Features of the motion of charged particles in the field of the high-frequency impulse of large intensity
The results of analytical and numerical examinations of features dynamic of charged particles in a field of intensive electromagnetic waves are reported. It is shown that the trajectories of particles, which has initially different phases concerning of the homogeneous wave, essentially discriminate....
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Національний науковий центр «Харківський фізико-технічний інститут» НАН України
2005
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| Cite this: | Features of the motion of charged particles in the field of the high-frequency impulse of large intensity / V.A. Buts, V.V. Kuzmin // Вопросы атомной науки и техники. — 2005. — № 2. — С. 137-139. — Бібліогр.: 2 назв. — англ. |
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| author | Buts, V.A. Kuzmin, V.V. |
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| citation_txt | Features of the motion of charged particles in the field of the high-frequency impulse of large intensity / V.A. Buts, V.V. Kuzmin // Вопросы атомной науки и техники. — 2005. — № 2. — С. 137-139. — Бібліогр.: 2 назв. — англ. |
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| description | The results of analytical and numerical examinations of features dynamic of charged particles in a field of intensive electromagnetic waves are reported. It is shown that the trajectories of particles, which has initially different phases concerning of the homogeneous wave, essentially discriminate. As a result, the accelerated bunch breaks down. Trajectories of particles in a field of an electromagnetic impulse differ from each other a little. This feature allows using impulses for effective acceleration of clots of charged particles.
Викладено результати аналітичного та чисельного досліджень особливостей динаміки заряджених часток у полі інтенсивних електромагнітних хвиль. Показано, що в полі однорідної хвилі траєкторії часток, що знаходяться в різних фазах хвилі, істотно розрізняються. Згусток, що прискорюється, при цьому розвалюється. Траєкторії часток у полі електромагнітного імпульсу мало відрізняються один від одного. Ця особливість дозволяє використовувати імпульси для ефективного прискорення згустків заряджених часток.
Изложены результаты аналитического и численного исследований особенностей динамики заряженных частиц в поле интенсивных электромагнитных волн. Показано, что в поле однородной волны траектории частиц, находящихся в разных фазах волны, существенно различаются. Ускоряемый сгусток при этом разваливается. Траектории частиц в поле электромагнитного импульса мало отличаются друг от друга. Эта особенность позволяет использовать импульсы для эффективного ускорения сгустков заряженных частиц.
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| first_indexed | 2025-11-24T08:19:16Z |
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FEATURES OF THE MOTION OF CHARGED PARTICLES IN THE FIELD
OF THE HIGH-FREQUENCY IMPULSE OF LARGE INTENSITY
V.A. Buts, V.V. Kuzmin
NSC Kharkov Institute of Physics & Technology,
Kharkov, Ukraine, e-mail: vbuts@kipt.kharkov.ua
The results of analytical and numerical examinations of features dynamic of charged particles in a field of intensive
electromagnetic waves are reported. It is shown that the trajectories of particles, which has initially different phases
concerning of the homogeneous wave, essentially discriminate. As a result, the accelerated bunch breaks down.
Trajectories of particles in a field of an electromagnetic impulse differ from each other a little. This feature allows using
impulses for effective acceleration of clots of charged particles.
PACS: 41.75.Jv
1. INTRODUCTION
The motion of charged particles in a field of intensive
electromagnetic waves has a series of the important
features. These features allow to offer a series of new
schemes of charged particles acceleration and generating
of a short-wave radiation. It is important, that acceleration
and a generating can be carried out in vacuum. The
parameter of a wave force /eE mcωε = (parameter of
nonlinearity) will use for quantitative measure of
intensity. The conventional labels here are used. In the
present report features of a motion of particles are
investigated depending on a spatial arrangement of
particles. It is shown that in a field of the homogeneous
wave trajectories of particles strongly differ. It is shown
that the electromagnetic impulse can be used for effective
acceleration of particles in vacuum.
2. THE STATEMENT OF PROBLEM AND
THE BASIC EQUATIONS
The components of electrical and magnetic fields of
an electromagnetic impulse can be presented as
01Re
c t
∂ = − ∂
AE , [ ]
0
1Re
k
=
H kE , (1)
where krtψ ω≡ − , 0 0 ( )Aα ψ=A ; { }, ,x y ziα α α α= - a
vector of polarization of a wave; 0 /k cω= ; ω , k -
frequency of filling and a wave vector of an impulse. We
shall use the following the dimensionless variable:
1 / mc=p p , 1 0/ k=k k , tτ ω= , 1 0k=r r ,
0 /e mcω=A A , 1 / c=v v .
