e s i s t a n c e . t hese p a r t i c l e s e n t e r as a h igh energy p la sma from a s o l a r f l a r e , t h e r i n g c u r r e n t is s t rongly enhanced. are dispersed throughout t h e magnetosphere once they have en te red is a s u b j e c t of controversy.

When

The p r e c i s e way i n which t h e s e p a r t i c l e s

There i s a l s o the p o s s i b i l i t y t h a t s o l a r par t ic les d i f f u s e i n t o the magnetosphere. Since t h e r e is always a s o l a r plasma ( i n the form of the s o l a r wind) surrounding the magnetosphere, p a r t i c l e s could e n t e r t he r a d i a t i o n zones i n t h i s manner. The problem arises whea one t r i e s t o exp la in how these p a r t i c l e s wi th energ ies of a few hundred e l e c t r o n v o l t s ( i n the so l a r wind) a re acce le ra t ed i n t o t h e MeV energy range. One might

10

suspec t t h a t the a c c e l e r a t i o n of p a r t i c l e s could take p lace i f t h e r e were a r a p i d change i n B y s ay during magnetic storms. A l a r g e v a r i a t i o n i n B would produce a pinch e f f e c t which i n t u r n could a c c e l e r a t e p a r t i c l e s t o high v e l o c i t i e s . There is a l s o a theory t h a t p a r t i c l e s may be acce l - e r a t ed by an electromagnet ic f i e l d exe r t ing a f o r c e on the charged p a r t i c l e s (Reference 39) .

V I . THE VAN ALLEN BELT MODEL

The Van Allen b e l t s c o n s i s t mainly of protons and e l e c t r o n s t rapped i n the magnetic f i e l d of the ear th . e l e c t r o n component of the Van Allen b e l t s and dea l on ly wi th the pro ton b e l t . f l u x a t - 1.5 measured a t the geomagnetic equator. according to f l u x and energy spec t ra of t h e p a r t i c l e s i s described.

In the present r e p o r t , we ignore t h e

This b e l t extends from about 1.1 R e ou t t o about 8 wi th peak The proton component

The ques t ion of what should be used as a threshold va lue f o r the energy spectrum is one which i s not e a s i l y answered. By moving the energy threshold up and down, one is i b l e tc? behold a uniquely changing p i c t u r e of t he r a d i a t i o n zones i n space. This is due t o the f a c t t h a t reg ions of h igh f l u x , low energy p a r t i c l e s w i l l be overlooked i f t he energy threshold is too high, whereas regions of h igh energy, low f l u x p a r t i c l e s might be obscured by s e t t i n g the energy threshold too low. T k e ~ ~ e r g y spectrum is a complicated func t ion when the energy threshold is low a l s o . Thus, f o r manned space f l i g h t , we u sua l ly consider only protons wi th E 2 40 MeV. For unmanned s a t e l l i t e s , the problem is even more complicated. Since many experiments and suppor t ing equipment may be exposed d i r e c t l y t o the f l u x of p a r t i c l e s i nc iden t upon them, i t is necessary t h a t we have a r e l i a b l e r a d i a t i o n environment f o r cons ide ra t ion i n designing the veh ic l e s . Obviously, then, we need t o s tudy the e n t i r e energy spectrum of trapped p a r t i c l e s .

This problem would be challenging enough even i f the trapped p a r t i c l e s were temporally s t a b l e . However, t h i s is f a r from t r u e , e s p e c i a l l y i n t h e case of ou te r zone e l ec t rons . These p a r t i c l e s undergo spa t i a l as we l l as temporal v a r i a t i o n s i n f l u x by as much as an order of magnitude i n a matter of a few hours , and f o r the coup de grgce, even the energy spectrum a t a p a r t i c u l a r po in t i n space has been observed t o change r a d i c a l l y i n a s h o r t time.

