Dynamics of charged particles in a field of intensive electromagnetic waves
The results of analytical and numerical investigation of charged particles dynamics in a field of intense electromagnetic waves and electromagnetic pulses are reported. Conditions for effective acceleration of charged particles by the field of high-frequency or laser radiation in vacuum are found....
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irk-123456789-793022015-03-31T03:01:55Z Dynamics of charged particles in a field of intensive electromagnetic waves Buts, V.A. Ускорители заряженных частиц The results of analytical and numerical investigation of charged particles dynamics in a field of intense electromagnetic waves and electromagnetic pulses are reported. Conditions for effective acceleration of charged particles by the field of high-frequency or laser radiation in vacuum are found. It is shown, that the presence of frictional force can promote power transmission from a high-frequency field to particles. There are regimes at which all moments grow in time. Moreover, the higher moments grow faster then lowest. It means existence of the superdiffusion. It is shown, that there are conditions, when the leading centers of particles with different masses move in different directions Изложены результаты аналитического и численного исследований особенностей динамики заряженных частиц в поле интенсивных электромагнитных волн и электромагнитных импульсов. Найдены условия, при которых возможно эффективное ускорение заряженных частиц полем высокочастотного и лазерного излучения в вакууме. Показано, что силы трения могут способствовать ускорению частиц. Обнаружены хаотические режимы, в которых все моменты растут во времени. Более того, высшие моменты растут быстрее низших. Это означает наличие супердиффузии. Показано, что существуют условия, при которых ведущие центры частиц с различными массами движутся в разных направлениях. Викладені результати аналітичного та чисельного дослідження особливостей динаміки заряджених часток у полі інтенсивних електромагнітних хвиль та електромагнітних імпульсів. Знайдені умови, при яких є можливість ефективно прискорювати заряджені частки полем високочастотного та лазерного випромінювання у вакуумі. Доведено, що сили тертя можуть допомагати прискоренню часток. Знайдені хаотичні режими, в яких усі моменти зростають у часі. Більш того, виші моменти зростають швидше ніж нижчі. Це означає наявність супердиффузіі. Доведено, що існують умови, при виконанні яких ведучі центри часток с різними масами рухаються у різних напрямках 2006 Article Dynamics of charged particles in a field of intensive electromagnetic waves / V.A. Buts // Вопросы атомной науки и техники. — 2006. — № 3. — С. 55-59. — Бібліогр.: 10 назв. — англ. 1562-6016 PACS:29.17.+w http://dspace.nbuv.gov.ua/handle/123456789/79302 en Вопросы атомной науки и техники Національний науковий центр «Харківський фізико-технічний інститут» НАН України |
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Ускорители заряженных частиц Ускорители заряженных частиц |
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Ускорители заряженных частиц Ускорители заряженных частиц Buts, V.A. Dynamics of charged particles in a field of intensive electromagnetic waves Вопросы атомной науки и техники |
| description |
The results of analytical and numerical investigation of charged particles dynamics in a field of intense electromagnetic
waves and electromagnetic pulses are reported. Conditions for effective acceleration of charged particles
by the field of high-frequency or laser radiation in vacuum are found. It is shown, that the presence of frictional
force can promote power transmission from a high-frequency field to particles. There are regimes at which all moments
grow in time. Moreover, the higher moments grow faster then lowest. It means existence of the superdiffusion.
