theoretical limiting ion flux - NTRS - NASA

14 downloads 0 Views 3MB Size Report
p her vat ions relating to the Van Allen belt turbulence. ..... cyclotron resonance wave -particle interaction, where the free particle ...... c.api';il letters. Titles in all ...
RESEARCH R E P O R T 259

VAN ALLEN BELT PLASMA PHYSICS bY C. F. Kennel a n d H . E. P e t s c h e k

AVCO E V E R E T T RESEARCH LABORATORY a division of AVCO CORPORATION E v e r e tt, Mas s achus e tts

December 1366

Supported jointly by DEPARTMENT O F THE AIR F O R C E AIR FORCE O F F I C E O F SCIENTIFIC RESEARCH O F F I C E O F AEROSPACE RESEARCH Arlington, Virginia 22209 under C o n t r a c t No. A F 49(638)-1483 P r o j e c t Task: 9752-01 HEADQUARTERS NATIONAL AERONAUTICS AND S P A C E ADMINISTRATION Washington, D. C. under Contract No. NASw- 1400

.

ABSTRACT

We review recemt theoretical developments i n understanding the p l a s m a turbulence in the Van Allen belts.

M o r e complex geophysical

turbulence phenomena, such a s the a u r o r a l zone, a r e not explicitly t r e a t e d , since t h e i r t h e o r e t i c a l description is still incomplete.

In

p a r t i c u l a r , i t now a p p e a r s likely that instability, and the resulting quasil i n e a r pitch angle s c a t t e r i n g , i n the s o - c a l l e d whistler and ion cyclotron m o d e s , l i m i t s the fluxes of energetic e l e c t r o n s and ions, r e s p e c t i v e l y , t h a t c a n be stably trapped in the Van Allen belts, where the E a r t h ' s m a g n e t i c lines have a dipole " m i r r o r " configuration.

We d i s c u s s s e m i -

quantitatively the f a c t o r s which affect the stability of such waves propagating obliquely to the l o c a l magnetic field direction, the velocity s p a c e diffusion resulting f r o m t h e i r nonlinear growth, and finally, s o m e p her vat ions r e l a t i n g

to the Van Allen belt turbulence.

...

-111-

TABLEOFCONTENTS

Page Abstract

iii

1.

Introduction

1

2.

Van Allen Belt Observations

5

3.

L i n e a r P i t c h Angle Anisotropy Instabilities i n the Magneto s p h e r e

11

G e n e r a l P r o p e r t i e s of Weak E l e c t r o m a g n e t i c Wave Turbulence

39

5.

Upper Limit to Stably Trapped P a r t i c l e F l u x e s

43

6.

P a r a s i t i c Diffusion

56

7.

Discussion and S u m m a r y

67

4.

-V-

1. Introduction In t h i s p a p e r , we will d i s c u s s s o m e a s p e c t s of p l a s m a turbulence in the Van Allen b e l t s , a s m a l l p a r t of the o v e r a l l complex of phenomena r e l a t e d t o the E a r t h - S o l a r Wind Interaction.

To put our d i s c u s s i o n in

p e r s p e c t i v e , we will first b r i e f l y outline the s t a t e of knowledge concerning the whole m a g n e t o s p h e r e , and then focus our attention on the Van Allen belts. Our knowledge of the E a r t h ' s n e a r environment in s p a c e h a s grown t r e m e n d o u s l y in the l a s t decade.

The E a r t h ' s magnetic field, once thought

t o be a dipole extending in s p a c e to g r e a t d i s t a n c e s , i s now known t o be g r e a t l y modified by i n t e r a c t i o n with the s o l a r wind p l a s m a flow.

The

E a r t h and i t s magnetic field p r e s e n t a blunt o b s t a c l e to the highly s u p e r s o n i c s o l a r wind flow.

J u s t a s in o r d i n a r y collisional g a s e s , a shock wave

s t a n d s u p s t r e a m f r o m the E a r t h ( N e s s , e t al, 1964). However, the d i s s i p a tion n e c e s s a r y to c r e a t e the shock m u s t a r i s e f r o m c o l l i s i o n l e s s p l a s m a turbulence p r o c e s s e s , a s y e t i m p e r f e c t l y understood.

The flow d o w n s t r e a m

f r o m the shock is a t l e a s t p a r t i a l l y r a n d o m i z e d in d i r e c t i o n and e n e r g y d i s t r i b u t i o n ( B r i d g e , e t al, 1965; Wolfe, 1966). f i e l d is highly turbulent ( N e s s , et al, 1964).

The d o w n s t r e a m magnetic

The t o t a l p r e s s u r e of the p o s t -

s h o c k s o l a r wind flow i s sufficient to confine the E a r t h ' s magnetic field t o a c a v i t y , "the m a g n e t o s p h e r e " , whose dimensions a r e fixed by the balance

of s o l a r wind p r e s s u r e t o E a r t h dipole magnetic p r e s s u r e .

The t r a n s i t i o n

l a y e r between the post-shock s o l a r wind and the magnetosphere a p p e a r s t o be quite thin (Cahill and Amazeen, 1963; N e s s e t a l , 1964).

The E a r t h ' s lines of f o r c e a r e coupled to those of the s o l a r wind by dissipation a t the t r a n s i t i o n l a y e r and a r e s t r e t c h e d into a n extended magnetic t a i l on the downstream side of the E a r t h .

H e r e a thin n e u t r a l

s h e e t of low magnetic and high p a r t i c l e p r e s s u r e h a s been o b s e r v e d (Ness, N . F .

1965; B a m e , e t a l , 1966). The flow of relatively d e n s e ,

hot p l a s m a f r o m the n e u t r a l s h e e t towards the E a r t h ' s night side is widely thought to be responsible for the complex phenomena o c c u r r i n g in the a u r o r a l zone (for instance, s e e Axford, e t al, 1965 o r O ' B r i e n , 1966). The a u r o r a l zone is a highly turbulent region of intense e n e r g e t i c

(M

1keV)

p a r t i c l e precipitation f r o m the magnetosphere to the a t m o s p h e r e on the E a r t h ' s night side, corresponding to e q u a t o r i a l plane d i s t a n c e s g r e a t e r than s i x E a r t h r a d i i f r o m the E a r t h .

Here auroral a r c s

- - intense,

spatially localized, s o m e t i m e s unsteady precipitation events o c c u r , s u p e r p o s e d on the a l r e a d y high background level.

No s a t i s f a c t o r y t h e o r e t i c a l explanation

f o r t h e s e e x t r a o r d i n a r y events e x i s t s a t this t i m e . We shall not cover in t h e s e l e c t u r e s the m a n y active a r e a s of r e s e a r c h concerning the s t r u c t u r e of the m a g n e t o s p h e r e s o briefly mentioned h e r e .

Those s o i n t e r e s t e d m a y t u r n to the extensive l i t e r a t u r e ,

( s e e , f o r instance, Levy, e t a l , 1964; N e s s , 1966; D e s s l e r and Juday, 1965; O ' B r i e n , 1966). Rather we will c o n c e r n o u r s e l v e s with the Van Allen t r a p p e d energetic p a r t i c l e radiation found on l i n e s of f o r c e deeper inside the magnetosphere, w h e r e the bulk i n t e r a c t i o n with the s o l a r wind is l e s s pronounced.

This m a y be i n f e r r e d f r o m the f a c t t h a t the magnetic l i n e s of

f o r c e r e t a i n their dipole topology and a r e only r e l a t i v e l y weakly d i s t o r t e d f r o m t h e i r unperturbed v a l u e s .

In this r e g i o n of s p a c e , the E a r t h ' s m a g -

netic f i e l d h a s a " m i r r o r " configuration, s i m i l a r to that in l a b o r a t o r y " m i r r o r " confinement devices for t h e r m o n u c l e a r f u s i o n , and should t r a p p a r tic le s .

The geometry of a n idealized s t e a d y magnetosphere i s i l l u s t r a t e d in Fig. 1.

Shown a r e the s o l a r wind ( l ) , the bow shock wave (2), the post-

shock p l a s m a flow ( 3 ) , the magnetosphere boundary (4), the magnetospheric tail (5), the n e u t r a l s h e e t (6), the a u r o r a l zone (7), and the Van Allen Zone (8). The Van Allen Zone is often s e p a r a t e d into a n Inner and Outer Zone. not d i s c u s s the Inner Zone.