It appears then t h a t , i f w e a r e t o cons t ruc t a model of low energy, h igh f l u x p a r t i c l e s i n the r a d i a t i o n zones, i t should be very s i m p l e . Then as our knowledge of the causa t ive e f f e c t s i nc reases , w e may update our model accordingly.

It would seem extremely inadvisable a t t h i s time t o a t tempt t o cons t ruc t a complex model based upon our present concepts of the Van Allen r a d i a t i o n

11

zones and t h e i r v a r i a t i o n s . Some of the problems which must be answered f i r s t a r e (1) how do trapped p a r t i c l e s r e a c t t o changes i n the e a r t h ' s r i n g cu r ren t , t o changes i n s o l a r a c t i v i t y , and as the sun -ea r th -pa r t i c l e angle v a r i e s l o n g i t u d i n a l l y , ( 2 ) how does the e a r t h ' s magnetic f i e l d r e a c t t o these same f a c t o r s , and ( 3 ) t o what o t h e r , i f any, pe r tu rb ing fo rces a r e trapped p a r t i c l e s s u b j e c t ?

Let us now e l abora t e somewhat on poss ib l e pre l iminary models of t he Van Allen r a d i a t i o n b e l t .

One of the p r i m a r y experimental problems i n measuring the p a r t i c l e s i nc iden t upon a counter i n space is t h a t of de f in ing the type of p a r t i c l e which causes a p a r t i c u l a r counter t o count. For in s t ance , some f r equen t ly used counters on board experimental s a t e l l i t e s a r e l i s t e d below (Table I) wi th the p a r t i c u l a r types of r a d i a t i o n t o which they a r e s e n s i t i v e .

TABLE I

Type of Detector Shie I d inq P a r t i c l e s t o which S e n s i t i v e

Anton GM 302 265 mg/cm2 Mg Protons (E _> 23 MeV) + 400 mg/cm2 s t e e l

E lec t rons (E - > 1 . 6 MeV)

Anton 213 1 . 2 mg/cm2 mica Protons (E 500 Kev) (Direc t ional )

Elec t rons ( E . > 40 Kev) - 48 mg/cm2 A 1

1 . 2 mg/cm2 mica p lus sweeping magnet

Protons (E 2 4.5 MeV)

Elec t rons (E 2 230 Kev)

Protons (E 2 500 Kev)

E lec t rons (E 2 200 Kev)

I f a l a rge a r r a y of d e t e c t o r s could be c a r r i e d on board a s a t e l l i t e wi th a highly e c c e n t r i c o r b i t and a reasonably long l i f e t i m e , a broad p i c t u r e of the Van Allen b e l t s could be obta ined .

12

The Van Al len inner zone is composed of protons w i t h peak i n t e n s i t y a t about 3600 ki lometers above the geomagnetic equator . inner zone is f a i r l y s t a b l e . This is t o say that the f l u x of p a r t i c l e s , as we l l as t h e energy spectrum, i s cons tan t over a long time per iod. However, one might suspec t t h a t eventua l ly a long-term v a r i a t i o n w i l l show up i n t h e inner zone, r e s u l t i n g from two e f f e c t s . F i r s t , t he cosmic ray f l u x i n c i d e n t upon the e a r t h ' s upper atmosphere is about a f a c t o r of two higher a t minimum s o l a r a c t i v i t y . Therefore , more albedo neutrons w i l l be a v a i l a b l e t o the magnetic f i e l d f o r decay and subsequent cap tu re of charged p a r t i c l e s (see Sec t ion V) . I n a d d i t i o n , a t least i n the lower p a r t of t he inner r a d i a t i o n b e l t , the atmosphere may be less dense (Ref. 25) during minimum s o l a r a c t i v i t y , thus g iv ing the p a r t i c l e s longer l i f e t i m e s . The l i f e t i m e s of trapped p a r t i c l e s depend upon t h e i r mean f r e e pa ths , which i n t u r n a r e inve r se ly dependent upon the average d e n s i t y of t h e medium through which the p a r t i c l e s p a s s .

