KINETI C SIMULA TION OF FIELDS EXCIT ATION AND PAR TICLE ACCELERA TION BY LASER BEA T W A VE IN NON-HOMOGENEOUS PLASMAS V.I. Karas’, Ya.B. Fainberg, Kharkov Institute of Physics and Technology, National Scientific Center, Kharkov, 310108 Ukraina, V.D. Levchenko and Yu.S. Sigov, M.V. Keldysh Institute of Applied Mathematics, Moscow, 125047 Russia Abstract Resonance excitation of longitudinal plasma electrostatic wave by double-frequency laser radiation is investigated numerically to study in deta il condi tions of parti cle beat wave acc eler a- tion. The compute r simulati on is base d on the highly sp ecia l- ized code SUR, using splittin g techn ique. Both the spac e uni- form and slightly non-uniform cases a re investigated. Maintain- ing of phase synchronism between accelerated particles and ex- ited longitu dinalwave is provid ed by a choic e of densi ty plas ma profile. I. INTRODUCTION The method of charged particle acceleration by charge den- sity waves in plasmas and in non-compensated charged parti- cles, which Ya.B. Fainberg proposed in 1956 [1], seems to be one of the promising method s of colle ctive acce lera tion [2], [3]. The primary challenge in all plasma acceleration schemes is to produce a substantial plasma density perturbation with a phase velocity to be close to velocity of light . At pres ent the most promising concepts are pla sma beat–wave accelera tion and plasma wake field acceleration. In the plasma beat –wave accelerationscheme [4], two copro p- agating laser beams with slightly different frequencies are in- jected into a plasma. C. Toshi at al (1993) obtained the electric fiel d str eng thsof the cha rge–dens ity wave of, an d de- tected the accelerated electrons with an energy of(in- jection energy was ). The resona nt plasma density was , but already in January 1994, the length, the electrons acquired . Reson ance exci tation of longitu dina l plasma elec trosta tic waves by elec troma gneti c wave s is inves tigate d nume rica lly wit h he lpof the SUR code. The SUR codeis ba se d onsolving the finite–difference analogs of the Maxwell and Vlasov–Fokker– Planckequati ons thr oughthe success ive use of thesplitti ngtech- nique over physical processes and variables of phase space. In order to economize our machine time, we do not yet pose the problem to be solved with its real parameters [5]. II. COMPUT A TIONAL MODEL Conside r a linea rly polar ized elec tromagnet ic wave propagat- ingin the direction with the elec tric vect or direc ted along the The workis partly suppor tedby the Inter natio nalScientifi c Foundat ion,grant U27000 and Russian Foundation for Fundamental Research, project no. 94-02- 06688. –axis an d the mag netic field vec tor ori ent ed along the –axis ( –polar izati on). The actio n of such a wave onto plasma parti- cles ca n give rise only to the and velocity comp onents . In the ca se whe re the dis tri but ionfunct ion does not dep end ini tia lly on and , three phase s pace coordinate s are sufficient to describe subse quent plasm a behavior; the rele vantdistribution function is . The plasma electron dynamics may by described the Vlasov equation This equation is solved by a variant of the method of splitting over phase–space coordinates[6]. Effects due to charged–particle collisions in the plasma can- not significantly affect the time of electromagnetic wave prop- aga tion through the simul ated syst em. Bec ause of this, we do not t ake t he Fokk er– Plank colli sion term in the e quation into ac- count. The similar equation might be written for the plasma ions; however, in these computa tions the ions, being heavy compared to electrons, were assumed to be motionless. The longitu dinalelectri c field isdetermine d from thePois- son equation, which, in one–dimensional case, can be written as where is the ion background; is the electron density; and represent the coordinate and field value on the system left boundary, respectively. The tra nsverse ele ctromagneti c fiel d mus t be sat isf y the Maxwell equations: where is the current density . The latter two equ ati onscan be wri tten in a for m more con ven ien t fornume ric al computations:
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V.I. Karas et al- Kinetic Simulation of Fields Excitation and Particle Acceleration by Laser Beat Wave in Non-Homogeneous Plasmas
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8/3/2019 V.I. Karas et al- Kinetic Simulation of Fields Excitation and Particle Acceleration by Laser Beat Wave in Non-Homoge…
KINETIC SIMULATION OF FIELDSEXCITATION ANDPARTICLE
ACCELERATION BY LASER BEATWAVE IN NON-HOMOGENEOUS
PLASMAS
V.I. Karas’, Ya.B. Fainberg,
Kharkov Institute of Physics and Technology, National Scientific Center, Kharkov, 310108 Ukraina,
V.D. Levchenko and Yu.S. Sigov,
M.V. Keldysh Institute of Applied Mathematics, Moscow, 125047 Russia
Abstract
Resonance excitation of longitudinal plasma electrostatic wave
by double-frequency laser radiation is investigated numerically
to study in detail conditions of particle beat wave accelera-
tion. The computer simulation is based on the highly special-
ized code SUR, using splitting technique. Both the space uni-
form and slightly non-uniform cases are investigated. Maintain-
ing of phase synchronism between accelerated particles and ex-
ited longitudinalwave is provided by a choice of density plasmaprofile.