It is shown, that there are conditions, when the leading centers of particles with different masses move in different
directions |
| format |
Article |
| author |
Buts, V.A. |
| author_facet |
Buts, V.A. |
| author_sort |
Buts, V.A. |
| title |
Dynamics of charged particles in a field of intensive electromagnetic waves |
| title_short |
Dynamics of charged particles in a field of intensive electromagnetic waves |
| title_full |
Dynamics of charged particles in a field of intensive electromagnetic waves |
| title_fullStr |
Dynamics of charged particles in a field of intensive electromagnetic waves |
| title_full_unstemmed |
Dynamics of charged particles in a field of intensive electromagnetic waves |
| title_sort |
dynamics of charged particles in a field of intensive electromagnetic waves |
| publisher |
Національний науковий центр «Харківський фізико-технічний інститут» НАН України |
| publishDate |
2006 |
| topic_facet |
Ускорители заряженных частиц |
| url |
http://dspace.nbuv.gov.ua/handle/123456789/79302 |
| citation_txt |
Dynamics of charged particles in a field of intensive electromagnetic waves / V.A. Buts // Вопросы атомной науки и техники. — 2006. — № 3. — С. 55-59. — Бібліогр.: 10 назв. — англ. |
| series |
Вопросы атомной науки и техники |
| work_keys_str_mv |
AT butsva dynamicsofchargedparticlesinafieldofintensiveelectromagneticwaves |
| first_indexed |
2025-07-06T03:23:10Z |
| last_indexed |
2025-07-06T03:23:10Z |
| _version_ |
1836866276529537024 |
| fulltext |
DYNAMICS OF CHARGED PARTICLES IN A FIELD OF INTENSIVE
ELECTROMAGNETIC WAVES
V.A. Buts
NSC KIPT, Kharkov, Ukraine
E-mail: vbuts@kipt.kharkov.ua
The results of analytical and numerical investigation of charged particles dynamics in a field of intense electro-
magnetic waves and electromagnetic pulses are reported. Conditions for effective acceleration of charged particles
by the field of high-frequency or laser radiation in vacuum are found. It is shown, that the presence of frictional
force can promote power transmission from a high-frequency field to particles. There are regimes at which all mo-
ments grow in time. Moreover, the higher moments grow faster then lowest. It means existence of the superdiffu-
sion. It is shown, that there are conditions, when the leading centers of particles with different masses move in dif-
ferent directions
PACS:29.17.+w
1. INTRODUCTION
Dynamics of charged particles in fields of moderate
intensity electromagnetic waves is well investigated.
We call a field –“field of a moderate intensity”
f the wave force parameter ε is much less then one.
(here /eE mcε ω= ; E − electric strength of the wave;
ω - its frequency)
A considerable success has been achieved recently
in generating electrоmagnetic fields of extremely large
intensity. The wave force parameter of such fields is al-
ready close to unity and can even be substantially large.
For, as an example, a ten-centimeter wave band it
means that the electric strength of the wave exceeds
105 V/cm. For a laser radiation ( 4~ 10λ − cm) this inten-
sity should be higher than 1010 V/cm.
In the 2-5 parts of this report we present the results
of investigation of particles dynamics under influence of
a field of one electromagnetic wave only or in a field of
an electromagnetic impulse of high intensity. Let’s men-
tion that there are many similar results published (see
ref. [1-8]). In the 6-8 parts we analyze the dynamics of
particles under influence of electromagnetic wave, ex-
ternal magnetic field and a friction force.
2. BASIC EQUATIONS AND INTE-
GRALS
Let's consider a charged particle, which moves in an
external permanent magnetic field of magnitude 0H in
a direction along Z-axis and in a field of an electromag-
netic wave of arbitrary polarization. The wave has fol-
lowing components:
( )Re exp ;E ikr i tε ω= −
rrr r
( ){ }0 , ,x y zE E iα α αє
r
, (1)
( )Re expcH kE ikr i tω
ω
й щ= −л ы
r rr r r
,
where { }, ,x y ziα α α αє
r
− vector of polarization of the
wave.
Without loss of generality it is possible to assume,
that the vector k
r
has only two non-zero components:
xk and zk . If one measures the time in the units of 1ω − ,
velocity in c , wave vector k in
c
ω
, impulse in mc ,
and introduces dimensionless amplitude of field as
0 0 /eE mcε ω= , the equations of a particle motion can
be rewritten in a form:
( ) [ ] ( )1 Re Re ;
/ ; / 1,
i iHkp kP e pe p e
r p kp
ψωε ε
γ γ γ
γ ψ γ
Ψцж
= − + +чз
и ш
= = −
r rrr r rrr r&
rr r r& &
(2)
where:
0 0, / ; / ;
.
