Charged particle motion in unidimensional model of magnetosphere transition laye

Samokhin, M. V.

English

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National Aeronautics and Space Administration 
Goddard Space,-Flight Center 
Contract W.NAS75-12487 
.!ST- PF- a4 -10569 A Ai. 
UNIDIMENSIONAL IWDEL OF M ? i m P H E R E ' S  
TRANSITIONAL LAYER 
J 
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. M. V. S m k h i n  1 
(USSR) 
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N67 25883 
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https://ntrs.nasa.gov/search.jsp?R=19670016554 2020-03-12T11:31:12+00:00Z
ST PF GM 10569 
ON TIE MOTION OF A CHARGED PARTICLE IN THE 
UNIDIMENSIONAL MODEL OF MAGNETOSPHERE'S 
TRANSITIONAL LAYER 
* 
Kosmicheskiye Issledovaniya 
Tom 5, vyp.1, 157-159 
Izdatel'stvo "NAUKA", 1967 
by M. V. Samokhin 
The trajectory of a charged particle in a unidimensional model of the 
transitional layer of the magnetosphere is discussed in the light of speci- 
fic hypotheses concerning the physical conditions in that layer, and as a 
function of particle's angle of incidence upon it. 
* 
* * 
Measurements of the magnetic field on AES Exp~rer-12 [l] and Explorer-18 
[21 (IMP.1) lead to the conclusion that there exists between the shock wave 
forming as aconsequence of sub-Alfve'n solar wind flow past the geomagnetic 
field and the outer boundary of the magnetosphere a region of irregular ma- 
gnetic field. This region is called the transition region of the magneto- 
sphere and is characterized by a chaotic variation of the magnetic field in- 
tensity vector in direction, as well as in magnitude. 
It should be noted that a transitional region with such magnetic field 
properties exists always, even during quiet geomagnetic periods. A rough es- 
timate according t o  data of Explorer-12 [l] gives for the characteristic am- 
plitude of oscillations 1Oy and for the characteristic macroscopic length - 
2 .IO3 lan. 
I S  stillobscure at present. 
either by turbulence, o r  are the consequence of contraction of the inhomoge- 
nous interplanetary medium in front of such an obstacle as the geomagnetic ca- 
vity is [3] .  
The question on the physical nature of this transitional region 
The irregular field variations are conditioned 
Digressing from the effects conditioned by the chaoticity of field struc- 
we shall neglect in the proposed model of magnetosphere's transitional 
ture, and taking into account only the effects linked with field variation in 
space, 
layer the Temporal variations of the magnetic field, and we shall subst.itute 
CHASTITSY V ODNOMERNOY MODEL PEREKHODNOGO 
J . -  
2 .  
€or the t rue pat tern of sharp spa t ia l  variations in  iiiagiiitmlc amJ t ioic oI' t 1 1 ~  
magnetic f i e l d  a unidimensional sinusoidal f ie ld  with ;I ~h i i r ac t e r i s t  ic m p l  i - 
tude of 10v and wavelength 
the t ransi t ional  layer and the magnetic f i e l d  B is directed tangentially (along 
the axis x) 
= 2 . 103hn. The plane z = 0 i s  the boundary of 
- 
B = Bx = Bo + B ~ C O S  kz (k = Zn/X).  (1) 
Let a charged pa r t i c l e  enter the considered region a t  the time t = 0 
under the following i n i t i a l  conditions: 
The equations of motion 
are easy t o  integrate.  As a resu l t  we obtain 
I 
dz 
@ 1/ I$ - 02 ( z + - sin kz 
k 
(3) 
Here o = -qBo/mc, b = B, /Bo .  
For the sake of simplicity we may assume tha t  the constant component Bo 
