Currents of quasi-trapped particles having discontinuities on earths day and night side

Pletnev, V. D.

English

NASA Technical Reports Server

General Disclaimer 
One or more of the Following Statements may affect this Document 
 
 This document has been reproduced from the best copy furnished by the 
organizational source. It is being released in the interest of making available as 
much information as possible. 
 
 This document may contain data, which exceeds the sheet parameters. It was 
furnished in this condition by the organizational source and is the best copy 
available. 
 
 This document may contain tone-on-tone or color graphs, charts and/or pictures, 
which have been reproduced in black and white. 
 
 This document is paginated as submitted by the original source. 
 
 Portions of this document are not fully legible due to the historical nature of some 
of the material. However, it is the best reproduction available from the original 
submission. 
 
 
 
 
 
 
 
Produced by the NASA Center for Aerospace Information (CASI) 
https://ntrs.nasa.gov/search.jsp?R=19690012937 2020-03-12T03:52:16+00:00Z
National Aeronautics and Space Administration
Goddard Space Flight Center
Contract No.NAS-5-12487
ST —PF —GM —10813
CURRENTS OF QUASI-TRAPPED PARTICLES HAVING DISCONTINUITIES
ON THE DAY AND NIGHT SIDES OF THE EARTH
by
V. D. Pletnev
0. A. Troshichev
'	 MAR 1969
f
f'.
RECEIVED
NASA STi FACILITY
INPUT BRANCH
(USSR)
I	 N69-22299
_	 (ACCESSION NUMBER)L ITNRU)
C	 (PAC e)J (COD
/N SA CR OR TMX O AD N^EpI (CATEGORY)
3 MARCH 1969
ST — PF — GM — 10813
CURRENTS OF QUASI TRAPPED PARTICLES HAVING DISCONTINUITIES
ON THE DAY AND NIGHT SIDES OF THE EARTH*
Kosmicheskiye Issledovaniya
	 by
	 D. Pletnev
Tom 7, vyp. 1, 103 - 108, 	 & 0. A. Troshichev
Izdatel'stvo "NAUKA", 1969
SUMMARY
The effect is investigated of the presence in the drift
current of a collisionless plasma of a source or of a discon-
tinuity. Applied to the geomagnetic field, the estimate is
conducted of the possible effects linked with discontinuities
in the currents of quasi-trapped particles on the day and night-
time sides of the Earth.
*
*	 *
The motion of a low-density i0r1i2.-A gas in a nonuniform magnetic field was
investigated by Parker [1]. In this work Parker considered a stationary system
of particles situated in a magnetic field without taking into accoup_t the possible
presence of a source region, or particle vanishing in the current. Therefore,
the solution found by Parker corresponds to a drift of particles along a closed
magnetic shell at invariable distribution of particles by velocities and pitch-
angles on the shell. As a consequence of that, the distribution of particle den-
sity along the line of force will not depend on longitude (i.e. the longitudinal
pressure gradient 3p/3(D = 0), and the flux of particles directed downward (toward
the specular points), will be equal to the flux of particles proceeding upward
(in the equatorial plane) at any point of the field line, i.e. current will be
absent along the field lines.
In its application to the geomagnetic field, such a statement of the problem
is valid only at computation of the effects of the closed ring current (see, for
example, [2]). In the case of drift current of quasi-trapped particles, having
A	 D	 C	 d4
3
which drift of particles takes place (point A) ; the second limit azimuth of
the source will be called the inner boundary. As previously only particles
of minimum pitch-angle 6 0
 - 0° will be present on the line AB.
However, on the line BC particles of all pitch-angles from 0 to 7/2 arri-
ving here either from various parts of the source, or the mirror-point reflected
ones, will fix themselves (Fig.2).
In the sector ABD the reflected particles are
	 s
totally absent, all particles moving here in a single
direction, from the source toward mirror points and
their density increases in the direction of the drift
(as a result of the dependence vdr = f(0 o ). The ref-
lected particles fix themselves only at transition
through the line BD and, as they approach the line BC,
their density increases. At the outset there will be
appearing particles with great values of initial
pitch-angles 0 0 , then to them will add up particles
with smaller and smaller 0 0 and, finally, reflected 	 Fig.2
particles will appear on the line BC, with minimum
possible pitch-angles 0 - 0 + F. Therefore, it is possible to fix on any ele-
ment S of the line BC particles with pitch-angles 0 < 0 < Tr/2, proceeding from
the source toward the side of mirror points with 0 = ff/2 (their initial pitch-
angle 0 0 * may be found from the condition sin@ O * = g 112) and particles with
0 < 0 < ,r/2, moving toward the inverse side (to the initial plane) after reflec-
tion in mirror points.
It is easy to find the density of these particles and the pressure indu':ed
by them if we know the distribution function by pitch-angles. Assume that
fo(e) = k p X sin a+10e cosa eo [3, 51,
where a and Q are the parameters characterizing the anisotropy of articles in
the source; ka8 is a constant. Then the density of particles on an element S
of the field line will be
e•fde
Ssin"+ ' 0(1 —  q sing 0) 9/2d6
n(5,6*)= n•ga,s e'	 (li
Ssing+' 0 cosa ed9
e
4The minimum transverse pressure on the line AB may be taken for zero, as
emin ` 0. The cross pressure on the line BC will be determined by the expression
XA
2 S sin"+'0(1—gsin2 0)0/2d0
P.L(S) = 
m 
2Re q°
A 0	 -- ^.
	