Ht e H H eH mc
kr
τ ω ω ω
ψ τ
є є є
= −
rr
rr
It is convenient to add to these equations the equa-
tion for energy:
( )Re iv e ψγ ε= r& (3)
From (2) and (3) one can found an integral of motion:
( ) [ ]Re i
Hp i e re k I constψε ω γ− + − =є
rrr rr
(4)
3. INTERACTION WITH A PLAIN
POLARIZED WAVE
The most important features of a particle dynamics
in a field of a plain polarized wave are summarized in
[1-2]. Here we only mention that charged particles are
dragged by a field of plain polarized wave in a direction
of propagation of this wave. The velocity of the entrain-
ment is sufficiently high. Such dynamics can be poten-
tially used for acceleration of charged particles. Howev-
er particles placed in different phases of an electromag-
netic wave, move differently. Therefore, a bunch of ac-
celerated particles scatters. Let's indicate also that dif-
ferent applications for this dynamics have been de-
scribed in [2].
4. INTERACTION OF PARTICLES
WITH A CIRCULARLY POLARIZED
WAVE
If a wave has elliptic, particularly circular polariza-
tion then the dynamics of particles has some important
features. Let's discuss some of them. Major feature of
dynamics of particles in a field of a wave with circular
polarization is the independence of a longitudinal mo-
mentum of a particle from its initial phase. This is illus-
trated by Fig.1. From Fig.1 one can see that the magni-
____________________________________________________________
PROBLEMS OF ATOMIC SCIENCE AND TECHNOLOGY. 2006. № 3.
Series: Nuclear Physics Investigations (47), p.55-59.
55
mailto:vbuts@kipt.kharkov.ua
tudes of longitudinal impulses of all particles complete-
ly coincide. From the equations (2) it is possible to ob-
tain an expression, which describes this important fea-
ture:
[ ]02 1 cos( )zP ψ ψ= − −E . (5)
From this expression follows, that the magnitude of
a longitudinal impulse is identical for all particles. It
does not depend on an initial distribution of particles
over initial phases.
Spatial dynamics of particles in a field of a wave
with circular polarization unfortunately is not so corre-
lated: in a longitudinal direction all particles trajectories
are completely similar, but in a transverse direction all
particles disperse.
0 5 10 15 20 25 0,0
0,5
1,0
1,5
2,0
Pz
τ
Fig.1. Dependence of longitudinal momentum of
particle from its initial phase: 0, π/4, π/2, 3π/4,
π at E =1
More detailed analytical and numerical examinations
reveal (see [10] for details), that the trajectory of a parti-
cle in a circularly polarized wave is a spiral with an axis
directed along the wave-vector of the wave. The radius
of the spiral is E in the impulse space. Thus, the accel-
eration of particles by a field of circularly polarized
wave can remove some problems with scattering of
electrons that occur in an acceleration system based on
linearly polarized waves.
5. INTERACTION OF A PARTICLE
WITH AN IMPULSE OF AN ELEC-
TROMAGNETIC WAVE
Let's consider a motion of a charged particle in a
field of an impulse of a plain electromagnetic wave
characterized by a vector potential:
( ) ( )A A t k r Aω ψ= −Ч Ч є
rr r rr
. The equation, which de-
scribes motion of particles in such a field in dimension-
less variables tτ ωє , 1k k kє
r r
, 1k cωє , v cβ є
r r
1 0p p m cє
r r
, ( vr -velocity of a particle, pr -its impulse),
0 1 0A ek A m cωє , becomes:
( )1dp A Ak k
d
β β
τ ψ ψ
цж∂ ∂= − − − чз∂ ∂и ш
r rr r r r r
. (6)
It is convenient to add to (6) the equation for the en-
ergy:
d A
d
γ β
τ ψ
цж ∂= − чз ∂и ш
rr
. (7)
From the equations (6) and (7) it is easy to find a fol-
lowing integral:
0 0 0=Const=p A k p A kγ γ+ − + −
r rr rr r . (8)
In a case of a pure transverse wave: ( || 1, 0k k⊥= = ,
|| || || 0k E k H k Aй щй щ й щ= = =л ы л ы л ы
rr r
), the equations (6)-(8) are
completely integrable in a laboratory coordinates. The
solution is:
( ) 2 2
0 0
|| ||0
2
A A p
p p
γ ψ
⊥
•
− +
− =
r r r
; ( )0 0p - p = A A⊥ ⊥ −
r rr r
; (9)
( )
( )
0
||0 0
|| ||0
2 2
0 02
1 ;
2
p
r r
A A p d
ψ
ψ
ψ ψ
γ ψ
ψ
γ ψ
•
⊥•
−
− = +
+ − +
ж ц
з чи ш
т
r r r (10)
( )
0
0 0 0
1r r A A p d
ψ
ψ
ψ
γ ψ
⊥ ⊥ ⊥•
− й щ− = − −л ыт
r rr r r
.