The

A good method of measuring the e x t e n t of t h e v a r i a t i o n i n atmospheric u=r.u ' - --:*-- & L , z t !:i=h - a l t i t u d e s might be t o monitor t h e change i n the decay r a t e of i nne r zone par t ic les . I f the decay r a t e increases d r a s t i c a l l y as s o l a r a c t i v i t y increases , t he i cc rease could probably be a t t r i b u t e d t o a n inc rease of a tmospheric d e n s i t y over the p a r t i c l e ' s l ength . This specu la t ion i s based upon the change i n decay r a t e s of a r t i f i c i a l r a d i a t i o n zones z:t:? by Hess (Ref. 25).

The inner zone protons were a t one t i m e thought t o be f a i r l y loca l i zed below about 2 Re; however, i t now appears t h a t l o w energy protons w i l l be found a l l t he way ou t t o the magnetospheric boundary on the sunward s i d e of t h e ea r th .

F igure 4 (curve M) shows t h e f l u x versus L va lues of McIlwain (Ref. 1) f o r p a r t i c l e s of energ ies g r e a t e r than 40 MeV. The hump a t 2.2 R e is due t o t h e a r t i f i c i a l r a d i a t i o n p a r t i c l e s , and the a r e a from 3 Re out r e s u l t s from estimates of upper l i m i t s of protons. Curve R i s a s i m i l a r , bu t hypo the t i ca l , curve constructed on the b a s i s of experimental d a t a gleaned from s e v e r a l sources (Ref. 1, 3 , 6, 7, 8, 11, 13, 3 5 ) . The second curve, however, assumes a low energy threshold l e v e l of 500 Kev f o r protons. Curve R does no t take i n t o account t he secondary proton peak shown on curve M, and inc lades an exponent ia l i n t e r p o l a t i o n of f l u x wi th he igh t .

Again, i t should be pointed out t h a t i n the cons t ruc t ion of t hese graphs no a t t e m p t w a s made t o account f o r temporal v a r i a t i o n s . I n t h e s a m e sense , the spur ious anomalous reg ions w i l l not be considered.

13

L (Earth Radii)

I

5

4

3

i

c

I I I

Curve M, E 2 40 Mev Curve R, E 2 500 Kev

1 I 2 3 4 5

FIG. 4. FLUX OF PROTONS IN THE GEOMAGNETIC EQUATORIAL PLANE

14

[ N ( L E ) ]

Energy (Mev)

FIG. 5. ENERGY - F L U X SPECTRUM FOR PROTONS AT VARIOUS L VALUES IN THE GEOMAGNETIC EQUATORIAL PLANE

15

Figure 5 i l l u s t r a t e s the flux-energy curve we have assigned t o these f l u x curves found i n Figure 4 . A family of curves was cons t ruc ted which seemed t o be b e s t ind ica ted by the var ious da t a sources mentioned i n conjunct ion wi th the cons t ruc t ion of Figure 4 . been found t o vary s p a t i a l l y as we l l as temporally, bu t no a t t e m p t is made he re t o account f o r t h i s v a r i a t i o n .

The energy spectrum has

A l e a s t squares polynomial f i t t o these curves y i e l d s a method of f ind ing the p rec i se va lue of N (2 E) f o r any given E and L va lue s p e c i f i e d . The d a t a used he re a r e aga in r e s t r i c t e d t o the magnetic e q u a t o r i a l plane. This method, programmed by M i s s Linda Flenker , is found i n Appendix A .

We s e e from our previous d i scuss ion t h a t t he proton b e l t is s u b j e c t t o the geomagnetic f i e l d . A t the n a d i r , t h i s f i e l d is much changed from the sunward s i d e of t he e a r t h . Thus, the proton b e l t w i l l no t extend t o the magnetopause. In s t ead , t he re w i l l be a sharp cu to f f of protons beyond about 5 Re. This is due t o the d i s t o r t i o n s of t he f i e l d by the e longat ion of t he magnetosphere through the a c t i o n of t he s o l a r wind (see Sec t ion 111). Because of t h i s d i s t o r t i o n , the p a r t i c l e s w i l l no t move along l i n e s of force def ined by the i n t e g r a l i n v a r i a n t , b u t i n s t ead w i l l be sub jec t t o pe r tu rba t ions caused by the s t r e t c h e d l i n e s .