We will

In the quasi-dipole Van Allen region, geophysi-

c i s t s often c h a r a c t e r i z e a n entire tube of f o r c e and the radiation t r a p p e d on it by the distance L

in E a r t h r a d i i f r o m the E a r t h ' s c e n t e r to the i n t e r s e c t i o n

of the line of f o r c e with the geomagnetic e q u a t o r i a l plane.

T h e s e a r e called

L - s h e l l s , with L z 3 denoting that tube which has its i n t e r s e c t i o n t h r e e E a r t h r a d i i f r o m the E a r t h , and s o on.

Henceforth, we will u s e this convenient

terminology. In keeping with the plasma turbulence motif of this institute, we will r e s t r i c t our d i s c u s s i o n to those turbulent p l a s m a p r o c e s s e s which m a y account f o r the o b s e r v e d anomalously l a r g e l o s s e s of protons and e l e c t r o n s ostensibly t r a p p e d in the Outer Van Allen Zone.

In addition, we s h a l l

p r e s e n t , in a n unnaturally linear fashion, p r i m a r i l y the c o u r s e of r e s e a r c h a s it was p u r s u e d a t the Avco E v e r e t t R e s e a r c h L a b o r a t o r y and at the International C e n t r e f o r T h e o r e t i c a l P h y s i c s , T r i e s t e .

Many of the ideas to be

p r e s e n t e d have been d i s c u s s e d previously by Dragt (1961), Wentzel (1963), Dungey ( l 9 6 3 ) , B r i c e (1964), Cornwall (1964, 1965, 1966), Andronov and T r a k h t e n g e h r t s (1964) and others.

Our debt to these and other a u t h o r s is

h e r e b y acknowledged. Since we w i l l s t r e s s physical concepts and linearity of p r e s e n t a t i o n , those r e a d e r s who s t i l l hanker for m o r e d e t a i l s should t u r n to the extensive l i t e r a t u r e .

A t h e o r e t i c a l d i s c u s s i o n of the l o s s of

ions f r o m l a b o r a t o r y m i r r o r machines, involving the " l o s s -cone instability" (Rosenbluth and P o s t , 1965; P o s t and Rosenbluth, 1966; Galeev, 1966), h a s r e c e n t l y been advanced.

This is s i m i l a r in many r e s p e c t s to the magneto-

s p h e r i c i d e a s t o be p r e s e n t e d , though the basic instabilities differ.

- 3-

E

MAGNETOSPHERE

I SHOCK

POST SHOCK FLOW

SOLAR WIND

Fig. 1

Magnetosphere This f i g u r e s c h e m a t i c a l l y s u m m a r i z e s o u r p r e s e n t knowledge of the E a r t h - S o l a r wind i n t e r a c t i o n . Shown i s an- i d e a l i z e d s t e a d y s t a t e m a g n e t o s p h e r e . T h e magnetos p h e r e boundary i s s p l i t up i n t o two d i s c o n t i n u i t i e s , corresponding to the standing w a v e s which a r e p a r t of the field annihilation r e g i o n ( w h e r e post-shock s o l a r wind and E a r t h magnetic l i n e s a r e c o n n e c t e d ) a s i n the t h e o r y of Levy, o t a l . ( 1 9 6 4 ) . Note t h e d i f f e r e n t l o c a t i o n s of the a u r o r a l and Van Allen zones, c o n s i d e r e d t o b e d i s t i n c t in t h i s p a p e r .

-4-

2.

Van Allen Belt Observations

4

In this section, we p r e s e n t a selective review of those Van Allen Belt p a r t i c l e observations we have found useful f o r inferring the p r o p e r t i e s of the turbulence t h e r e .

F o r m o r e complete reviews of the o b s e r v a t i o n a l

l i t e r a t u r e , the r e a d e r m a y t u r n to F r a n k (1965), Brown (1966), O ' B r i e n (1966), and o t h e r s . 7-8

In the Van Allen Zone a r e l a r g e fluxes (10

/cm

2

- s e c ) of e n e r g e t i c

e l e c t r o n s and protons which a r e at l e a s t quasi-trapped on those lines of f o r c e which a r e topologically dipole.

Most d e t e c t o r s of energetic e l e c t r o n s

and protons have had e n e r g y thresholds of,say, a few tens of keV. this h a s been sufficient f o r the Van Allen Zone.

L a r g e fluxes (-10

Fortunately,

9

/cm

2

-sec)

of m u c h lower e n e r g y e l e c t r o n s , a few keV, have been o b s e r v e d i n the a u r o r a l zone, j u s t outside the Van Allen region.

While the a u r o r a l and Van Allen

r e g i o n s s e e m intimately r e l a t e d (O'Brien and Taylor, 1964; O ' B r i e n , 1966),

it a p p e a r s that a s e p a r a t e discussion of the Van Allen Zone m a y be f e a s i b l e to lowest approximation, s i n c e p a r t i c l e s of low

~1keV a u r o r a l e n e r g y a r e

not o b s e r v e d in the Van Allen Zone. The precipitation of energetic e l e c t r o n s f r o m the E a r t h ' s magnetosphere t o its a t m o s p h e r e , long o b s e r v e d visually f r o m the ground by the a u r o r a l light e x c i t e d by

electron

i m p a c t , was f i r s t d i r e c t l y o b s e r v e d by d e t e c t o r s

mounted on r o c k e t s and balloons (Van Allen, 1957; Winckler, e t a l , 1963; A n d e r s o n and Milton, 1964 and many o t h e r s ) .

Subsequently, s u r v e y s by the

Alouette I (McDiarmid, e t al, 1964) a n d Injuns I a n d I11 s a t e l l i t e s ( O ' B r i e n , 1962, 1964) which c i r c l e d the E a r t h in North-South o r b i t s a t altitudes n e a r the e l e c t r o n s ' m i r r o r points, g r e a t l y i n c r e a s e d o u r understanding of p a r t i c l e precipitation. F i g u r e 2 is a s a m p l e of the >40 keV e l e c t r o n fluxes m e a s u r e d by the n e a r - E a r t h s a t e l l i t e Injun 111 (O'Brien, 1964) a t v a r i o u s pitch angles

a

DISTANCE (KM) INJUN III SPLASH ELECTRONS E A 40 Kev 1819 U.T. JAN. 2 2 , 1963 O

r

ALTITUDE -

250 KM -

FLUX PARTICLES CM-'

SEC-'

s T ER A D"

10'

io3

DETECTOR

ORIENTATION

A B 102

1 0

IO

20

30

TIME (SECONDS)

Fig. 2

O'BRIEN

JGR

69

1 , 1964

Injun I11 > 40 keV e l e c t r o n p r e c i p i t a t i o n fluxes Irijun 111 was o r i e n t e d with r e s p e c t to the l o c a l magnetic field d i r e c t i o n . a = 7r/2 signifies e l e c t r o n s m i r r o r i n g 0 locdlly a t t h e s a t e l l i t e , T h e a = 0 e l e c t r o n s a r e plunging 0 towards t h e a t m o s p h e r e . a = 5 5 is a n i n t e r m e d i a t e c a s e . Notice that t h e r e a p p e a r s to be a p r e c i p i t a t i o n background throughout, that l a r g e , r a p i d fluctuations o c c u r , d u r i n g which t h e e l e c t r o n s > 40 keV a p p r o a c h pitch a n g l e i s o t r o p y locally. A l l t h e s e e l e c t r o n s h a v e small pitch a n g l e s i n the e q u a t o r i a l plane.

-6-

~

~~

f-

The c u r v e s labelled a = 90

r e l a t i v e to the local magnetic field.

0

, measure

e l e c t r o n s 240 keV with flat pitch angles which a r e locally m i r r o r i n g and will be r e t u r n e d back towards the e q u a t o r i a l plane. trapped.

The a = 0

0

detector m e a s u r e s s m a l l pitch p a r t i c l e s with velocities

d i r e c t e d along the magnetic field direction. the a t m o s p h e r e .

These e l e c t r o n s a r e

The a = 55

0

T h e s e will be precipitated into

electrons a r e a n intermediate c a s e .

If the

e l e c t r o n s o b s e r v e d c o n s e r v e their f i r s t adiabatic invariant in t h e i r motion along the line of f o r c e between the Injun I11 s a t e l l i t e and the e q u a t o r i a l plane ( a n assumption to be shown theoretically r e a s o n a b l e ) , they a l l would have v e r y small equatorial pitch angles. F i g u r e 2 is probably a n exaggeratedly complex swath of data.

