Accleration mechanism of electron plasma outside magnetosphere near bow shock regio

Davis, L., Jr.

Jokipii, J. R.

English

NASA Technical Reports Server

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J. R. Jokipii' and Leverett Davis, Jr. 
California Institute of Technology, Pasadena, California 
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( Received October 1964) * . 
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Ising IEIP-1, have observed >3O kev electrons outside the metosphere. 
Similar but less extensive earlier observations have been reported and 
discussed bjr Van Allen and Frank3, Frank, Van Allen and Macagno , and 
Socett . 
rates of tfie order of 10 times background which last only a few minutes, 
corresponding to-the passage of the satellite through regions about 2,000 
hi thick if they are stationary with respect to the earth. Fan -- et al.l
suzgest that the electrons occur in a thin region at the bow shock aut- 
side of the magnetosphere, locating the buw shock at the outermost point 
x:ere electrons are observed on each orbit. 
model interpreting the pulses as thin layers, with the outmost layer 
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-- 5 The observations of Fan et al. show pulses having counting 
However, we feel that the 
,ually beiw at the IXJW shock, is unlikely on both theoretical and obser- 
im $w??,mCi; rrnd mt uu alternative interpretation. T- 
Any >w ker W t r o n s  must drift through the magnetic field 
with the bulk velocitx @ %be solar wind. They also spira3. rapidly 
( >lo1' cm/sec) along the lines of force. Thus a few thousand kilometers 
behind the shock the f l a x  of energetic electrons, in the model of Fan - et 
- do1, should be essentislly the same as in the shock, the electrons having 
been convected away fran t lm shoe bv the wind or bavina flawed - alom the 
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.lines of force that lead through the shock. 
would explain the observations, it could be argued that  they are both 
accelerated and then decelerated i n  the shock structure, as i n  the soli- 
tary wave of Adlam and Allen 6 , or  h ~ s ,  L f k t  and Schlffter7. But aypazent- 
ly the  only way t o  accelerate electrons to >30 kev i n  a stationary shock 
is by stochastic processes, and these cannot be reversed to decelerate the 
electrons behind the shock. 
If 1 or 2 kev electrons 
Consideration of these arguments led us t o  compare care- 
Figure 2 of Fan e t  aL', which shows the locations of the electron pulses 
they interpret as being at the shock front, with the corresponding figures 
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for the IMP-lmagletometer and plasma results of mess, Scearce and Seek 8 , 
and Bridge, Egidi, Lazarus, Lyon and Jacobsong. 
and magnetic f i e ld  data agree w e l l  on the location of the shock, but that  
the o u t e m s t  high energy electron fluxes are usuaUy a few earth radii 
outside the shock, on one occasion at  least six earth radii outside, and 
on a few occasions aze seen only inside the shock if  at  all. Except for 
one disturbed period when the cosmic ray background was high and they 
detected pulses of electrons far outside the shock, the observations of 
Anderson e t  al.2, which show pulses with fluxes of 10 5 6  -10 an-* sec'l on a 
background of about 7 x lo3 sec", appear to be consistent with th i s  
picture, although we have not made a detailed canparison of the i r  results 
It appears that  the plasma 
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with those of Fan e t  ale1. -- 
We therefore suggest that rather than interpreting the structures 
where electrons are found as thin, relatively permanent and stationary 
layers i n  space, they be interpreted as regions transient i n  time and much 
more extended in space. 
las t ing a f e w  minutes and blowing aww with the solar wind. 
They should occur typically every hour or so, 
A w i n d  velo- 
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city of 400 km/sec w i l l  move them lo5 km, or abaut the radius pf the 
shock surface, i n  4 minutes. 
the shock front, during which no energetic electrons were seen (except fo r  
one storm period), it appears that  bar shock-associated electrons are 
confined to a region that rarely, :f ever, extends more than a few earth 
radii outside the shock front. 