I. INTRODUCTION
The method of charged particle acceleration by charge den-
sity waves in plasmas and in non-compensated charged parti-
cles, which Ya.B. Fainberg proposed in 1956 [1], seems to be
one of the promising methods of collective acceleration [2],
[3]. The primary challenge in all plasma acceleration schemes
is to produce a substantial plasma density perturbation with a
phase velocity to be close to velocity of light c . At present the
most promising concepts are plasma beat–wave acceleration and
plasma wake field acceleration.In the plasma beat–wave acceleration scheme [4], two coprop-
agating laser beams with slightly different frequencies are in-
jected into a plasma. C. Toshi at al (1993) obtained the electric
field strengths of the charge–density wave of 0 7 1 0
7
V
c m
, and de-
tected the accelerated electrons with an energy of 9 1 M e V
(in-
jection energy was 2 M e V ). The resonant plasma density was
8 6 1 0
1 5
c m
3 , but already in January 1994, the 1 c m length,
the electrons acquired2 8 M e V
.
Resonance excitation of longitudinal plasma electrostatic
waves by electromagnetic waves is investigated numerically
with helpof the SUR code. The SUR codeis based on solving the
finite–difference analogs of the Maxwell and Vlasov–Fokker–
Planck equations throughthe successive use of the splittingtech-
nique over physical processes and variables of phase space.
In order to economize our machine time, we do not yet pose
the problem to be solved with its real parameters [5].
II. COMPUTATIONAL MODEL
Consider a linearly polarized electromagnetic wave propagat-
ingin the x direction with the electric vector ~
E directed along the
The workis partly supportedby the InternationalScientific Foundation,grantU27000 and Russian Foundation for Fundamental Research, project no. 94-02-06688.
y –axis and the magnetic field vector ~
B oriented along the z –axis
( p –polarization). The action of such a wave onto plasma parti-
cles can give rise only to the V
x
and V
y
velocity components. In
the case where the distributionfunction does not depend initially
on y and z , three phase space coordinates x V
x
V
y
are sufficient
to describe subsequent plasma behavior; the relevant distribution
function is f ( ~ r ; ~ p ) = f ( x V
x
V
y
) ( V
z
) .
The plasma electron dynamics may by described the Vlasov
equation
@ f
e
@ t
+ V
x
@ f
e
@ x
e ( E
x
+
V
y
c
B
z
)
@ f
e
@ p
x
e ( E
y
V
z
c
B
z
)
@ f
e
@ p
y
= 0
This equation is solved by a variant of the method of splitting
over phase–space coordinates[6].
Effects due to charged–particle collisions in the plasma can-
not significantly affect the time of electromagnetic wave prop-
agation through the simulated system. Because of this, we do
not take the Fokker–Plank collision term in the equation into ac-
count.
The similar equation might be written for the plasma ions;
however, in these computations the ions, being heavy compared
to electrons, were assumed to be motionless.
The longitudinalelectric field E
x
is determined from thePois-
son equation, which, in one–dimensional case, can be written as
E
x
= E
x L
+ 4 e
x
Z
x
L
( n
i
( ) n
e
( ) ) d
where n
i
( x ) is the ion background; n
e
( x t ) =
R
f d ~ p is the
electron density; x
L
and E
x L
represent the coordinate and field
value on the system left boundary, respectively.The transverse electromagnetic field must be satisfy the
Maxwell equations:
1
c
@ B
z
@ t
=
@ E
y
@ x
1
c
@ E
y
@ t
=
@ B
z
@ x
4
c
j
y
where j
y
= e
R
f
e
V
y
d ~ p is the current density. The latter two
equationscan be written in a form more convenient fornumerical
computations:
8/3/2019 V.I. Karas et al- Kinetic Simulation of Fields Excitation and Particle Acceleration by Laser Beat Wave in Non-Homoge…