From (9), (10), one can see that the particles are
dragged by the field of a wave. Their longitudinal im-
pulses oscillate, but keep their direction, and a longitu-
dinal coordinate is determined by an integral of a non-
negative function. The most interesting and important
feature characterizes dynamics of particles in a field of a
circularly polarized impulse. The interaction of particles
with a wave in this case does not depend on their initial
location. An entrainment of particles in a longitudinal
direction occurs and this entrainment happens on a spi-
ral trajectory. Moreover, the longitudinal momentum of
all particles follows the shape of the field envelope.
Fig.2 illustrates these features and shows temporal
dependence of particles momentums obtained from nu-
merical solution of equation (6). The components of an
electromagnetic impulse are defined by a relation:
2
0 0/ exp[ ( ) ] cosxA Aψ β ψ ψ ψ∂ ∂ = − − Ч , with 0 3A = ,
0.01β = , 0 50ψ = . If the particles of a bunch have ini-
tial energy 0 10γ = then they gain energy of 100γ ≈ on
a distance of 0.4 cm. In addition, these particles do not
disperse in transverse direction. Such laser impulse is
convenient for an acceleration purposes.
0 20 40 60 80 100 0,0
0,1
0,2
0,3
0,4
0,5
0,6 Pz
τ
Fig.2. Dependence of longitudinal momentum of
particle from its initial phase: 0, π/4, π/2, 3π/4,
π at 3A =
Above we have considered dynamics of charged parti-
cles in a field of an intensive electromagnetic wave and
an opportunity to use it for the purposes of acceleration.
However, some features of this dynamics can be useful
for other applications too. Let's indicate an opportunity
to use these results for excitation of intensive short-
wave coherent radiation. For example, if there is a clus-
ter of particles in a wave, then the charge of this cluster
56
will be in N − times higher then the charge of one par-
ticle ( N − number of electrons in the cluster). If cluster
size is smaller than a length of wave, in which it moves,
all particles emit together and the radiation is coherent.
The intensity of radiation from such a bunch will be
proportional to 2N . Usual number of electrons in a clus-
ter is ~108…1010. Therefore, it is possible to use such
clusters for the purposes of excitation of intensive short-
wave coherent radiation.
6. ROLE OF FRICTIONAL FORCE
AT INTERACTION OF ADIATION
WITH CHARGED PARTICLES
When charged particles are in a field of electromag-
netic waves then they are move with acceleration. Thus
there is a radiation. The particles lose energy. There is a
radiation friction. As any frictional force radiation fric-
tion will brakes, in most cases, charged particles. The
force of radiation friction promptly grows with energy
of particles (~ 4γ ). Therefore this friction restricts ener-
gy, which can be received particles. The maximal ener-
gy can be estimated by equating accelerating forces to
forces of radiation friction. So, for example, in work [6],
studied acceleration of electrons by a field of a laser ra-
diation, the authors have equated force of radiation fric-
tion to accelerating forces (forces of high-frequency
pressure). In result they have found, that in a field of a
laser radiation the electrons can not gain energy large,
than 200 MeV ( ~ 1 kλ µ ).
In the present section we shall show, that the fric-
tional force, including forces of radiation friction, can
promote power transmissions from an external laser
field to accelerated particles. Let's mark, that for the
first time on an unusual role of frictional force at a mo-
tion of charged particles in a field of an intensive elec-
tromagnetic wave was pointed in work [7].