pulses were observed much m r e  often when fa r  fkomthe subsolas point than 
when near it. This suggests that  the layer of energetic electrons may, on 
different occasions, have i ts  upwind edze a t  various distances f'rom the 
subsolar point. 
region behind the shock. Thus, Tar  f'rom the subsolar p i n t ,  several such 
regions are l ikely t o  mreep.past during one passage of the satel l i te ,  while 
nearer the subsolar point it i s  mare l ikely that only one occurs. 
Since DIP-1 spent long periods well outside 
Between the shock and the magnetopause, 
The solar wind extends the regions downwind into the 
Consider now possible explanations both of the occasional 
presence of energetic electrons and the fact  that they tend not to be 
observed more than a f e w  earth radi i  outside the shock. 
t h i s  discussion implausible mechanisms hvolving Mach 20-30 non-linear 
mves propagating outward f r o m  the shocklo, which accelerate electrons 
and protons t o  high energies and then decelerate them as part of the wave 
structure, and mechanisms producing semipermanent thin layers i n  the 
region downwind xfrm certain unusual tubes of force i n  which electrons are 
accelerated, we note two models tha t  seem t o  m e r i t  serious consideration. 
They m e  depicted schematically i n  figure 1. 
Excluding from 
It may be that  electrons with energies well above 30 kev are 
either always or occasionally produced in  or  behind the shock, perhaps as 
a non-exponential t a i l  t o  the few kev Boltnann distribution suggested by 
the observations of Rreqa.n, Van Allen and Ca,hiUu.. 
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The source may be located anywhere behind or near the shock, so long as 
electrons may leak out i n  front of the shock layer along lines of force. 
If the density of these pir t ic les  a t  the  shock, and hence their flux out, 
i s  low they w i l l  ordinarily not be observable. 
the interplanetary field w e r e  t o  became more irregular than usual, or 
developed a precursor as suggested by Ness -- e t  do8, the electrons may 
mirror and become temporarilytrapped in  front of the shock. 
F3ut if from time t o  time 
I The local 
density w i l l  build up t o  a value limited by slow diffusion along the f ie ld  
and by the sweeping may of the entire structure by the solar wind. 
th i s  trapping raises the flux of  3 kev electrons t o  105 cm-2 sec’l, i.e. 
aboutlo 
If 
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of the flux expected for 1 kev electrons behind the shock, the 
observations w o u l d  be explained. Alternatively, of course, the f ie ld  
fluctuations could be continually present t o  provide the confinement t o  
regions near the shock, but the source could be intermittent. 
variations i n  the f ie ld  found by Ness -- e t  aL8 both inside and, at times, 
outside the  shock and the very short period fluctuations observed by 
Pioneer I= suggest that at times the f ie ld  may contain irregularities 
The RIB 
that  serve as mirror points and occasional weak shocks tha t  can change 
the pitch angles of the electrons. 
the order of lo9 cm along lines of force, the confinement to a thin layer 
outside the shock would be explained. 
RMS fluctuations behind the shock, the diffusion length there should be 
shorter. 
If these produce a diffusion length of 
Since N e s s  -- e t  find larger 
Because these irregularities (sausages closed off by mirror points) 
may become f i l l e d  with energetic electrons near the shock and then be 
convected away by the wind ,  the thickness of the region behind the shock 
should increase downwind from i t s  leading edge. Fermi acceleration i n  
th i s  region may be a factor i n  both  t h i s  and the following model. 
A variant of this is sufficiently attractive that  we would l ike 
to regard it as a dis t inct  second model. 
than a few radii outside the shock seems t o  require mirror points moving 
w i t h  the sal= wind which ref lect  the outward moving electrons back toward 
the shock. 
f ie ld  strength at the shock should scatter electrons back out into the 
wind, 
and the shock, are accelerated by a first order Fermi process. 
they me reflected in the wind, the electrons receive a velocity increment 
2vw C O S X ,  where 
wind velocity and + B 
cisely, i f  n is the outward directed normal to  the shock front, 