I n t h i s reg ion of the magnetosphere, the f i e l d seems t o r e a c t s t r o n g l y t o such things as s o l a r f l a r e s , enhanced r i n g c u r r e n t s , etc. The e f f e c t is t h a t these pe r tu rba t ions s e r v e t o keep the magnetosphere beyond about 5-8 Re r e l a t i v e l y c l e a r of trapped protons on the side of the e a r t h away from the sun.

Electrons i n t h i s reg ion do appear b u t t h e i r occurrence is , a t the p re sen t time, unpredic tab le . The e l e c t r o n component of t he r a d i a t i o n b e l t w i l l be t h e s u b j e c t of a l a t e r r e p o r t .

16

APPENDIX A

METHOD OF CURVE FITTING BY LEAST SQUARES POLYNOMIALS

This method gives a s i n g l e equat ion r ep resen ta t ion of a family of curves ( i . e . , a means of ob ta in ing a func t ion i n terms of more than one independent v a r i a b l e ) .

Given: E (Energy i n Mev); L; N (Flux)

To Find: N = f (E, L)

F i r s t ,

L = 1.5, I n N, = alo + allE + a1g2 + a13E3 + a14E4

L = 2.0, I n N, = a20 + a21E + a,$* + aZ3E3 + a,,E4

I, = 3-0, I n N7 = n - .-. 4- .q--?? + a--F2 ~ ~ ~ 2 7 4 -c _ _ _ - ,<, 7 I -

L = 4.0, In N, = a40 + aelE + + a43E3 + a44E4

L = 5.0, In N, + a50 + a51E + a s s 2 + a53E3 + a,,E4

A f o u r t h degree curve w a s used s i n c e higher degrees increased the accuracy only s l i g h t l y . The e r r o r s incurred i n the f o u r t h degree curve f i t a r e i n t h e hundredths decimal place.

This curve f i t g ives the c o e f f i c i e n t s (ao, al, . . . a,) f o r which the equat ion

I n N = a. + alE + a g 2 + a,E3 + a 4 E 4

is s a t i s f i e d . I n t h i s f i r s t s t e p I n N is obtained as a func t ion of E, because the c o e f f i c i e n t s (ao, a,, ... a,) a re a func t ion of E.

Second ,

ao' s = A. + AIL + A S 2 + A1L3

al's = Bo + BIL + BA2 + B3L3

a2's = c0 + C,L + ~ 9 2 + C3L3

a3's = D o + DIL + D&2 + D3L3

a4's = Fo + FIL + F S 2 + F3L3 1 7

A third-degree polynomial w a s f i t i n t h i s case wi th e r r o r s occurr ing i n the hundredths decimal place.

These f i n a l c o e f f i c i e n t s (A, B , C, D, F) (see Table 11) are a func t ion of both E and L; and a r e obtained by f i t t i n g t h e c o e f f i c i e n t s (a all, . . . a5*) h o r i z o n t a l l y w i t h r e spec t t o L.

Third ,

In N = (Ao + AIL + A S 2 + A3L3)

+ (Bo + BIL + B&* + B3L3)

+ (C, + CIL + C&2 + C3L3)

+ (Do + DIL + D G 2 + D3L3)

+ (Fo + FIL + F S 2 + F3L3) = X

TABLE I1

A 0 = +.249547875 + 02 A 1 = -.694389747 + 01

A, = -.785188961 - 01

A, = +.125157848 + 01

Bo = -.295686833 - 00 B 1 = -.513692717 - 01

B, = -.126209083 - 02

Co = +.574196303 - 02 C, = +.13114399 - 02 C, = -.224835894 - 03

C, = +.288122124 - 05

D,= -.963839773 - 05

D, = +.585676357 - 06

F l = -.255271946 - 07

F, = -.698480307 - 08

B2 = -.224835894 - 03

D o = -.816146665 - 04 D, = -.144865679 - 05

Fo = +.462310907 - 06 F, = +.392723857 - 07

18

where

I n N = f (E, L)

t o ob ta in

Input values:

Each input va lue cons i s t s of an E va lue and i ts corresponding L va lue .