In these variable the equation of motion gains a view (the
coefficient "1" is fall down)
( )Re 1d
dτ τ τ
∂ ∂ ≡ = − − − ∂ ∂
A App kv k v& . (2)
The equation (2) have known integrals:
( ) ( )0 0Re Re consti iγ γ− + = − + = =p k A p k A C , (3)
where 21 pγ = + – the dimensionless energy of a
particle (measured in units 2mc ).
The equation (2) with taking into account integral (3)
completely integrable in a laboratory frame. The solution
looks like
( )0 0p - p = A A⊥ ⊥ −
r rr r
,
2 2
0
|| ||0
2
p pp p
γ ψ
⊥ ⊥
•
+
− =
r r
. (4)
Let's consider that the wave is propagating along an
axis z , i.e. {0,0, }k=k .
3. DYNAMIC OF PARTICLES IN THE FIELD
OF THE PLANE-POLARIZED WAVE
At examination dynamic of a particle in a field of a
plane-polarized homogeneous plane wave ( 0
ie ψ=A A ,
0A =const) it has been shown, that their dynamic
essentially depends from initial disposition of particles
concerning a phase of a wave. So, if particles originally
rested and were in phases nπ they only entrain by the
wave in a longitudinal direction. In a transverse direction
they oscillate. The mean transverse momentum of them is
equal to null. Such particles are displaced only in a
longitudinal direction. The particles, which were in other
phases, gain unequal to null mean transverse momentum.
Quantity of this medial impulse and its direction depend
from initial phases of particles concerning a wave. This
particles scatter in different directions. Presence such
scattering destroys structure of a bunch. Therefore, such
scheme of charged particles acceleration is ineffective. In
Figures 1 and 2 results of calculations of impulses and
displacement of particles presented accordingly at a
various initial arrangement concerning a phase of a wave
(π, π/4, π/2, 3π/4, π).
0 5 10 15 20 25 -1,0
-0,5
0,0
0,5
1,0
1,5
2,0
Px
τ
а
0 5 10 15 20 25
0,0
0,5
1,0
1,5
2,0
Pz
τ
b
Fig. 1. Impulses of particles at 1=0A а) cross, b) a
longitudinal impulse
Problems of Atomic Science and Technology. Series: Plasma Physics (11). 2005. № 2. P. 137-139 137
mailto:vbuts@kipt.kharkov.ua
0 5 10 15 20 25
0
3
6
9
12
Ζ
τ
а
0 5 10 15 20 25
0
3
6
9
12
15
X
τ
b
Fig. 2. Entrainment of particles at 1=0A
а) longitudinal, b) a transverse direction
The scattering is considerably smaller for particles
that initially have large longitudinal impulse. Such
particles equally entrain in a longitudinal direction
without dependence from their initially arrangement on
phases of a wave. But in transverse direction this particles
still scattered, however in much smaller degree. Results
of calculations of particles displacement as function their
initial standing concerning a phase of a wave (π, π/4, π/2,
3π/4, π) and their initial longitudinal impulse are
presented in Figure 3.
0 5 10 15 20 25
0
5
10
15
20
25
Z
τ
a
0 5 10 15 20 25
-1,2
-0,8
-0,4
0,0
0,4
0,8
1,2
X
τ
b
Fig.3. Entrainment of particles at 0 5zP = and
1=0A а) longitudinal, b) a transverse direction
4. DYNAMIC OF PARTICLES IN THE FIELD
OF THE WAVE WITH CIRCULAR
POLARIZATION
In a field of a wave with circular (elliptic) polarization
the basic features of a motion of particles are similar to
features of motions in a field with the linear polarization.
Main distinctive feature dynamic of particles in a field
of a wave with circular polarization is immunity of a
longitudinal impulse of a particle from its initial phase. In
Figure 4 it is visible, that quantities of longitudinal
impulses of all particles completely coincide.
0 5 10 15 20 25
0,0
0,5
1,0
1,5
2,0
Pz
τ
Fig. 4. Longitudinal impulse of particles
From the equations (4) it is possible to receive
expression motions of particles featuring these important
feature.
[ ]02 1 cos( )zP ψ ψ= − −E (5)
From this expression it is visible, that quantity of a
longitudinal impulse is equal to all particles and does not
depend on a initial arrangement of particles on phases.
Really, because initial value of ψ is 0ψ , the zP for all
particles coincide. The trajectories of particles in impulse
space have form of spirals (look Fig. 5).
Fig. 5. Trajectory of particles in space of impulses
5. DYNAMIC OF PARTICLES IN THE FIELD
OF THE HIGH-FREQUENCY IMPULSE
It has been investigated dynamic of particles in a field
of an impulse ( ) 2
0exp iβ ψ ψ ψ = − − + 0A A . Main
feature dynamic is that fact that this of dynamic
practically does not depend on a initial arrangement of
particles in space. Their trajectories are similar. All of
them entrain in a longitudinal direction and oscillate in
cross, and this entrainment happens on a spiral trajectory
(look Fig. 7). Interesting significant feature of a motion of
particles in a field of the high-frequency impulse having
circular polarization, is that fact that the longitudinal
impulse reproduces the shape enveloping an impulse.