cosx = -(f$ . v ) (5 . :)/ Bo vw 1% . E 1 .  Assume that some of the L L  
kev electrons found behind the shockn leak out ahead of the shock along 
the f ie ld  l ines and are accelerated. For a nominal 2 vw cos x = 5 x lo7 
cm/sec it takes of the order of 200 reflections t o  accelerate them to  
'j0 kev. The trapping must therefore be quite efficient;  about 90-955 of 
the electrons approaching the mirror points must be reflected to  produce 
The absence of electrons more 
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Irregularities in and just behind the shock and the enhanced 
'Ihese electrons, reflecting back and forth between the mirror points 
Each time 
is the wind velocity and X is  the angle between the 
the magnetic f ie ld  outside the shock. More pre- - 4' 
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4 the  requisite fluxes. Also, i n  order to keep the pitch angles of the 
electrons from decreasing as they gain energy, a plausible model requires 
eff ic ient  randomization of pitch angles by shocks or magnetic irregulari- 
t i es ,  The time available to  accelerate the particles is the time a f i e ld  
l i ne  takes t o  cross a region t h e  size of  the magnetosphere, or about lo2 
seconds,unless the interplanetary f ie ld  is  precisely parallel to the solar 
wind velocity. 
t h i s  limits the distance from the shock a t  which acceleration can proceed. 
This l i m i t  i s  of the order of lo9 cm. for 1 kev electrons, in excellent 
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Since particles must mirror many times to gain energy, 
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agreement with the observed cutoff at a few earth radii.. 
We suggest that a mechanism similar to this, which we are 
exploring in more detail, may accelerate particles in other situations 
where 8 p k s m  containing a fluctuating magnetic field flows through a 
shock with high Mach number. 
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Since the region outside the shock that is filled with energetic 
electrons depends on the direction of the field outside the shock, and the 
effectiveness of the trapping and accelerating mechanism depends on the 
kind of magnetic irregularities present, intercomparison of the energetic 
electron and magnetometer observations should provide many obvious tests 
of these models. 
We are indebted to Professors J. A. Simpson and K. A. Anderson 
for most helpful discussions of their observations. 
W i s  work has been supported in part by NASA under Grant NsG 426. 
+ NSF Predoctorsl Fellow 
C. Y. Fan, G. Gloeckler and J. A. Simpson, Phys. Rev. Letters, & 149, 1 r 
(1964) 
I(. A. Anderson, H. K. Harris and R. J. Paoli, University of California at 2 
Berkeley, Space Sciences Laboratory, Series 5, No. 50, (1961). 
3J. Van Allen and L. Frank, Nature, 184, 219, (199). 
4 
'C. P. Sonett, J. Geophys. Res., 68, 1265, (1963). 
L. Frank, J. Van Allen and J. Macagno, J. Geophys. Res., E, 3543, (1963). 
6 J. H. Adlam and J. E. Allen, Phil. Mag.,  2, 448, (19%). 
7L. Davia, Jr., R. L&t and A. Schldter, Z. Hsturforschg., -* 13a 916 (1958). 
8 
%. Bridge, A. Egidi, A. Alzarus, E. m n  and L. Jacobson, Preliminary 
N. F. Ness, C. S. Scearce and J. B. Seek, J. Geophys. Res., 3531, (1964). 
Results of plersma Measurements OI? XMP-A, presented at 1964 
&spar Meeting, Florence, Italy. 
lop. G. SaffWm, J. Fluid Wch., -3 ll 16. (1961). 
uJ. 11. Freeman, J. Pirn U e n  and L. J. Cahill, J. ceaphys. Res., 68, 21p, 
t 
(1963) 
=C. P. Sonett and I. J. Abrams, J. Ceaphys. Res., 3 1233, (1963). 
-4” 
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Figure Caption. 
Fig. 1 
Schemtic representation. 
i-- 
In modell, acceleration occurs either dong NB or in region E. 
In model 2, the particles are accelerated in NAB and possibly in 
N E .  Boundaries Hp9 and NCF w i l l  not be sharp because of 
diffusion along field lines. N can occur at various distances 
from S, the subsolar point. The solar wind blows accelerated 
pazticles into the region ABCFD and beyond. When trapping or 
acceleration ceases, the whole region drifts downwind. 
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>30 kev ELECTRONS 
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MAGNETOPAUSE 
ETlC FIELD LINE 


Acceleration of Electrons near the Earth's Bow Shock

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