(Our

purpose in showing it is to instill a s e n s e of humility in t h e o r i s t s . ) Nevert h e l e s s , i t does contain f e a t u r e s which O ’ B r i e n (19b4) h a s succeeded in showing hold m o r e o r l e s s generally f o r a l l the >40 keV e l e c t r o n precipitation. E l e c t r o n s >40 keV s e e m often to be precipitating into the a t m o s p h e r e f r o m the Outer Van Allen Belts.

Injun I observations (O’Brien, 1962) of the

e l e c t r o n precipitation r a t e together with e s t i m a t e s of the total number of e n e r g e t i c Van Allen e l e c t r o n s >40 keV trapped on a tube of f o r c e obtained independently by equatorial plane s a t e l l i t e s enabled e s t i m a t e the e l e c t r o n lifetime as 10 t o a day.

3- 5

B r i e n (1962) to

seconds, i. e . , twenty minutes

>40 keV e l e c t r o n precipitation typically c o v e r s a r a n g e of

L - s h e l l s b o r d e r e d on its i n n e r edge at L zoiie arid at

0 1

o-cter edge at

L

M

6-8

I.--

uy

M

2 by the Inner Van Allen

+Ln - - * - n - - l LLLCI

au&v& CSL

4tqLIVII~.D v a o ; nFA”’

tion of e n e r g e t i c >40 keV electrons i n c r e a s e s with i n c r e a s i n g

L

I

_ _ A

L and maxi-

m i z e s in the a u r o r a l zone (O’Brien, 19b4; Gurnett and F r i t z , 1965).

The

a u r o r a l light i t s e l f is thought to be due to the intense precipitation of other low e n e r g y e l e c t r o n s with a few keV e n e r g y (O’Brien and Taylor, 1964). LOW e n e r g y a u r o r a l e l e c t r o n precipitation does not o c c u r on Van Allen L - s h e l l s ;

- 7-

I

I

the Van Allen e l e c t r o n s have m u c h higher e n e r g i e s but m u c h s m a l l e r intensities than the a u r o r a l e l e c t r o n s .

We will not d i s c u s s the a u r o r a l

precipitation h e r e . Since the number of >40 keV e l e c t r o n s observed in the Van Allen Belts over many y e a r s h a s never fallen to z e r o , and since precipitation s e e m s often, if not always, to o c c u r , t h e r e m u s t be active a c c e l e r a t i o n m e c h a n i s m s maintaining the trapped >40 keV fluxes.

What those m e c h a n i s m s could be is

a subject of active investigation in the r e s e a r c h l i t e r a t u r e .

O ' B r i e n (1966)

h a s adduced arguments that at l e a s t one s u c h m e c h a n i s m l i e s in the a u r o r a l zone.

We will find that the precipitation of p a r t i c l e s , while strongly

coupled to the r a t e of a c c e l e r a t i o n to e n e r g i e s above the d e t e c t o r threshold, can be understood, in i t s b r o a d outlines, without r e f e r e n c e to the specific details of the acceleration m e c h a n i s m s .

T h e r e f o r e , we will henceforth

neglect to a f i r s t approximation both specific a c c e l e r a t i o n m e c h a n i s m s and/or the poorly understood interaction between the a u r o r a l and Van Allen Zone, and c o n s i d e r the m o r e well-defined p r o b l e m of the l o s s of p a r t i c l e s f r o m the E a r t h ' s quasi-dipole field. F i g u r e 2 i l l u s t r a t e s that the a = 0

0

precipitation fluxes of e l e c t r o n s

L 240 keV undergo violent fluctuations of o r d e r 1 0 in t i m e s c a l e s of one second.

Anderson and Milton, (1$64), M o z e r e t al, 1965, M o z e r and Bouston, 1966, have o b s e r v e d precipitation r a t e fluctuations i n t i m e s c a l e s a s s h o r t a s 0 . 1 seconds.

F r o m t h e s e s h o r t t i m e s c a l e s we c a n induce a r g u m e n t s about the

precipitation mechanism.

In the a b s e n c e of fluctuating fields, t h e p a r t i c l e s

should c o n s e r v e t h e i r adiabatic i n v a r i a n t s .

T h e s e a r e , i n o r d e r of i n c r e a s i n g

stringency: ( a ) The t o t a l magnetic flux contained i n one c o m p l e t e guiding c e n t e r d r i f t orbit about the E a r t h

- - the

so-called third invariant.

Fluctua-

tions oI' the o r d e r of the guiding c e n t e r d r i f t period around t h e E a r t h (a few thousand s e c o n d s ) a r e needed t o violate t h i s i n v a r i a n t .

- 8-

+P

v,, d e , where de

( b ) the longitudinal invariant -

element of length along the line of f o r c e , velocity component and

ill

i s an

1 I

v,, the p a r a l l e l

, the m i r r o r points.

Fluctuations

with t i m e s c a l e s the o r d e r of the p a r t i c l e bounce period between m i r r o r points, a few seconds, a r e needed f o r violation. 2 sin Q ( c ) the magnetic moment o r f i r s t invariant p =, where B a i s the pitch angle and B the magnetic field strength.

period fluctuations, -10

-4

Gyro-

seconds in the equatorial plane and

f a s t e r e l s e w h e r e along a line of f o r c e , will violate this invariant. P a r t i c l e a c c e l e r a t i o n and precipitation c a n r e s u l t f r o m violation of any of t h e s e invariants.

F o r a review of the geophysical consequences of second

and t h i r d invariant violations, see Dungey ( 19b5). Suppose that precipitation is due to a velocity-space diffusion p r o c e s s , a c u r r e n t l y popular hypothesis in p l a s m a physics.

Then fluctua-

tions in e a c h range of c h a r a c t e r i s t i c p e r i o d will c a u s e the p a r t i c l e d i s t r i b u tions to diffuse slowly in adiabatic invariant velocity s p a c e .

Generally

speaking, it would take s e v e r a l of the b a s i c periods outlined above f o r the diffusion f r o m a given adiabatic invariant violation to be effective.

It is t h e r e f o r e difficult to a s s o c i a t e second and t h i r d invariant violation with the 0. 1 - 1 second fluctuations in precipitation r a t e .

This l e a d s us t o

f i r s t invariant violation. McDiarmid and Budzinski (1964) noted that the fluxes of e l e c t r o n s >40 keV and t h e i r distribution with e n e r g y o b s e r v e d both in the vicinity of

the equatorial plane and n e a r the m i r r o r points n e a r the E a r t h a r e quite similar.

If e l e c t r o n s conserve t h e i r f i r s t invariant a s they change f r o m

t r a p p e d to precipitated by penetrating regions of e v e r increasing magnetic f i e l d s t r e n g t h in going f r o m equatorial to high latitude m i r r o r points, they

would a c q u i r e a n enormous energy.

This e n e r g y gain would be h a r d to

r e c o n c i l e with the o b s e r v e d s p e c t r a l s i m i l a r i t i e s .

This suggests:

( a ) The f i r s t adiabatic invariant i s violated. ( b ) Electron pitch angles m u s t change m u c h m o r e than t h e i r energy in the precipitation p r o c e s s . That it is p r i m a r i l y the pitch angle and not the energy which changes during e l e c t r o n precipitation is suggested f r o m the tendency shown in F i g . 2 and cited in many instances by O ' B r i e n (1964), f o r the o v e r a l l fluxes to approach pitch angle i s o t r o p y a t -high.

l e a s t n e a r the l o s s cone when the precipitation r a t e is

Thus , the p a r a l l e l e l e c t r o n motion i s not significantly e n e r g i z e d r e l a t i v e

to the perpendicular.

When the 340 keV precipitation r a t e is e x t r e m e l y high,

for instance, outside the Van Allen Zone on a u r o r a l lines of f o r c e , the p r e c i p i t a t e d flux i s comparable with the t r a p p e d fluxes m e a s u r e d in the e q u a t o r i a l plane.

F r o m this we infer that the e n t i r e pitch angle distribution becomes

roughly isotropic when precipitation i s r a p i d . P r o t o n precipitation is much m o r e difficult to detect.