Such features of dynamic of particles in an impulse allow
using it for effective acceleration of charged particles.
Fig.6. Trajectories of particles
0 20 40 60 80 100
0
2
4
6
8
10
τ
Z
Fig.7. Entrainment of particles in longitudinal
direction
Time dependence of an impulse and the coordinates of
a particle found at the numerical solution of the equation
(2) for case of circular polarization of a field of an
138
impulse are represented in Fig.8. The solution is obtained
for particles, which initially were in rest at 0 1A = ,
0.01β = , 0 50ψ = .
0 20 40 60 80 100
-1,0
-0,5
0,0
0,5
1,0
τ
Px
а
0 20 40 60 80 100
0,0
0,1
0,2
0,3
0,4
0,5
0,6
Pz
τ
b
Fig.8. Impulses of particles
а) cross, b) a longitudinal impulse
As an example of high efficiency of charged particles
acceleration we shall consider bunch, which have initially
energy 0 10γ = . Let on such clot acts the impulse with
amplitude 3=0A . In this case it is useful to investigate
two different cases.
In the first case we shall consider, that initially the
impulse is far enough from charged particles. In this case
the field strength of the impulse in the place where are
bunch is slowly builds up. This case corresponds to a
large value 0ψ . In particular, at 0 50ψ = dependence of a
longitudinal impulse on time it presented in Figure 9а.
From this figure it is visible, that all particles have
practically equal trajectories. In a transverse direction the
particles do not scattered. Such laser impulse is very
convenient for using for acceleration. Thus, as a result of
interaction of particles with a field of such impulse,
particles were accelerated to energies 100γ ≈ , and
acceleration happens at a distance that equal 0.4 cm.
In the second case - the beginning of interaction
corresponds to the peak value of pulse amplitude. It
means, that quantity 0ψ is equal to null. Dependence of a
longitudinal impulse on time for this case presented in
Figure 9b. As a result of interaction of particles with a
field of such impulse they were accelerated to large
energies ( 350γ ≈ ). This acceleration happens at a
distance ~ 0.8сm.. To a regret, in this case there are
some particles that are scattered in a transverse direction.
So at 410λ −≈ the cross size of bunch will have
transversal size 33 10x cm−∆ ≈ ⋅ . It is necessary to note,
that maximal quantity of a longitudinal impulse in this
case can be estimated by formula: ( )2
max 0 1 4 Aγ γ≈ + ⋅ ,
which coincides with the formula obtained in [2] for a
case of a homogeneous field.
0
10000
20000
30000
40000
0
20
40
60
80
100
Pz
τ
а
0 10000 20000 30000 40000 50000 0
50
100
150
200
250
300
350 Pz
τ
b
Fig. 9. Dependence of a longitudinal impulse on time а)
0 50ψ = . b) 0 0ψ =
REFERENCES
1. L.D. Landau, E.M. Livshits. Theory of field. M.:
“Science”. 1973.
2. V.A. Buts, A.V. Buts. Dynamic of charged particles
in a field of intense transversal electromagnetic wave
// JETF, 1996, v.110, N. 3(9), p. 818 – 831.
ОСОБЕННОСТИ ДВИЖЕНИЯ ЗАРЯЖЕННЫХ ЧАСТИЦ В ПОЛЕ ВЫСОКОЧАСТОТНОГО
ИМПУЛЬСА БОЛЬШОЙ НАПРЯЖЕННОСТИ
В.А. Буц, В.В. Кузьмин
Изложены результаты аналитического и численного исследований особенностей динамики заряженных
частиц в поле интенсивных электромагнитных волн. Показано, что в поле однородной волны траектории
частиц, находящихся в разных фазах волны, существенно различаются. Ускоряемый сгусток при этом
разваливается. Траектории частиц в поле электромагнитного импульса мало отличаются друг от друга. Эта
особенность позволяет использовать импульсы для эффективного ускорения сгустков заряженных частиц.
ОСОБЛИВОСТІ РУХУ ЗАРЯДЖЕНИХ ЧАСТОК У ПОЛІ ВИСОКОЧАСТОТНОГО ІМПУЛЬСУ
ВЕЛИКОЇ НАПРУЖЕНОСТІ
В.О. Буц, В.В. Кузьмін
Викладено результати аналітичного та чисельного досліджень особливостей динаміки заряджених часток у
полі інтенсивних електромагнітних хвиль. Показано, що в полі однорідної хвилі траєкторії часток, що
знаходяться в різних фазах хвилі, істотно розрізняються. Згусток, що прискорюється, при цьому розвалюється.