n/2	 (2)
S sina+
1 a coss ede
0
Consequently on the outer boundary the transverse pressure between the lines
AB and BC will vary from 0 to pl (S). For the determination of the longitudinal
interval over which this variation is observed we have Ap_ L(S) = py(S) and it is
sufficient to find A(D = AC, that is, the magnitude of azimuthal displacement of
particles with pitch angle Amin = 0 + ^ for a half-period of oscillation between
the mirror points. For simplicity we may assume that the pressure on the outer
boundary is linearly dependent on longitude; then the azimuthal gradient will be
VP1(S) = K3 
OPl (S) = K3 Pl (S)
a(D
	 A0 (S)
Here and further K 1 , K2 , K 3 are metric coefficients.
Behind the line BC multiply reflected narticles will add up to the above
considered particles; the transverse pressure induced by them will gradually
grow until attaining the maximum near the inner boundary of the source. Subsequent-
ly the transverse pressure remains invariable along the drift trajectory up to
the region of particle destruction, where the pressure gradient will have the op-
posite sign. In the case when the extension of the source Al = AC, the pressure
remains invariable from the outer boundary (line BC) to the region of destruction.
The appearance in the magnetic field of longitudinal pressure gradients per-
pendicular to the field results in emergent? of currents
i = - c - [B X OP.L],
I3^
flowing in the direction of the normal to the magnetic field and to pressure gra-
dient.
The total intensity of such currents may be found by integrating over the
area da	 dS•d(p/K 1 K 3 (dS being an element of the field line)
s c [B X VPAS)]
	
0 
[^-	 ti 1	 (S)
(3)
(4)
n
SIn application to the geomagnetic field let us compute the strength of
currents induced by longitudinal pressure gradients, limiting ourselves to the
outer boundary of the source. Starting from the hypothesis on particle pene-
tration into the magnetosphere through the neutral points and their s_^sequent
escape into the Earth's magnetic tail [6], we must place the source of particles
near the noon meridian, and the region of destruction in the night sector of the
magnetosphere.
For partic es arriving from the tail the inverse pattern will be valid:
the source on the night side and the region of destruction on the daytime side.
In the first approximation we shall consider the geomagnetic field as a
dipole, and we shall denote:
re = fea as the distance from the center of the Earth to the field line (in
the equatorial plane), a as the radius of the Earth, ^ as the geomagnetic latitude
of the point on the field line, B o
 as the field on the ground at the equator.
Then,
1
K1 _ 
rQ (1 + 3 sine qj)'/2cos T
(1 + 3sin2 qp)'/,_
KZ	
Coss	 '
i
Ks _r. 
cos3 4
	
_	 cos°q— 
y1 +3sin2(p
The density of currents conditioned by longitudinal gradients, in the dipole
field will be
_	 c	 8p„ _
	 cf,= cos3 q;	 8p„
j	 B(g1)rcOS3 q) 8Q)	 Boa (1+3sin2 q))'/s
 80	 (6)
The relation between the longitudinal displacement of the particle and the
shift along the field line was obtained for the dipole field by Alfven [7]:
Cal
sine 80
co
S 
3toss4p(! + sinZ0 [ i--
Ah((P) =
	. 
2q
2q	 d ^	 (7)0	 (1+3sin2 jp )% L1— 
si 
4 -^
6Taking into account (6) and (7), the total intensity of currents (5) may
be represented in the form
I = toa2p S D(T)d40
	where io — cmv 2 ne/aB o
	1.57.10-16nOE a/cm 2 , n o E is the energy density expressed
in kev/cm 3 , DM is a coefficient characterizing the variation of current's in-
tensity with latitude.
The dependence I1w, computed for certain cases of angular anisotropy, is
p lotted in Fig.3. Calculations show that the total force of currents conditioned
by pressure gradients may reach at the outer
4^P1	 boundary of the source the magnitude I 0 =
= 1.25 10 a ( at the condition n o E = 100 kev/
oar--/ , p=2
oa,_^ ,0 ,0	 /cm3, fo = 10). As the distance from the
•a=o,0
	
center of the Earth decreases, the currentp--
azr	 strength decreases by - f e . The direction
	