However,

Haerendel ( l 9 b 6 ) , a f t e r a study of the fluxes of t r a p p e d e n e r g e t i c proton fluxes o b s e r v e d by Davis and Williamson (1963), h a s concluded that f i r s t invariant violation is also n e c e s s a r y f o r protons.

While we will bias our d i s c u s s i o n in

t e r m s of e l e c t r o n s , t h e r e i s a n e n t i r e l y s i m i l a r d i s c u s s i o n f o r proton p r e c i p i tation.

Moreover, s i n c e the t r a p p e d proton e n e r g y density o b s e r v e d in s p a c e

is m u c h l a r g e r than that for e l e c t r o n s , protons a r e actually the dominant c o m ponent of the Van Allen belts.

-10-

,

3.

Linear P i t c h Angle Anisotropy Instabilities in the Magnetosphere

3 . 1)

Introduction In this section, we d i s c u s s instabilities in those e l e c t r o m a g n e t i c

p l a s m a waves which c a n violate the f i r s t adiabatic invariant.

For a system

a s complicated a s the magnetosphere, evaluating even i m p r e c i s e l y the f a c t o r s affecting i t s stability p r o p e r t i e s is, unhappily, complex.

However,

a good understanding of t h e s e f a c t o r s is n e c e s s a r y f o r the i n t e r p r e t a t i o n of e x p e r i m e n t s . The conditions f o r first adiabatic invariant violation a r e quite stringent.

A p a r t i c l e m u s t s e e fluctuating wave fields n e a r its own g y r o -

frequency.

The wave-particle interaction is p a r t i c u l a r l y s t r o n g when i t

is r e s o n a n t , i. e.

, when the r e l a t i v e phase of p a r t i c l e and wave changes

slowly with t i m e , s o that the r e s o n a n t p a r t i c l e f e e l s the wave f o r c e f o r a long t i m e . wave.

H e r e t h e r e can be a n energy exchange between p a r t i c l e and

On the o t h e r hand, the f o r c e s between waves and non-resonant p a r t i c l e s

a v e r a g e to zero.

In p l a s m a s with an e x t e r n a l magnetic field, we a r e led to the

c y c l o t r o n r e s o n a n c e wave - p a r t i c l e interaction, where the f r e e p a r t i c l e motion p a r a l l e l to the e x t e r n a l field Doppler shifts the wave frequency to the p a r t i c l e ' s gyrofrequency.

where

The condition f o r this r e s o n a n c e is

VI, is the p a r t i c l e velocity component p a r a i i e i to the field,

p a r a l l e l wave n u m b e r ,

w the wave frequency, and

f o r i o n s (t)o r for e l e c t r o n s (-).

K,, the

the gyrofrequency

Since t h e r e c a n a l s o be r e s o n a n c e s at

h a r m o n i c s of the gyrofrequency, we distinguish this "lowest" r e s o n a n c e f r o m t h e o t h e r s by calling it the principal cyclotron r e s o n a n c e .

-11-

In the following, we will consider the cyclotron r e s o n a n c e couplings of w h i s t l e r s to electrons and of ion cyclotron waves to protons.

In 3 . 2 , we

d i s c u s s the s p e c i a l c a s e of couplings to those waves which propagate s t r i c t l y along the magnetic field.

H e r e we show that the Van Allen e l e c t r o n s and

protons have the a p p r o p r i a t e e n e r g y to be in cyclotron r e s o n a n c e with w h i s t l e r s and ion cyclotron waves, respectively.

F u r t h e r m o r e , the

cyclotron resonance interaction c a u s e s p a r a l l e l propagating waves to grow when the p a r t i c l e pitch angle distributions have a m i r r o r type pitch angle anisotropy, with m 3 r e energy i n mDtion perpendicular to the field than i n parallel.

In 3 . 3 , we a r g u e that w h i s t l e r s as they propagate m u s t change

t h e i r wave n o r m a l angles to the magnetic field, necessitating the c o n s i d e r a tion of the m u c h m o r e complex l i n e a r instability p r o b l e m for obliquely propagating waves, which i s then outlined in 3 . 4 . calculations a r e combined in 3. 5.

I

The r a y path and instability

H e r e we conclude that growth along a

r a y path will occur when the trapped low e n e r g y p a r t i c l e fluxes a r e sufficiently weak.

In 3 . b , we account s c h e m a t i c a l l y f o r o t h e r non-resonant

l o s s e s of wave energy f r o m the m a g n e t o s p h e r e .

3. 2 ) P a r a l l e l Propagating Whistlers and Ion Cyclotron Instabilities As a f i r s t approximation, a s s u m e that the r e a l p a r t w of the wave frequency i s given by the cold p l a s m a d i s p e r s i o n r e l a t i o n (Stix, 1 9 6 2 ; Allis, e t al, 1 9 6 3 ) .

Then using 3 . 1 , we m a y e s t i m a t e the e n e r g y of

r e s o n a n t p a r t i c l e s and c o m p a r e with o b s e r v e d Van Allen p a r t i c l e e n e r g i e s . The ion cyclotron wave is a left-hand c i r c u l a r l y p o l a r i z e d e l e c t r o m a g n e t i c wave with a frequency below the ion gyrofrequency

Q+ '

and a cold-plasma

where V

A

= B/(4nNM,)'/2,

the Alfven velocity,

N the total e l e c t r o n o r ion number density.

M

t

is the ion mass, and

Since O < o / s 2 40 KEV (OMNIDIRECTIONAL

-- WHISTLER

MODE LIMITING FLUX

lo"

(LN G Z 3 )

\

:\". +. \ \

\ x

\' \

I' 0

'.

NOON

\

{ >

y

;VAEW"ING

MIDNIGHT

lo"

0 d

A

W

X

lo"

2 -I

IL

IO*

-L *

lo" 1

2

I

IO

' 2

AVERAGE DIRECTIONAL FLUX OF PRECIPITATED ELECTRONS > 4 0 K E V (INJUN III)

I

I

1

I

1

I

I

I

3

4

5

6

7

8

9

10

EQUATORIAL DISTANCE (EARTH RAD1I 1

Fig. 10

Limitation on t r a p p e d > 40 keV e l e c t r o n fluxes. The t h e o r e t i c a l limiting flux J::: i s c o m p a r e d with E x p l o r e r 14 equatorial t r a p p e d fluxes a s a function of the e q u a t o r i a l radial d i s t a n c e . T h e l a r g e s t o b s e r v e d t r a p p e d fluxes a r e indeed c l o s e t o the t h e o r e t i c a l u p p e r l i m i t . We a l s o show the distribution with L s h e l l of Injun 3 p r e c i p i t a t e d e l e c t r o n s A s expected, s t r o n g precipitation o c c u r s only w h e r e t r a p p e d fluxes c a n be c o m p a r a b l e with t h e c a l c u l a t e d limiting flux. The distributions of p r e c i p i t a t e d and t r a p p e d e l e c t r o n s > 40 keV a p p e a r t o be mutually c o n s i s t e n t .

-50A3969

~

F i g u r e 1l p e r m i t s an e s t i m a t e of the long t e r m behavior of the Van Allen Belt >40 keV cyclotron e l e c t r o n s .

Plotted a r e E x p l o r e r

XIV

fluxes m e a s u r e d n e a r the equatorial plane over a ten-month period.

The

o b s e r v e d e l e c t r o n intensities w e r e m o r e often s u b c r i t i c a l than unstable. F u r t h e r m o r e , the whistler mode upper limit a p p e a r s to be a good one, in the s e n s e that the t r a p p e d fluxes a r e often n e a r t h e i r c r i t i c a l intensity limit.

This suggests that all other instabilities which could a l s o l i m i t

the Van Allen e l e c t r o n flux have higher onset trapped e l e c t r o n intensities. 5.2b)

Trapped P r o t o n Fluxes

F i g u r e 1 2 c o m p a r e s the trapped ion fluxes m e a s u r e d by E x p l o r e r XI1 (Davis and Williamson, 1963) with the ion cyclotron upper l i m i t to the proton fluxes.

Again the a g r e e m e n t is r e a s o n a b l e .

An i n t e r e s t i n g f e a t u r e

is that the trapped ion c r i t i c a l fractional number densities c a n be a f a c t o r 40

l a r g e r than the corresponding limiting number densities f o r e l e c t r o n s .

Thus,

m o s t of the high e n e r g y p a r t i c l e s in the magnetosphere a r e protons, when a c c e l e r a t i o n keeps both e l e c t r o n and proton fluxes n e a r the onset intensity f o r instability.