'LO run chis program tne programmer needs the equat ion given i n s t e p 3, t he c o e f f i c i e n t va lues f o r t h i s equat ion ( the c o e f f i c i e n t s a r e cons tan ts f o r a l l runs ) , and a s e t of p and L va lues -

ou tput :

On p r i n t out shee t

Name

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23

14. Dessler , A. J. and B. J. O'Brien, "Penet ra t ing P a r t i c l e Radiation," S a t e l l i t e Environment Handbook, Stanford Univers i ty P res s ; S tanford , Ca l i fo rn ia , 1965.

15. Vernov, S. N . , e t a l . , " Inves t iga t ion of the Van Al len Bel t s i n the Region of the B r a z i l i a n Magnetic Anomaly a t A l t i t u d e s of 235-345 km," Kosmicheskiue Is ledovaniya, Vol. 11, No. 3, 1964.

16. S p i t z e r , Lyman, Physics of Fu l ly Ionized Gases, In t e r sc i ence Publ ishers (John Wiley and Sons), New York, 1962.

17. Hess, Wilmot N. , "Earth 's Radiat ion Environment," Space/Aeronautics, Vol. 42, No. 6, November 1964.

18. Lingenfe l te r , R. E . and E. J. F l a m , "Solar Neutrons and the Ea r th ' s Radiation Bel t s , " Science, Vol. 144, A p r i l 1 7 , 1964.

19. Rosser, W. G . V., '!Changes i n the S t r u c t u r e of the Outer Radiat ion Zone Associated wi th the Magnetic Storm of September- 30, 1961," Journal of Geophysical Research, Vol. 68, No. 10, May 15, 1963.

20. Vernov, S. N . , e t a l . , " Inves t iga t ion of the Ea r th ' s Radiat ion Be l t s a t the Al t i t udes of 200-400 km," COSPAR Meeting and I n t e r n a t i o n a l Space Science Symposium, Florence, I t a l y , May 8-20, 1964.

21. Hones, Edward W. Jr., "Motions of Charged P a r t i c l e s Trapped i n t he Ea r th ' s Magnetosphere," Journa l of Geophysical Research, Vol. 68, No. 5 , March 1, 1963.

22 . Roberts, W. T. , "Space Radiat ions: A Compilation and Discussion," NASA TM X-53018, George C. Marshall Space F l i g h t Center, Hun t sv i l l e Alabama, March 5 , 1964.

23. McIlwain, Carl E . , "The Radiat ion Bel ts , Natural and A r t i f i c i a l " Science, Vol. 142, October 18, 1963

24. Tverskoi, B. A . , "On the Nature of t h e E a r t h ' s Radiat ion Belts," COSPAR Meeting, and I n t e r n a t i o n a l Space Science Symposium, Florence, I t a l y , May 8-20, 1964.

25. Hess, Wilmot N., "Energet ic P a r t i c l e s i n the 1nner.Van Al len Be l t , " NASA TN D-1749, Washington, D. C., J u l y 1963.

26. Naumann, Robert J., "A Q u a l i t a t i v e Determinat ion of t he Lower Extremit ies of t he Radiat ion Be l t s , " NASA MTP-M-PR-61-7, George C. Marshall Space F l i g h t Center, Hun t sv i l l e , Alabama, March 2 1 , 1961.