is small by comparison with the amplitude B , ,  which i s  ju s t i f i ed ,  inasmuch 
as in  rea l  t ransi t ional  region of the magnetosphere the f i e l d  varies sharply 
in  direction. Neglecting the constant f i e l d  component, we obtain from (3) 
Here W, = -qBl/mc, and F(k,$) is an e l l i p t i c a l  integral .  
The pa r t i c l e  t ra jectory equation of f i r s t  kind is of i n t e re s t ;  it has 
the following form 
If I x I >> 1, the t ra jectory (7) becomes the Larmor circumference. 
Expression (4)  describes an in f in i t e  motion that  takes place for  
3 .  
In the opposite case (vo < / w l  I / k ) ,  the motion of the par t ic le  is  
f i n i t e .  
suff ic ient ly  small impulse. 
wi th  small impulse has a Larmor radius smaller than the character is t ic  
scale of f i e l d  var ia t ion,  so that  during i ts  motion the pa r t i c l e  does not 
"perceive" the variation of the f i e l d  i n  space. 
Therefore, the sinusoidal magnetic f i e l d  may re ta in  par t ic les  with 
The explanation consists i n  tha t  a par t ic le  
For the assumed values of B, and k ,  electrons,  moving with the velocity 
of the solar  wind, have f i n i t e  t ra jec tor ies  (they a re  Larmor circumferences, 
since K d o 3 ) .  
j ec tor ies .  
For v o  > v 
sphere with such parameters, while for  vu < vpc 
jectory i n  the region of the f i r s t  magnetic f i e l d  m a x i m u m .  
Fig.1 below are  the t ra jectory of proton 
motion a t  vo  = 400 kmlsec (the curve 1 is 
an open trajectory) and vo = 300 lunlsec 
(curve 2 ,  closed t r a j ec to ry ) .  
If the par t ic le  incidence upon the 
tr;insitional layer of  the magnetosphere 
takes place a t  a cer ta in  angle t o  the 
axis z (oblique incidence), the condi- 
t ion  5f f ini teness  of the t ra jectory (4) 
changes i n  i t s  form. 
v,(O) = v COSCX, v to) = vosina,  where 
--TT/Z - z u s  7/2.Considering that  the 
constant component B 
t ing  the equations of motion (2), 
taking into account the boundary con- 
d i t ions ,  we sha l l  obtain: 
A s  t o  ions, they may move along e i the r  closed or  open t r a -  
For protons the c r i t i c a l  velocity vo c rcons t i tu tes  311 km/sec. 
the proton permeates the t ransi t ional  layer of the magneto- kr it describes a closed t r a -  
Plotted i n  the 
Indeed, assume 
0 Y 
= 0 and integra- 
Fig. 1 
I t  i s  c lear  t ha t  the t ra jectory of the pa r t i c l e  is f i n i t e  when the 
radicand i n  the right-hand par t  of (8) becomes zero. Hence it follows tha t  
the condition for  t ra jectory f ini teness  has the form 
A t  a = - / 2 ,  the t ra jectory of the charged pa r t i c l e  is always f i n i t e ,  
no matter what i t s  energy (a t  r e l a t i v i s t i c  veloci t ies  theLuiescent mass m 
must be replaced in the equations of motion (2) by m / (1 - vo2]?). 
* A *  T H E E N D 
-__ I 
Received on 15  Nov.1965 
4. 
R E F E R E N C E S  
1. L. J. CAHILL, P. G. AMAZEEN. J.Geophys. Res., 68, 1835, 1963. -
2. N. F. NESS, C. S. SCEARCE, J. B. SEEK. Ibid., 69, 3531, 1964. 
3. D. B. BEARD. Rev. Geophys., 2, 335, 1964. 
-
- 
CONTRACT No.NAS-5-12487 
VOLT TECHNICAL CORPORATION 
1145 19th St.NW 
1>. C. 20036. Telephone: 223-6700 
Translated by ANDRE L. BRICHANT 
on 23 February 1967 
DISTRIBUTION 
SAME AS FOR ST-PF -CN-t0557 


On the motion of a charged particle in the unidimensional model of magnetosphere's transitional layer

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