Cornwall (1966) h a s a l s o d i s c u s s e d the t r a p p e d proton

fluxes and found r e a s o n a b l e a g r e e m e n t with the c r i t e r i o n ( 5 . 7 ) . 5. 2c)

Whistler Wave Intensity

The o b s e r v e d Van Allen e l e c t r o n lifetimes c o r r e s p o n d to wide-band w h i s t l e r magnetic field amplitudes in the e q u a t o r i a i piane of i 0 - 2 - I,UA - 3 .. y , where

-5 l y = 10 g a u s s (Kennel and P e t s c h e k , 1966). A s we have indicated,

the r e g i o n of v e r y l a r g e wave amplitudes could be localized t o the e q u a t o r i a l plane, s i n c e t h e r e the growth i s positive and Landau damping and o t h e r wave l o s s e s l i m i t the amplitude away f r o m the e q u a t o r i a l plane.

-51-

In addition,

.-.

Jo IO6

104

t

I

J o IOb

IO 4

I

I

0600

000

I

I

I800

1200

-'..C

Fig. 11

Limitation on t r a p p e d e l e c t r o n s > 4 0 keV. T h i s d i a g r a m p e r m i t s an e s t i m a t e of t h e d e g r e e to which o b s e r v e d p a r t i c l e f l u x e s approach t h e i r 1irr;iting value. W e h a v e s u p e r p o s e d t h e calculated J::: on E x p l o r e r 14 d a t a published by F r a n k ( 1 9 6 5 ) . The m a j o r i t y of points a r e c l e a r l y below t h e predicted l i m i t . T h e small s c a t t e r of points n e a r but below t h e l i m i t a t L = 6 s u g g e s t s that a continuous acceleration mechanism i s operative h e r e . The electron f l u > . e y > 40 keV s e e m n e a r e s t t h e i r p r e c i p i t a t i o n l i m i t on the m o r n i n g s i d e of the E a r t h , w h e r e p r e c i p i t a t i o n i s known t o be high. T h e l a r g e s c a t t e r of points a t L = 10 m a y a r i s e f r o m t h e o t h e r violent p r o c e s s e s which a r e expected t o o c c u r i n t h e a u r o r a l zone. -52-

4

b

lo9

I

I

I

---

I

I

1

THEORETICAL LIMITING ION FLUX (Ln G x 3 ) EXPLORER XI1 EQUATORIAL FLUXES (INDIVIDUAL PASSES)

\

( DAVIS

6

WILLIAMSON 1

% . % %

\

\

- - -kOON

DAWN

OR

',EVENING

-

\

\ I o6 3

4

5

6

7

8

\ 9

IO

R A D I A L D I S T A N C E ( E A R T H RADII 1 Fig. 1 2

Limitation on t r a p p e d protons.

H e r e we have s u p e r p o s e d

E x g l s r e r 1 2 r a d i a l distributions of t r a p p e d protons with

e n e r g i e s between i 2 0 keV and 4. 5 Mev and t h e t h e o r e c i c d limiting protons flux J::: ( > 1 2 0 keV). F o r L > 4 i t a p p e a r s that protons a r e a l s o a c c e l e r a t e d t o t h e i r limiting fluxes. T h e s e proton fluxcbS a r e c o m p a r a b l e with the e l e c t r o n fluxes of F i g s . 1 0 and 11. T h e r e f o r e e n e r g e t i c protons c a n and often do have a much l a r g e r n u m b e r density than energetic electrons.

-53-

A3590

s i n c e the lower hybrid r e s o n a n c e r e f l e c t s waves a t intermediate latitudes, a v e r y s m a l l f r a c t i o n of the equatorial whistler amplitude should r e a c h the

ionosphere, where published observations by Injun I11 (Gurnett and O ' B r i e n , 1964) w e r e taken.

T h e r e f o r e , it is not s u r p r i s i n g that t h e i r o b s e r v e d

amplitudes were considerably s m a l l e r than those needed in the e q u a t o r i a l plane to account f o r Van Allen e l e c t r o n precipitation. More recent m e a s u r e m e n t s with the OGO-I s a t e l l i t e indicate that -2-3 b u r s t s of whistler radiation with wide band amplitudes the o r d e r of 1 0 y in the equatorial plane a r e a r e a s o n a b l y c o m m o n o c c u r r e n c e .

( R . A. Helliwell,

private communication. ) Intermittent turbulence is to be expected since the trapped electron fluxes a r e m o r e often than not below the instability l i m i t and turbulence should occur only when t h e r e i s a s o u r c e of new cyclotron electrons.

This noise a p p e a r s to be limited to the Van Allen Zone, w h e r e

the lines of force a r e topologically dipole. intermediate latitudes, a t m o s t

X

M

50

0

The amplitudes m e a s u r e d at

f o r OGO-I, w e r e often c o m p a r a b l e

with those in the e q u a t o r i a l plane, suggesting, p e r h a p s , that e l e c t r o n Landau damping was not a c t i v e , a t l e a s t a t those t i m e s .

5 . 2d)

Ion Cyclotron Wave Intensity

The precipitation r a t e of protons h a s , to o u r knowledge, not yet been s a t i s f a c t o r i l y m e a s u r e d .

N e v e r t h e l e s s , F i g . 12and ~ o r n w a l l ' s ( 1 9 6 6 )

r e s u l t s indicate that ion cyclotron instability m u s t o p e r a t e a t l e a s t p a r t of the t i m e .

Since we do not know the ion p r e c i p i t a t i o n r a t e , we do not know

the s o u r c e strength of new protons driving the pitch angle diffusion.

- 54-

>-

We m a y e s t i m a t e a lower limit f o r the equatorial plane ion cyclot r o n wave intensity a s follows: It i s known that the lifetime of 60 keV p r o -

-

!J

tons against a t m o s p h e r i c c h a r g e exchange p r o c e s s e s is roughly 6 x 10 at L x 6

.

sec

(Cornwall, 1966) When the ion cyclotron upper l i m i t i s obeyed,

the s o u r c e s t r e n g t h and t h e r e f o r e the proton lifetime m u s t be f a s t e r than that given by c h a r g e exchange p r o c e s s e s . The lifetime

is r e l a t e d to the pitch angle diffusion coefficient T L

roughly a s follows: (Kennel and Petschek, 1966) TLt and D M S-2

(5. 8 )

3/Dt

p (Eq. 4. 3 ) . Substituting the c h a r g e exchange lifetime as a

t o

lower limit, and taking

Bo

M

200y a p p r o p r i a t e to L x 6 , we find

B' > 1 0 - l ~

(5.9)

This e s t i m a t e was f i r s t m a d e by Cornwall (1966),using a variation upon this reasoning. In the absence of coordinated r a y path and instability calculations, it i s not possible to e s t i m a t e a c c u r a t e l y the width of the region of high ion

c y c l o t r o n wave intensity n e a r the equatorial plane.

In addition, propagation

and a b s o r p t i o n e f f e c t s through the ionosphere m a k e e s t i m a t i o n s of the wave a m p l i t u d e s i n s p a c e using ground-based m e a s u r e m e n t s , a subtle and complic a t e d p r o c e d u r e (Wentworth, 1964a and b). Wentworth' s e s t i m a t e s .

(5.9) does not d i s a g r e e with

M o r e r e c e n t low altitude s a t e l l i t e observations

f r o m 1963 38C ( Z m u d a , e t a l , 1966) and OGO-I1 (Brody, et a l , 1966) indicate

that e x t r e m e l y l a r g e amplitude (30 y < B' < 300 y)

t r a n s v e r s e hydromagnetic

w a v e s , with f r e q u e n c i e s below the equatorial proton gyrofrequency, a r e o b s e r v e d

- 55~~

high a l t i t u d e s , roughly corresponding to the high latitude b o r d e r of the a u r o r a l e l e c t r o n precipitation zone.

T h u s , the connection with proton

precipitation within the Van A l l e n z o n e i s at p r e s e n t u n c l e a r .

Since

the lowest intensity m e a s u r a b l e by 1963 38C was 30y , m o r e sensitive m e a s u r e m e n t s in the 1/ 1Oy r a n g e m a y eventually c l a r i f y the situation. The OGO-I1 r e s u l t s indicated that the hydromagnetic e m i s s i o n s w e r e often s t r u c t u r e d , r a t h e r than broad-band, indicating that a t h e o r e t i c a l a n a l y s i s m o r e complete than that given h e r e is needed f o r t h e s e observations.