27. Pieper , G. F., C. 0. Bostrum, and A . J. Zmuda, "Trapped P r o t o n s - i n the South A t l a n t i c Magnetic Anomaly, July through December 1961," Journal of Geophysical Research, Vol. 70, No. 9 , May 1, 1965.

26

28.

29.

30.

31.

32.

33.

34.

35.

36.

37.

38.

39.

Freden, S . C., J. B. Blake, and G. A. Paul ikas , "Spa t i a l Var i a t ion of the Inner Zone Trapped Proton Spectrum," Journa l of Geophysical Research, Vol. 70, No. 13, July 1, 1965.

Russak, S . and K. Richardson, "Proton Flux, Dosage and Damage Estimates i n the Van Al l en B e l t , " Second Symposium on P r o t e c t i o n Against Radia t ion i n Space, Gatlinburg, Tennessee, October 12-14, 1964.

Heckman, Harry H. and George H. Nakano, "East-West Asynunetry i n t h e Flux of Mirror ing Geomagnetically Trapped Protons , I 1 Journa l of Geophysical Research, Vol. 68, No. 8., A p r i l 15, 1963.

Freden, S tan ley C. and George A. Paul ikas , "Trapped Protons a t Low A l t i t u d e s i n the South At l an t i c Magnetic Anomaly," Journa l of Geophysical Research, Vol. 69, No. 7 , Apr i l 1, 1964.

Hess, Wilmot N., "The A r t i f i c i a l Radiat ion B e l t Made on July Journa l of Geophysical Research, Vol. 68, No. 3, February 1,

Van Allen, J. A., L. A. Frank, and B. J. O'Brien, " S a t e l l i t e Observations of t h e A r t i f i c i a l Radia t ion B e l t of J u l y 1962," Journa l of Geophysical Research, Vol. 68, No. 3, February 1,

9, 1962," 1963.

1963.

Ness, Norman F., e t a l . , "A Summary of Resul t s from the IMP-I Magnetic F ie ld Experiment," NASA TM X-612-65-180, Goddard Space F l i g h t Center, Greenbelt , Maryland, May 1965.

Le Gal ley, Donald P., Space Science, John Wiley and Sons, New York, 1963.

Smith, Robert E. , Edi to r , "Space Environment Criteria Guidel ines f o r Use i n Space Vehicle Development," NASA ?M X-53142, George C. Marshal l Space F l i g h t Center, Huntsvi l le , Alabama, September 30, 1964.

"National Environment and Physical Standards f o r t he Apollo Program," NASA Of f i ce of Manned Space F l igh t , M-D E 8020.008B, SE 015-001-1, Washington, D. C., A p r i l 1965.

Van Al len , James A., " F i r s t Public Lecture on the Discovery of t h e Geomagne t ically-Trapped Radiation," Department of Phys ics and Astronomy, S t a t e Univers i ty of Iowa, Iowa City, S U I 60-13, May 1958.

Boyer, J. M. and W. T. Roberts, "An Untra-Low Frequency Wave Forve Mechanism f o r the Ionosphere," NASA TM X-53147 , George 'C. Marshall Space F l i g h t Center , Huntsv i l le , Alabama, October 5 , 1964.

27

APPROVAL TM X-53351

AN ENVIRONMENTAL MODEL FOR VAN ALLEN BELT PROTONS

By W i l l i a m T. Roberts

The information i n t h i s r e p o r t has been reviewed f o r s e c u r i t y c l a s s i f i c a t i o n . Review of any information concerning Department of Defense o r Atomic Energy Commission programs has been made by the MSFC Secur i ty C l a s s i f i c a t i o n Of f i ce r . This r e p o r t , i n i t s e n t i r e t y , has been determined to be u n c l a s s i f i e d .

This document has a l s o been reviewed and approved f o r t echn ica l accuracy .

ROBERT E. SMITH Chief , Space Environment Group

WILLIAM W. VAUGHAN v Chief, Aerospace Environment Of f i ce

E. D. GEISSLER Di rec to r , Aero-As trodynamics Laboratory

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