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14THE EFFECT OF ELECTRIC DRIFT ON THE MOVEMENT OF A CHARGED PARTICLE IN THE FIELD OF AN ACCELERATED ELECTROMAGNETIC WAVE
Shaar Y.
Associate professor Institute of Physical Research and Technology Russian University of Peoples' Friendship - Moscow
Karnilovich S. Associate professor Institute of Physical Research and Technology Russian University of Peoples' Friendship - Moscow
Hassan N. Associate professor Institute of Physical Research and Technology Russian University of Peoples' Friendship - Moscow
Abstract
In this work we considered the possibility of accelerating charged particles in a field of a linearly polarized electromagnetic wave traveling along a constant magnetic field crossed with an electrostatic one under conditions close to resonance
Keywords: Autoresonance, Motion of charged particles, Acceleration of charged particles.
Studies of the motion of charged particles in various types of electric and magnetic fields are of great importance for solving a number of fundamental problems, as well as for numerous practical applications [1],
[2]. Of particular interest are the modes of motion in which particles acquire significant energy. One of these modes is associated with the cyclotron autoresonance mechanism discovered by Kolomensky and Lebedev
[3]. Cyclotron autoresonance is carried out in the case of a vacuum electromagnetic wave under rather severe conditions for the injection of accelerated particles. If these conditions are violated, it is possible to maintain cyclotron resonance in various ways. One of them is
Source equations
based on the use of crossed static electric and magnetic fields [4]. In [4], it was shown that it is possible to maintain cyclotron resonance in a concomitant reference frame moving with the speed of electric drift in the case of a slow wave whose phase velocity is less than the speed of light in vacuum. It was assumed that the static electric field is weaker than the leading magnetic field. In this paper, we consider the possibility of cyclotron acceleration of charged particles by linear and elliptical polarizations accelerated by an electromagnetic wave in the case when the electrostatic field is stronger than the magnetic. The conditions of such an acceleration mode are found.
= (E cos6, E2 sin6,0)
B„ = (~NE2 sin 6,NEl cos6,0)
Eo= ( E,0,0)
Bo = (0, B0,0)
dP a PzQ NsP . = s cos 6 + vQ - —---— cos 6
dr
7
7
dPy . a Ns P = s sin 6-
dr
^ sin 6
7
(1)
dPz Nsi Px _ Ns2 Py . a Px„ z - 1 x cos 6 +-- sin 6 + — Q
dr
7
d6 NPP
dr
7 -1
7
7
d7 sl Px _ S2 p- . a T/„PX - 1 x cos 6 +-y sin 6 + VQ—
where
dr 7
om0c
7
P =
s =
7 eE
V = E0
a m0c B0
(2)
mc
Consider the case when the wave is linearly polarized in the direction of the electrostatic field (X)
g = 0
dP NP P
= g (1 - np^) cos e + Q(v - p) dz у у
dP
—— = 0 dz
dPz Nei Px _ Px„ z - 1 x cose + —— Q
dz у de NPP
у
-1 (4)
dz у
dL=£1PL cose + VQ^ dz у у
p
(3)
If n =
1
V
Then P - Ny = Const или —- P = C z I V z 1
(5)
(6)
уо
Assuming Ci = 0 then the initial parameters of the particle will have to satisfy the condition Pz 0 = — which
will be maintained for the whole particle's motion.
E
Such a condition means that V = — > 1
Bn
у
P 1
From the condition P = — follows that — = — (6)
z V y V
In this case, the equations system (4) takes the form
dP P P
= ei(i -P)cos0 + QV(i -P) dr Vy Vy
dP
—— = 0 dr
dP2 ei Px _ Px„ z - 1 cos# + — Q
dz Vу
у
de= P -1
dz Vу
V
(7)
Then, using (5), the equation for the phases has the form
de=_1 -1=-c
dz V2 Ce
(8)
By Integrating (8), we obtain the expression for the phase in the form
в = во -Cez
Now system (6) has the form:
P
dz
= Ce (g cose + vQ)
dPy
= 0
dr
dP P
d-z- = p (e cos 6» + vQ) dr Vy
d6
-T = -Ce (10)
dr
dyy = P (e cos 6 + vQ) dr y
dy P dP
This shows that v— = ^x--- and P2 = Cy -C
x ei 2
dr Ce dr
Using (6) and the energy conservation equation y 2 = P^ + Py2 + P^ +1 We get the expression for C2 in the form
c2 = py20 +1 then Pi = cy - Py0 -1
From where
P 2 + P 2 +1
2 P x + P y 0 + 1
y =—— (11)
C6
Now system (10) is rewritten in the form
dP
x = Ce e cos(60-ce r) + C0VQ
dr
dr
dPy
y = 0
dP P
z = p (e cos(60-cer) + vQ)
dr Vy c dr
d6
-T = -Cg (12)
Finally
y dy = Px (elcos{60-Cer) + VQ) dr
Px = CgVQr - e1 sin(g0-Cgr) + Cpx , Cpx = Px0 + e1 sin g0
px = Px0 + e sm g0 + CgVQr - e sin( eo-C0 r) (13)
Py = Py0 (14)
P =
y = V,
Px2 + Py2 + 1
, (15)
v 2 -1
6 = 60 - Cer (16)
Px + py2, + 1
V2 -1
(17)
REFERENCES: 3. Kolomenskii A A, Lebedev A N Sov. Phys.
1. Artsimovich, L.A. and Lukyanov, S.Yu. JETP 17 179 Moscow 1963
"Motion of Charged Particles in Electric and Magnetic 4. Milantiev V.P. // TECHNICAL PHYSICS
Fields", Mir Publishers, Moscow 1980. JURNAL. 1994.V. 64 (6). S.166. Moscow 1994.
2. Morozov, A. I.; Solov'ev, L. S. "Motion of Charged Particles in electromagnetic Fields", Reviews of Plasma Physics, Volume 2, New York, 1966.