6.

P a r a s i t i c Diffusion

6 . 1) P a r a s i t i c P i t c h Angle Diffusion In this section we consider the possibility that the turbulent wave distributions c r e a t e d and maintained by the a c c e l e r a t i o n s o u r c e s of, s a y ,

40 keV cyclotron e l e c t r o n s and protons, d r i v e precipitation of higher e n e r g y cyclotron p a r t i c l e s a s well.

This c a n happen in a t l e a s t two w a y s .

First,

the waves c r e a t e d a t the equator can propagate into regions where the cyclot r o n r e s o n a n t energies a r e higher than a t the e q u a t o r .

Secondly, pitch

angle diffusion at higher cyclotron r e s o n a n c e s could a l s o occur when the wave s p e c t r u m has a distribution of wave n o r m a l angles with r e s p e c t to the magnetic field. R e f e r r i n g to Table I of section 2 , we s e e that the p r i n c i p a l n = *1 3 cyclotron resonant e n e r g i e s v a r y along a r a y path a s B /N f o r w h i s t l e r s

4

and f o r ion cyclotron waves a s B /N.

Therefore, these resonant particle

e n e r g i e s i n c r e a s e rapidly upon leaving the e q u a t o r i a l plane.

While t h e s e

high e n e r g y off-plane r e s o n a n t p a r t i c l e s m a k e a small contribution to the

o v e r a l l growth r a t e , they will be s c a t t e r e d in pitch angle by whatever wave amplitude r e a c h e s high latitudes.

If the wave e n e r g y density w e r e

constant going f r o m the e q u a t o r i a l plane to the higher latitude s c a t t e r i n g region, the r a t i o of the high latitude diffusion coefficient to that in the e q u a t o r i a l plane would be i n v e r s e l y proportional to the r a t i o of magnetic field s t r e n g t h s .

Then the high latitude s c a t t e r i n g r a t e f o r high energy

p a r t i c l e s would be reasonably f a s t .

However, Landau damping cuts in, 0

a t l e a s t f o r w h i s t l e r s , a t latitudes above 8 , and the wave amplitudes should be diminished somewhat.

At a latitude of 8O the dipole magnetic

s t r e n g t h h a s only i n c r e a s e d by a few p e r c e n t and the cyclotron e n e r g i e s by 207'0, r e l a t i v e to those in the equatorial plane.

It i s probably safe to

s a y t h a t cyclotron e l e c t r o n s with energies a factor two g r e a t e r than those in the e q u a t o r i a l plane cannot be efficiently precipitated by off-plane w h i s t l e r interactions.

On the other hand, this conclusion depends strongly

on the intensity of 1 0 0 eV Landau e l e c t r o n s . We have d i r e c t e d our attention p r i m a r i l y to p a r a l l e l propagating w h i s t l e r s and ion cyclotron waves, and the e l e c t r o n s and ions r e s o n a n t with t h e m , a s the m o s t unstable, and contributing the lion's s h a r e to o v e r a l l instability.

However, especially when t h e r e a r e relatively few 100 eV

Landau damping e l e c t r o n s , the wave s p e c t r u m in the e q u a t o r i a l plane t u r b u l e n t region will have a s p r e a d of wave n o r m a l angles r e l a t i v e to the l o c a l magnetic field.

T h e r e f o r e , in addition to wave-particle interactions

a t t h e n = 0 Landau resonance a l r e a d y d i s c u s s e d , a l l the higher cyclotron r e s o n a n c e interactions ( I n l > l ) a r e no longer forbidden when KL

i s nonzero.

Kennel and Engelmann ( 1 966) have shown that s o long a s the resonant

- 57-

p a r t i c l e p a r a l l e l velocity i s m u c h l a r g e r than the m a x i m u m p a r a l l e l wave phase velocity i n the excited s p e c t r u m , the behavior of a l l higher cyclotron r e s o n a n c e s i s s i m i l a r to that of the principal n = *1 heretofore discussed.

cyclotron r e s o n a n c e

In other w o r d s , higher cyclotron harmonic diffusion The diffusion

i s a l m o s t purely in pitch angle and a l s o leads to precipitation.

r a t e will, in g e n e r a l , be slower since the wave p a r t i c l e coupling s t r e n g t h , denoted by-

It,IrJ”

in (4.l ) , i s weaker for the higher cyclotron r e s o n a n c e s .

Since the instability i s caused by the n = *1 principal resonance e l e c t r o n s , the diffusion of the higher resonance e l e c t r o n s i s , in s o m e s e n s e , gratuitous. When the n = * l

e l e c t r o n s approach t h e i r c r i t i c a l unstable intensity,

whistler instability o c c u r s , s c a t t e r i n g both n = *1 and higher cyclotron e l e c t r o n s in pitch angle.

The higher cyclotron e l e c t r o n s need not be n e a r

t h e i r limiting flux to be precipitated by w h i s t l e r turbulence. they do not, in g e n e r a l , limit their own i n t e n s i t i e s .

However,

F o r this r e a s o n , we

c a l l this p a r a s i t i c diffusion. F i g u r e 13 s c h e m a t i c a l l y i l l u s t r a t e s p a r a s i t i c diffusion. s e g m e n t of (VL, V,,) velocity s p a c e , with VI, >O.

Shown i s a

This h a s negative (n 40 kev beyond 5 e a r t h r a d i i with E x p l o r e r 14, J . Geophys. R e s . , 70(7), 1593-1626, 1965. F r i t z , T . A . , and D.A. Gurnett, Diurnal a n d latitudinal e f f e c t s o b s e r v e d f o r 10 kev electrons a t low s a t e l l i t e a l t i t u d e s , J. Geophys. R e s . , 70, 2485 -2502, 1965. Galeev, A . A . , Ion E s c a p e f r o m a magnetic m i r r o r t r a p due t o development of instability connected with t h e ' l o s s cone , ' I Sov. P h y s . (English T r a n s . ) J E T P 22, 466-472, 1966 Galeev, A . A . , and V. I. Karpman, T u r b u l e n c e t h e o r y of a weakly nonequilibrium low density p l a s m a a n d s t r u c t u r e of shock waves, SOV. P h y s . J E T P , 17, - 2, 403-409, 1963. Gurnett, D. A . , and B. J . O'Brien, High-latitude s t u d i e s with satellite Injun 3, 5, Very low frequency e l e c t r o m a g n e t i c radiation, J . Geophys. R e s . 69(1), 65-90, 1964. Haerendel, G . , On t h e violation of t h e second and t h i r d adiabatic i n v a r i a n t s , J. Geophys. R e s . , 71, 1857-1868, 1966. Helliwell, R. A . , W h i s t l e r s and r e l a t e d i o n o s p h e r i c phenomena, Stanford P r e s s , 1965. Helliwell, R . A . , J. Katsufrakis, M. T r i m p i , a n d N. B r i c e , A r t i f i c i a l l y s t i m u l a t e d v e r y low f r e q u e n c y radiation f r o m t h e ionosphere, J. Geophys. R e s . , 69, 2391-2394, 1964. Kantrowitz, A . R . , and H. E. P e t s c h e k , MHD c h a r a c t e r i s t i c s a n d shock waves, Plasma P h y s i c s i n T h e o r y a n d Application, E d . by Wulf B. Kunkel, McGraw-HillBook Co, New York, 1966. Kennel, C. F . , Low F r e q u e n c y Whistler Mode, P h y s . F l u i d s , 9, 11, 1966. Kennel, C . F . , and F. Engelmann, Velocity s p a c e diffusion f r o m weak p l a s m a turbulence i n a magnetic field, P h y s . F l u i d s , 9, 12, 1966. Kennel, C. F . , and H. E. P e t s c h e k , A limit o n s t a b l y t r a p p e d p a r t i c l e fluxes, J. Geophys. R e s . , 71, 1, 1-28, 1966. Kennel, C. F . , and R . M. T h o r n e , Unstable g r o w t h of unducted w h i s t l e r s propagating a t a n angle t o t h e geomagnetic f i e l d ( t o be published i n J. Geophys. R e s . ) J u n e 1966.