Let's consider most simple model, which can de-
scribe dynamics of a charged particle in a field of a laser
radiation. Let particle is moving in a field of a homoge-
neous flat electromagnetic wave. Field of this wave we
shall present as:
( ){ } { }0 0Re exp ; Re /E E i H kE kй щ= Ψ = л ы
rr r r r
,
Here t k rωΨ = −Ч Ч
r r , 0 0E Eα= Ч
r r , { }, ,x y ziα α α α=r
,
0k cωє .
Except this field we shall consider that there is fric-
tional force, which brakes a particle. In the beginning
we shall consider model, in which we shall not point
concrete the nature of these forces. Then, we shall con-
sider concretely forces - radiation friction. Equation of
motion of a charged particle in dimensionless variables:
p p mc=r r
, tτ ω= , 0r k r=r r
, 0k k k=
r r
, 0eE mcε ω=
rr ,
tτ ω= Ч is possible to write as:
( ) ( ){ }Re (1 v) (v ) expdp k k i v
d
ε ε µ
τ
= − + Ψ −
r r rr rr r r
. (11)
This equation differs from investigated in [2] and
from (2) only by presence of a frictional force. From
(11) it is possible to receive the following relation:
( ) 2{ Re exp( ) }d p k i i v kv
dt
γ ε µ й щ− + Ψ = − −л ы
r rrr r
. (12)
If the friction absent ( )0µ = , then the expression in
curly brackets represents integral of the equation (11).
To simplify represented below formulas, we shall con-
sider, that the interaction of a particle with wave hap-
pens in vacuum; that the wave is linearly polarized and
is going along an axis z , i.e. we shall consider (count),
that
( ),0,0ε ε=
r
; ( )1,0,0α =
r
, ( )0,0,1k =
r
. In this case vec-
tor equation (11) can be essentially simplified:
( )cos /x xp p Iε µў = Ψ −Ч ,
( )( / ) cos /z x zp p I p Iε µў = Ψ −Ч Ч ,
0yp ў = , ( )1 1/I Iµ γў = − − Чй щл ы . (13)
Such quantities and labels here are introduced:
zI pγ= − ; /I dI dўΨє .
In system (3) first three equations completely self-
consistent. The last, fourth equation, is a corollary these
three. Let's note that in absence of frictional force the
equations (13) are completely integrated. At presence of
friction system (13) is convenient to rewrite as:
( ) [ ]/ sinx xIρ µ ρ εў = − + ΨЧ ;
( ) ( ) ( )2 2/ / 2 /z z x xI p I p Iρ µ ρ γў й щ= − + −Ч Чл ы . (14)
Where ( ),0 0sin sinx x xp pε ε ρ= Ψ + − Ψ +Ч Ч ,
( ) ( )2 2
,0 ,0 0/ 2 / 2z x z x zp p I p p I ρ= + − + .
The obtained above equations are rigorous. From these
equations it is visible, that new variable xρ and zρ , and
also quantity I vary slowly ( 1µ < < ). The analysis of
the equations (14) shows, that asymptotically
( ),0 0sin sinx xp pε ε= Ψ + − ΨЧ Ч . At realization of an
inequality 1Iγ >Ч the presence of frictional force al-
ways gives in acceleration of charged particles. Let's
mark, that at the zero starting conditions this inequality
is always fulfilled. Besides at 1ε > > always 1Iγ >Ч . If
1ε < , it is possible to find conditions, at which a fric-
tional force will lead to brake particles.
So, for example, at ,0 ,00, 3x zp p= = , ~ 0.5ε , the
quantity Iγ Ч will be less unity ( 1Iγ <Ч ). Thus the par-
ticles are broken by frictional force. As an example in
Fig.3 the dependence of a longitudinal impulse of a par-
ticle on time is given at 3, 0.01ε µ= = , ,0 ,0 0x zp p= = .
It is visible, that the quantity of a longitudinal impulse
monotonically increased. In a Fig.4 the case is given,
when the frictional force brakes particles
( 0.2, 0.01ε µ= = , ,0 ,00, 2x zp p= = ).
____________________________________________________________
PROBLEMS OF ATOMIC SCIENCE AND TECHNOLOGY. 2006. № 3.
Series: Nuclear Physics Investigations (47), p.55-59.
57
Fig.3
It is necessary to note, that in all cases at small
strengths of a field ( 1ε < < ) the frictional force brake
fast particles ( 1zp > > ).