Траєкторії часток у полі електромагнітного імпульсу мало відрізняються один від одного. Ця особливість
дозволяє використовувати імпульси для ефективного прискорення згустків заряджених часток.
139
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| id | nasplib_isofts_kiev_ua-123456789-79800 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1562-6016 |
| language | English |
| last_indexed | 2025-11-24T08:19:16Z |
| publishDate | 2005 |
| publisher | Національний науковий центр «Харківський фізико-технічний інститут» НАН України |
| record_format | dspace |
| spelling | Buts, V.A. Kuzmin, V.V. 2015-04-04T19:53:07Z 2015-04-04T19:53:07Z 2005 Features of the motion of charged particles in the field of the high-frequency impulse of large intensity / V.A. Buts, V.V. Kuzmin // Вопросы атомной науки и техники. — 2005. — № 2. — С. 137-139. — Бібліогр.: 2 назв. — англ. 1562-6016 PACS: 41.75.Jv https://nasplib.isofts.kiev.ua/handle/123456789/79800 The results of analytical and numerical examinations of features dynamic of charged particles in a field of intensive electromagnetic waves are reported. It is shown that the trajectories of particles, which has initially different phases concerning of the homogeneous wave, essentially discriminate. As a result, the accelerated bunch breaks down. Trajectories of particles in a field of an electromagnetic impulse differ from each other a little. This feature allows using impulses for effective acceleration of clots of charged particles. Викладено результати аналітичного та чисельного досліджень особливостей динаміки заряджених часток у полі інтенсивних електромагнітних хвиль. Показано, що в полі однорідної хвилі траєкторії часток, що знаходяться в різних фазах хвилі, істотно розрізняються. Згусток, що прискорюється, при цьому розвалюється. Траєкторії часток у полі електромагнітного імпульсу мало відрізняються один від одного. Ця особливість дозволяє використовувати імпульси для ефективного прискорення згустків заряджених часток. Изложены результаты аналитического и численного исследований особенностей динамики заряженных частиц в поле интенсивных электромагнитных волн. Показано, что в поле однородной волны траектории частиц, находящихся в разных фазах волны, существенно различаются. Ускоряемый сгусток при этом разваливается. Траектории частиц в поле электромагнитного импульса мало отличаются друг от друга. Эта особенность позволяет использовать импульсы для эффективного ускорения сгустков заряженных частиц. en Національний науковий центр «Харківський фізико-технічний інститут» НАН України Вопросы атомной науки и техники Plasma electronics Features of the motion of charged particles in the field of the high-frequency impulse of large intensity Особливості руху заряджених часток у полі високочастотного імпульсу великої напруженості Особенности движения заряженных частиц в поле высокочастотного импульса большой напряженности Article published earlier |
| spellingShingle | Features of the motion of charged particles in the field of the high-frequency impulse of large intensity Buts, V.A. Kuzmin, V.V. Plasma electronics |
| title | Features of the motion of charged particles in the field of the high-frequency impulse of large intensity |
| title_alt | Особливості руху заряджених часток у полі високочастотного імпульсу великої напруженості Особенности движения заряженных частиц в поле высокочастотного импульса большой напряженности |
| title_full | Features of the motion of charged particles in the field of the high-frequency impulse of large intensity |
| title_fullStr | Features of the motion of charged particles in the field of the high-frequency impulse of large intensity |
| title_full_unstemmed | Features of the motion of charged particles in the field of the high-frequency impulse of large intensity |
| title_short | Features of the motion of charged particles in the field of the high-frequency impulse of large intensity |
| title_sort | features of the motion of charged particles in the field of the high-frequency impulse of large intensity |
| topic | Plasma electronics |
| topic_facet | Plasma electronics |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/79800 |
| work_keys_str_mv | AT butsva featuresofthemotionofchargedparticlesinthefieldofthehighfrequencyimpulseoflargeintensity AT kuzminvv featuresofthemotionofchargedparticlesinthefieldofthehighfrequencyimpulseoflargeintensity AT butsva osoblivostíruhuzarâdženihčastokupolívisokočastotnogoímpulʹsuvelikoínapružeností AT kuzminvv osoblivostíruhuzarâdženihčastokupolívisokočastotnogoímpulʹsuvelikoínapružeností AT butsva osobennostidviženiâzarâžennyhčasticvpolevysokočastotnogoimpulʹsabolʹšoinaprâžennosti AT kuzminvv osobennostidviženiâzarâžennyhčasticvpolevysokočastotnogoimpulʹsabolʹšoinaprâžennosti |