Kennel, C. F. and H. V. Wong, Resonant p a r t i c l e i n s t a b i l i t i e s i n a uniforin magnetic iield ( t o be published) Kennel, C. F. and H. V. Wong, Resonantly unstable off-angle h y d r o m a g n e t i c waves, J. Plasma P h y s i c s , i, I, 19b7. K i m u r a , I. , Effects of ions on w h i s t l e r mode r a y t r a c i n g , Radio Science, 1, 3, 269-283, 1966. Levy, R. H. , H. E. P e t s c h e k , and G. L. S i s c o e , A e r o d y n a m i c a s p e c t s of t h e m a g n e t o s p h e r i c flow, AIAA J . 2:2065-2076, 1964. Liemohn, H. B. , Cyclotron Resonance Amplification of V L F and U L F w h i s t l e r s , ( t o be published i n J . Geophys. R e s . ). Lyon, E. F. , E x p l o r e r 18 p l a s m a m e a s u r e m e n t s , i n T h e S o l a r Wind R. J. Mackin and M. Neusebauer, e d s . , P e r g a m o n P r e s s , Oxford, 1966, pp. 295-314. M c D i a r m i d , I. B. , and E. E. Budzinski, Angular d i s t r i b u t i o n s a n d e n e r g y s p e c t r a of e l e c t r o n s a s s o c i a t e d with a u r o r a l events, Can. J . Phys., 42 ( l l ) , 2048-2062, 1964. M c D i a r m i d , I. B. , J. R. B u r r o w s , E. E. Budzinski, a n d M. D. Wilson, Some a v e r a g e p r o p e r t l e s of t h e o u t e r radiation zone a t 1000 km, Can J . P h y s . , 41, 2064-2079, 1963. M c D i a r m i d , I. B. , and J. R . B u r r o w s , E l e c t r o n fluxes at 1 0 0 0 kilometers a s s o c i a t e d with the tail of the m a g n e t o s p h e r e , J . Geophys. R e s . 70, 3031-3044, 1365. M o z e r , F. S., Rocket m e a s u r e m e n t s of e n e r g e t i c p a r t i c l e s , 2, E l e c t r o n r e s u l t s , J. Geophys. R e s . , 70, 5709-5716, 1965. M o z e r , F. S. , J. F. Crifo, and J . E. Blamont, Kocket M e a s u r e m e n t s of e n e r g e t i c p a r t i c l e s , 1, D e s c r i p t i o n of t h e e x p e r i m e n t , J . Ge ophys. R e s . 70, 5699-5707, 1965. M o z e r , F . S . and P. B r u s t o n , P r o p e r t i e s of t h e a u r o r a l zone e l e c t r o n S G G ~ C Cdeduced frnrn e l e c t r o n s p e c t r u m s and a n g u l a r d i s t r i b u t i o n s , J. Geophys. R e s . , 71, 4451-4460, 1966. M o z e r , F . S. and P. Bruston, A u r o r a l zone p r o t o n - e l e c t r o n a n t i c o r r e l a t i o n , p r o t o n angular d i s t r i b u t i o n s , and e l e c t r i c fields, J. Geophys. R e s . , 7 1 , 4461-4468, 1966.

,

Nakada, M. P. , J. W . Dungey, and W. N. H e s s , On the o r i g i n of o u t e r b e l t protons, J. Geophys. R e s . , 70, 3529-3532, 1965. N e s s , N . F . , T h e e a r t h ' s magnetic tail, J . Geophys. R e s . , 70, 29893006, 1965.

-75-

N e s s , N. F . , Observations of t h e s o l a r wind i n t e r a c t i o n with the geomagnetic field: Conditions quite, NASA document X-612-66-381, 1966. N e s s , N . F . , C.S. S c e a r c e and J . B. Seek, Initial r e s u l t s of t h e I m p 1 m a g n e t i c field e x p e r i m e n t , J . Geophys. R e s . , 69, 17, 3531-3569, 1964.

O ' B r i e n , B. J . , L i f e t i m e s of o u t e r - z o n e e l e c t r o n s and t h e i r p r e c i p i t a t i o n into t h e a t m o s p h e r e , J . Geophys. R e s . , 67, 36873706, 1962. O ' B r i e n , B. J . , High latitude geophysical s t u d i e s with satellite Injun 3, 3, P r e c i p i t a t i o n of e l e c t r o n s i n t o the a t m o s p h e r e , J. Geophys. R e s . 69(1), 13-44, 1964. O ' B r i e n , B. J . , I n t e r r e l a t i o n s of e n e r g e t i c c h a r g e d p a r t i c l e s i n t h e m a g n e t o s p h e r e , Rice University S p a c e S c i e n c e s P r e p r i n t , t o b e published i n the proceedings of t h e Inter-Union Symposium on S o l a r T e r r e s t r i a l P h y s i c s , B e l g r a d e , Yugoslavia, Aug. 29Sept. 2, 1966. O ' B r i e n , B . J . and T a y l o r , H. , High latitude geophysical s t u d i e s with s a t e l l i t e Injun 3, 4. A u r o r a s and t h e i r excitation, J . Geophys. Res. 69, 1, 45-64, (1964). P e a r l s t e i n , L. D . , M. N. Rosenbluth, and D. B. Chang, High f r e q u e n c y " L o s s - C o n c " flux i n s t a b i l i t i e s i n h e r e n t t o two-compoent p l a s m a s , P h y s . F l u i d s 9, 953-955, 1966. P o s t , R. F. a n d M. N. Rosenbluth, E l e c t r o s t a t i c i n s t a b i l i t i e s i n finite m i r r o r confined p l a s m a s , P h y s . F l u i d s 9, 730-749, 1966. Rosenbluth, M. N . , and R . F. P o s t , High f r e q u e n c y e l e c t r o s t a t i c p l a s m a instability i n h e r e n t t o " L o s s - C o n e " p a r t i c l e d i s t r i b u t i o n s , P h y s . F l u i d s 8, 547-550, 1965. Sagdeev, R. Z . , and V. D . Shafronov, On t h e i n s t a b i l i t y of a p l a s m a with a n a n i s o t r o p i c d i s t r i b u t i o n of v e l o c i t i e s i n a m a g n e t i c field, Soviet P h y s i c s , J E T P English T r a n s l . , 12(1), 130-132, 1961. S c a r f , F. L. , G. M. Crook, and R. W. F r e d r i c k s , P r e l i m i n a r y r e p o r t on d e t e c t i o n of e l e c t r o s t a t i c ion w a v e s i n t h e m a g n e t o s p h e r e , ( I J . Geophys. R e s . 70, 3045-3060, 1965. S e r b u , G. P . , and E. J. R. M a i e r , Low e n e r g y e l e c t r o n s m e a s u r e d on I m p 2, J. Geophys. R e s . 71, 15, 3755-3766, 1966. Stix, T . H. , T h e Theory of Plasma Waves, M c - G r a w - H i l l Book Company, New York, 1962.

- 76-

. Stix, T . H. , Radiation a n d absorption via m o d e c o n v e r s i o n i n a n inhomogenous collisionfree plasma, P h y s . Rev. L e t t e r s , 15, 878-882, 1965. Thorne, R . M. and C. F. Kennel, Quasi-trapped V L F propagation i n t h e o u t e r magnetosphere, Avco E v e r e t t R e s e a r c h R e p o r t 251, 1966, t o b e published iil J . Geophys. R e s . Van Allen, J . A . , F i r s t public l e c t u r e on t h e d i s c o v e r y of geomagnetically trapped radiation, t r a n s c r i p t of remarks a s d e l i v e r e d on May 1, 1958, t o the National Academy 0: Sciences, Washington, D. C . , IGY S a t e l l i t e R e p o r t #13, J a n . 1961, IGY World Data C e n t e r A, Rockets a n d Satellites, National Academy of Sciences, National R e s e a r c h Council. Vedenov, A . A . , E . P. Velikhov, and R. Z . Sagdeev, Q u a s i - l i n e a r t h e o r y of p l a s m a o s c i l l a t i o n s , Salzburg, 1961; Nucl. F u s i o n Suppl., 2, 465475, 1962. Watanabe, T . , Determination of t h e E l e c t r o n Distribution in t h e m a g n e t o s p h e r e using hydromagnetic w h i s t l e r s , J. Geophys. R e s . 70, 5839-5848 (1965). Wentzel, D. G . , Hydromagnetic waves and t r a p p e d radiation, 1, Breakdown of t h e adiabatic invariance; 2, Displacement of t h e m i r r o r points, J . Geophys. R e s . , 66, 359-362, 363-369, 1961. Wentworth, P. C . , Evidence f o r m a x i m u m production of hydromagnetic e m i s s i o n s above the afternoon h e m i s p h e r e of t h e e a r t h , 1, Extrapolation t o t h e b a s e of t h e exosphere, 2, A n a l y s i s of s t a t i s t i c a l s t u d i e s , J . Geophys. R e s . , 69, 2689-2698, 2699-2706, 1964. W i l l i a m s , D. J. and A. M. Smith, Daytime t r a p p e d e l e c t r o n i n t e n s i t i e s at high latitudes at 1000 kilometer-s, J. Geophys. R e s . , 70, 541-556, 1965.