Let's consider now role of radiation friction forces.
We shall interest with large strength of fields ( 1ε і ).
Therefore we can be restricted to a case of a relativistic
motion. For this case the dimensionless force of radia-
tion friction can be presented as [8]:
( ) ( )k mn
f ik nF F u F u vω= Ч Ч Ч Ч
Ω
r r
, (15)
where ikF − tensor of an electrоmagnetic field; ku −
four-vector of velocity; vr − three-dimensional vector of
velocity, "frequency" 3 2 233 / 2 1,8 10e mc eΩ = = Ч s-1.
In our case we have only two components of an
electrоmagnetic field ( ,x yE H ). Taking into account,
that x yE H= , and also, that the four-vector of velocity
in our notation looks like ( ), , ( , )k
nu p u pγ γ= = −r r
, the
force of radiation friction can be presented by the fol-
lowing expression:
2 2 2cos ( )f
pF Iω ε ψ
γ
= − Ч Ч Ч Ч
Ω
rr
. (16)
From the formula (16) it is visible, that in this case
coefficient µ already is a complicated function of time.
However qualitative analysis of quantity I can be car-
ried out, to the similarly previous case. From here fol-
lows, that influence of friction force is qualitatively simi-
larly to the previous case. Thus, dynamics of particles in
a field of a laser radiation has the important feature,
which allows to use frictional force for arising of efficien-
cy of power transmission from a wave to particles.
7.1. DYNAMICS OF PARTICLES AT PRESENCE
OF A CONSTANT MAGNETIC FIELD
The motion of particles in a field of an electromag-
netic wave qualitatively varies at presence of an external
magnetic field. The most important difference is that
fact, that in a field of an intense electromagnetic wave
the nonlinear cyclotron resonances are overlapped. In
result the local instability arise. The charged particles
stochastically accelerated by a field of an electromag-
netic wave.
The analysis of dynamics of particles in this case
show, that the dynamic chaos is alternated. It means that
the casual ejections arise seldom. However the more
seldom these casual ejections appear, the more intensity
it is.
The characteristic of such process can be the mo-
ments nM . Under it, the higher moment, the more it is
(see Fig.5). The analytical and numerical examinations
of dynamics of particles show namely such dependence.
As an example in Fig.6 the evolution a cross impulse (
P ) from time represented at 0.5ε = , (0) 1P = . Besides
it is possible to show, that the moments grow in time
and the higher moments grow faster lowest. It means
existence super diffusion.
Fig.5
Fig.6
7.2. DYNAMICS OF LEADING CENTERS
In stationary values homogeneous external magnetic
fields dynamics of leading centers of charged particles
is expressed feebly. She is determined only by nonlinear
effects. In most cases this dynamics can be neglected.
Such situation arise, for example, in masers on cy-
clotron resonances or when we are doing analyze of
high-frequency instruments, which operation grounded
on cyclotron resonances. However dynamics of leading
centers in a homogeneous constant magnetic field and in
a field even of a homogeneous flat electromagnetic
wave has a series of features, which can be useful for
the application. In particular, we shall show lower, that
in such fields it is possible to create condition, at which
the leading centers of one isotope will move in one di-
rection, and other isotopes will move in an opposite di-
rection. Such feature of a motion of leading centers can
be useful for an isotope separation. Let's mark, that this
feature of dynamics of leading centers was found to-
gether with Stepanov К.N.
The full set of the equations, which describe a mo-
tion of charged particles in our case, coincides with set
equations (2) of first part.
Let's mark, that only the conditions that are close to
ionic cyclotron resonances will interest. It means that
the frequency of an external electromagnetic wave is
close to ionic cyclotron frequency. In this case the pa-
rameter of a wave force can be rewritten as the relation
of an electric field intensity of an electromagnetic wave
to intensity of a constant magnetic field ( /E Hε = ).
