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.
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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.
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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.
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. 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.
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R t P O R T SECURITY
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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
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TOTAL NO
O F PAGES
77
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176.
NO. OF R E F S
79
NO(S)
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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
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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
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