Winckler, J. R . , P. D. B h a v s a r , and K.A. Anderson, A study of t h e precipitation of e n e r g e t i c e l e c t r o n s f r o m the geomagnetic field d u r i n g magnetic s t o r m s , J . Geophys. Z e s . , 67, 3?!?-3?36, 1962, Wolfe, J. H . , R. W . Silva, and M. A . M y e r s , Observations of t h e s o l a r wind during t h e flight of I m p I, J. Geophys. R e s . , 71, 1319-1340, 1966. Zniuda, A . J . , J. H. Martin, and F. T . Heuring, T r a n s v e r s e hydromagnetic d i s t u r b a n c e s at 1 1 0 0 k m i n the a u r o r a l region, J. Geophys. R e s . , 71, 5033-5046, 1966.

- 77-

a

-

I

U x l a s s if ie d See uri t V C Iassi f ica t io n

OQIGINATIN G A C T I U I T Y (Cbrporere a t i f h o r )

*

28

Avco E v e r e t t R e s e a r c h L a b o r a t o r y 2385 R e v e r e Beach P a r k w a y

R t P O R T SECURITY

C LAS51FlCATION

Unclassified 26

GROUP

REPORT TITLE

VAN ALLEN B E L T PLASMA PHYSICS D E S C R I P T I V E HOTES

1

(Type o f report and inclusive dotes)

- R e s e a r ch R e p o r t 259 i AUTHOR(S) ( L e s t name, f i r s f name, initial)

Kennel, C. F . , a n d p e t s c h e k , H. E. i REPORT DATE

D e c e m b e r 1966

I7e

I

C

I

d

TOTAL NO

O F PAGES

77

9b. OTHER REPORT this raporf)

176.

NO. OF R E F S

79

NO(S)

( A n y othernumbsrs that may be a s s i g n e d

I O A V A I L A B I L I T Y / L I M I T A T I O N NOTICES

f

I

C

s p a c e R e s e a r c h , Arlington, Va.

W e review r e c e n t theoretical developments in understanding the p l a s m a turbulence i n the Van Allen belts. M o r e complex geophysical t u r bulence phenomena, s u c h a s the a u r o r a l zone, a r e not explicitly t r e a t e d , s i n c e t h e i r t h e o r e t i c a l description i s s t i l l incomplete. In p a r t i c u l a r , it now a p p e a r s likely that instability, a n d the resulting q u a s i - l i n e a r pitch angle s c a t t e r i n g , i n the s o - c a l l e d whistler and ion cyclotron m o d e s , l i m i t s thc fluxes nf e n e r g e t i c e l e c t r o n s and ions, respectively, that can be stably t r a p p e d in the Van Allen belts, where the E a r t h ' s m a g n e t i c iinss 'riave a dipole " m i r r o r " configuration. We d i s c u s s semi-quantitatively the f a c t o r s which affect the stability of s u c h waves propagating obliquely to the local m a g n e t i c field direction, the velocity s p a c e diffusion r e s u l t i n g f r o m t h e i r nonlinear growth, and finally, some observations relating to the Van Allen b e l t turbulence.

Unclas s i f ied Security Classification

U ncla s s if ie d

F

I‘Trrr.

. .

.

Sccriri t y

(: I . i i :i i f l r a t ion

K € ‘ I WORDS

E

1. 2. 3.

i

4.

i

5.

ROLE

INSTRUCTIONS

1. O R I G I N A T I N G ACTIVITY: E n t e r t h e n a m e a n d a d d r e s s o f t h e contr.ictor, s u b c o n t r a c t o r , g r a n t e e , D e p a r t m e n t ot fiei e n s r .ictir.it y or o t h e r o r g a n i z a t i o n ( c o r p o r a t e a u t h o r ) i s s u i n g t h e report. ? a . RI.;PORT S E C U R I T Y C L A S S I F I C A T I O N : E n t e r t h e overall >:ec.iirit> c l a s s i f i c i t i o n of t h e report. I n d i c a t e w h e t h e r “Kt-s*ric.led 1).*1a” I S included. Marking is t o b e in accordu i i L e w i t l , .appr,Jpriate s e c u r i t y r e g u l a t i o n s . ? h . (;I?OUP: Aut$>niaticd o w n g r a d i n g i s s p e c i f i e d i n r e c t i v e L;.!OO. 10 a n a Armed F o r c e s I n d u s t r i a l Ma,xial. the ,:r~ n2n:hc.r. A l s o , when a p p l i c a b l e , sho:, t h a t r ~ 1 ~ r i i . i . 1 p . i ti,iv:* ! ) w n used for Group 3 a n d C r o u p 4 as 1ze.i.

DoD DiEnter optional author-

T I T L E : F n t e r the c o m p l e t e report t i t l e i n a l l l e t t e r s . T i t l e s i n all c a s e s s h o u l d be u n c l a s s i f i e d . If a m e a n i n g f u l t i t l e c a n n o t b e s e l e c t e d ’ without c l a s o i f i c a tinth. v e a . , o r month, year. If more t h a n o n e d d ! ~a p p e a r s u n ( I I c . repctrt, u s e d a t e of publir.ation.

7e. TOTAL NUMBER O F P A G E S : T h e t , > t : i l p a g e c o u n t s h \ ~ u l df c , l l o w normal p a g i n a l l o n p r o c e d u r e s . L e . , e n t e r t h e nLiimI>vr o f p a e r s c o n t a i n i n g i n f o r m a t i o n 7 b . NI!MLjER O F R E F E R E N C E S reftvc.nt cs r.ited in t h e report.

Enlet t h e t o t a l n u m b e r of

X C ~ . C O N T R A C T O R GK.*NT NUMBER: If a p p - o p r i a t e , e n t e r r h r a p p l i c a b l e i,urnt>rr of t h e c o n t r ~ c to r q a n t u n d e r w h i c h

t h e reliort w a x ‘vritten. tlb, tk-, & Ed. P R O J E C T NUMBER: ICrIter t h e a p p r o p r i a t e niilitary d e p a r t m e n t i d r n ’ i f . r a t i o n , s u c h a s p r o j e c t number, subproject n.:mber. s)‘ [ e m n u m b r r s , t a s k nulr5er. etc.

ORI(;INATOR’.> R E P O R T NUMREH(S): E n t e r t h e offi:qJort number b y ivhich t h e docurn-nt will be i d e n t i f i e d and c . r ~ n t r ~ > l l by P d tlic oriKinating activik,. T h i s n u m b e r must b e u n i q u e to t h i s repnr!. Ya.

ciili

rJb. OTIlI-:H R L P O R T NUMRER(S): 1; t h e report h a s b e e n as*,il:rlc~l ;any o t h e r report n u m b e r s f e r l h c r h y t h e o r i g i n a t o r r h ) the .spnnyor), a l s o e n t e r t h i s number(s).

10.

-

impos1.d b y s e c u r i t y c l a s s i f i c a t i o n , u s i n g s t a n d a r d s t a t e m e n t s s u c h as:

.(

W T

P l a s m a turbulence Van Allen belts Trapped particles W h i s t l e r mode P i t c h Angle s c a t t e r i n g

-

,.

LINK C

LlYK A

_____--

(5)

-

“ A l l d i s t r i b u t i o n o f t h i s report i s c o n t r o l l e d . @ a l ified D D C u s e r s s h a l l r e q u e s t t h r o u g h

_

_

~

..

__-

I f t h e report h a s b e e n furnis!iid I C t h e O f f i r c o f ’I‘ecti:iic.,l S e r v i c e s , D e p a r t m e n t of C o m m e r c e , i,,r s a l e to the pubIi