Practically always this parameter is small. Therefore,
having used a smallness of this parameter, it is possible
58
Fig.4
to receive the following system of the shortcut equa-
tions, which is valid in a neighborhood of ionic cy-
clotron resonances
( )
2
2
1 11 1 5 1 sin
2 2H
V V
V
εθ ω θ
й щцж
= − − − −Чк ъчз
и шл ы
& ;
10.5 cosV ε θ= − Ч Ч& ; 12 sinVξ ε θ= − Ч Ч Ч& ,
where − /H q H M cω ω= Ч Ч Ч dimensionless ionic cy-
clotron frequency.
From these equations it is visible, that the first two
equations represent completely closed system of the
equations concerning variable V and. 1θ . After the solu-
tion of this pair of the equations, there is easily to find
solution, defining dynamics of leading centre ξ :
( )τωθ 11 −= Н ; ( ) 1(0) sin
2 1H
V V ε θ
ω
= −
− ;
( )122 −⋅≈ Нωτεξ ; (0)V V= .
Fig.7 Evolution of leading
center
at 0.001ε = and 0.05µ =
Fig.7.
Here angular brackets designate an average on a
phase 1θ . From expression for average coordinate of
leading centre ξ follows, that it is possible to choose
such frequency ω , that the particles with one mass will
move in one direction ( 1Hω > ), and particle with other
mass ( 1Hω < ) − in the other direction. In Fig.7 depen-
dence of evolution of leading center at ε=0.001 and
µ=0.05 on time are represented. It is visible, that leading
centers of particles with different masses are moving in
opposite directions.
8. CONCLUSION
Dynamics of charged particles in fields of intensive
electromagnetic waves can be useful both for the pur-
poses of acceleration and for making new sources of in-
tensive radiation.
The work was partially supported by the State fund
for basic research МES in Ukraine, the grant number
02.07/213.
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ДИНАМИКА ЗАРЯЖЕННЫХ ЧАСТИЦ В ПОЛЕ ИНТЕНСИВНЫХ ЭЛЕКТРОМАГНИТНЫХ ВОЛН
В.А. Буц
Изложены результаты аналитического и численного исследований особенностей динамики заряженных
частиц в поле интенсивных электромагнитных волн и электромагнитных импульсов. Найдены условия, при
которых возможно эффективное ускорение заряженных частиц полем высокочастотного и лазерного излуче-
ния в вакууме. Показано, что силы трения могут способствовать ускорению частиц. Обнаружены хаотиче-
ские режимы, в которых все моменты растут во времени. Более того, высшие моменты растут быстрее низ-
ших. Это означает наличие супердиффузии. Показано, что существуют условия, при которых ведущие цен-
тры частиц с различными массами движутся в разных направлениях.
ДИНАМІКА ЗАРЯДЖЕНИХ ЧАСТОК У ПОЛІ ІНТЕНСИВНИХ ЕЛЕКТРОМАГНІТНИХ ХВИЛЬ
В.О. Буц
Викладені результати аналітичного та чисельного дослідження особливостей динаміки заряджених
часток у полі інтенсивних електромагнітних хвиль та електромагнітних імпульсів. Знайдені умови, при яких
є можливість ефективно прискорювати заряджені частки полем високочастотного та лазерного
випромінювання у вакуумі. Доведено, що сили тертя можуть допомагати прискоренню часток. Знайдені
хаотичні режими, в яких усі моменти зростають у часі. Більш того, виші моменти зростають швидше ніж
нижчі. Це означає наявність супердиффузіі. Доведено, що існують умови, при виконанні яких ведучі центри
часток с різними масами рухаються у різних напрямках.
____________________________________________________________
PROBLEMS OF ATOMIC SCIENCE AND TECHNOLOGY. 2006. № 3.
Series: Nuclear Physics Investigations (47), p.55-59.
59
1. INTRODUCTION
2. BASIC EQUATIONS AND INTEGRALS
3. INTERACTION WITH A PLAIN POLARIZED WAVE
4. INTERACTION OF PARTICLES WITH A CIRCULARLY POLARIZED WAVE
5. INTERACTION OF A PARTICLE WITH AN IMPULSE OF AN ELECTROMAGNETIC WAVE
6. ROLE OF FRICTIONAL FORCE AT INTERACTION OF ADIATION WITH CHARGED PARTICLES
7.2. DYNAMICS OF LEADING CENTERS
8. CONCLUSION
|