/+!	 of currents depends on the sign of particles.
x	 In the region of the source the current will
0,2' 	 1	 be directed inside the magnetosphere for ne-
gatve particles, and outside for the posi-
t P	 ve ones.
e	 If the source is not stationary, the
0,
o^	 magnitude of the transverse pressure will be
a function of longitude (and time) beyond
	
g	 ^ the limits of the source also. The conside-
ration of temporal effects is contemplated
0	 20	 ad	 170 W	 for a later date. Here we shall note only
	
Fig.3	 that with the increase of source's activity
a rise in transverse pressure will be obser-
ved from the outer boundary of the source to the inner one, with subsequent drop in
the direction of the region of destruction, which will apparently result in the
settling of a system of currents of the form shown in Fig.4.
Besides the above considered currents, other ones, directed along the field
lines will also be observed at the boundary of the source. This effect is the
result of the fact that the direct (from source to reflection points and the
,ion of
rticles' sourceregion of
destruc
7
reflected particle fluxes are displaced relative to one another in longitude.
Because of that there takes place near the source's boundar y a noncompensated
charge transfer directed toward the reflection points. As the range from the
boundary line AB in the direction of the drift increases (see Fig.l), the direct
and reflected fluxes are equalizing and the charge transfer ceases. The density
of the longitudinal currents on an element S of the line of ford are easy to
Fig.2
estimate if the initial density ne of particles and the character of angular ani-
sotropy are known
z
^sin" ,1 0 cos 0(1—gsin"0)''/2
= en (S) v u (S) = en.v.gG12 0 Z.
. 
sins+t 0 cos; 0 d0
0
However, the total intensity of longitudinal currents I = J jdS of such an
origin is found to be negligibly small because of the fact that the currents flow
only in a narrow boundary layer.
The effect induced by particles with pitch-angles lying in the cone of losses
may result to be more interesting in the application to the geomagnetic field.
These particles will be fully absorbed in the Earth's atmosphere and, consequently,
the direct flux of such particles will not be compensated by the inverse flux.
(It is assumed here that the condition of particle flux's quasi-neutrality is not
fulf'_lled) .
8Let now the cone of losses be determined by the critical angle E oc = 2-,
and the intensity of the source be n p v	 1.0A CM-2 -sec -1 ; then for an angular
anisotropy of the form((' _ —1, = 0; a -^ —^, S = 2) the density of currents
along the line of force ,fll have a magnitude
j — en0 r,0q-'1, sin2° z q-'/,•0,2.10-z CGSE.
Multiplying by the area of the source
dS = q • a4M jed(D
and assuming d(A °2 °, ht = 6, ja = 10, we shall obtain that the intensity of currents
flowing along the field lines will vary from I - 2 . 10 5 a at the equator to I - 10 4 a
at ionosphere heights.
**** T H E E N D ****
Manuscript received on
8 August 1968
REFERENCES
1. E. N. PARKER. Phys. Rev., 107, 924, 1957.
2. S. J. AKASOFU, S. CHAPMAN, J. Geophys. Res. 66, 1321, 1961.
3. V. D. PLETNEV, 0. A. TROSHICHEV. Kosm. Issl. 6, 5, 707, 1968.
4. J^kMES A. VAN ALLEN. Earth'S Radiation Belts. (For.Lit.)1962.
5. V. D. PLETNEV, 0. A. TROSHICHEVA. Kosm. Issl. 6, No.3, 471, 1968.
6. V. D. PLETNEV, G. A. SKURIDIN, V. P. SHALIMOV, I. N. SHVACHUNOV.-
Sb. "Issledov. Kosm. Prostranstva", NAUKA, 1965.
7. G. ALFVEN, K. G. FEL'THAMMAR. Kosm Elektrodinamika., "MIR", 1967.
CONTRACT No.NAS-5-12487
VOLT INFOR14ATION SCIENCES, INC.
1145 - 19th St. NW
WASINGTON D.C. 20036.
Telephone: (202)-223-6700 (X-36)
Translated by ANDRE L. BRICHANT
on 1 and 2 March 1969


Currents of quasi-trapped particles having discontinuities on the day and night sides of the earth

Abstract

Similar works

Full text

Available Versions

NASA Technical Reports Server