Peculiarities of particles and field dynamics at critical intensity of electromagnetic waves (Part I)
Some results of study of the charged particles that are moving in a field of intensive electromagnetic waves are represented. The integrals are investigated and some schemes of laser acceleration are considered. It was revealed that the most effective scheme of acceleration is the scheme, in which t...
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Buts, V.A. 2015-03-22T10:27:12Z 2015-03-22T10:27:12Z 2005 Peculiarities of particles and field dynamics at critical intensity of electromagnetic waves (Part I) / V.A. Buts // Вопросы атомной науки и техники. — 2005. — № 1. — С. 119-121. — Бібліогр.: 3 назв. — англ. 1562-6016 PACS: 41.75.Jv https://nasplib.isofts.kiev.ua/handle/123456789/78891 Some results of study of the charged particles that are moving in a field of intensive electromagnetic waves are represented. The integrals are investigated and some schemes of laser acceleration are considered. It was revealed that the most effective scheme of acceleration is the scheme, in which the laser pulse with circular polarization is used. Is shown that the forces of radiating friction can promote transferring of energy from a laser field to particles. Besides is shown, that for laser acceleration the force of radiating friction are considerably less essential, than in cyclic accelerators. Викладено деякі результати вивчення динаміки заряджених часток у полі інтенсивних електромагнітних хвиль. Досліджено інтеграли і розглянуто деякі схеми лазерного прискорення. Показано, що найбільш ефективною схемою прискорення є схема, у якій використовується лазерний імпульс із круговою поляризацією. Показано, що сили радіаційного тертя можуть сприяти передачі енергії від лазерного поля до часток. Крім того, показано, що для лазерного прискорення сили радіаційного тертя значно менш істотні, ніж у циклічних прискорювачах. Изложены некоторые результаты изучения динамики заряженных частиц в поле интенсивных электромагнитных волн. Исследованы интегралы и рассмотрены некоторые схемы лазерного ускорения. Показано, что наиболее эффективной схемой ускорения является схема, в которой используется лазерный импульс с круговой поляризацией. Показано, что силы радиационного трения могут способствовать передаче энергии от лазерного поля к частицам. Кроме того, показано, что для лазерного ускорения силы радиационного трения значительно менее существенны, чем в циклических ускорителях. en Національний науковий центр «Харківський фізико-технічний інститут» НАН України Вопросы атомной науки и техники Plasma electronics Peculiarities of particles and field dynamics at critical intensity of electromagnetic waves (Part I) Особливості динаміки часток і полів при критичних напруженостях електромагнітних хвиль (Частина I) Особенности динамики частиц и полей при критических напряженностях электромагнитных волн (Часть I) Article published earlier |
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Peculiarities of particles and field dynamics at critical intensity of electromagnetic waves (Part I) |
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Peculiarities of particles and field dynamics at critical intensity of electromagnetic waves (Part I) Buts, V.A. Plasma electronics |
| title_short |
Peculiarities of particles and field dynamics at critical intensity of electromagnetic waves (Part I) |
| title_full |
Peculiarities of particles and field dynamics at critical intensity of electromagnetic waves (Part I) |
| title_fullStr |
Peculiarities of particles and field dynamics at critical intensity of electromagnetic waves (Part I) |
| title_full_unstemmed |
Peculiarities of particles and field dynamics at critical intensity of electromagnetic waves (Part I) |
| title_sort |
peculiarities of particles and field dynamics at critical intensity of electromagnetic waves (part i) |
| author |
Buts, V.A. |
| author_facet |
Buts, V.A. |
| topic |
Plasma electronics |
| topic_facet |
Plasma electronics |
| publishDate |
2005 |
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English |
| container_title |
Вопросы атомной науки и техники |
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Національний науковий центр «Харківський фізико-технічний інститут» НАН України |
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| title_alt |
Особливості динаміки часток і полів при критичних напруженостях електромагнітних хвиль (Частина I) Особенности динамики частиц и полей при критических напряженностях электромагнитных волн (Часть I) |
| description |
Some results of study of the charged particles that are moving in a field of intensive electromagnetic waves are represented. The integrals are investigated and some schemes of laser acceleration are considered. It was revealed that the most effective scheme of acceleration is the scheme, in which the laser pulse with circular polarization is used. Is shown that the forces of radiating friction can promote transferring of energy from a laser field to particles. Besides is shown, that for laser acceleration the force of radiating friction are considerably less essential, than in cyclic accelerators.
Викладено деякі результати вивчення динаміки заряджених часток у полі інтенсивних електромагнітних хвиль. Досліджено інтеграли і розглянуто деякі схеми лазерного прискорення. Показано, що найбільш ефективною схемою прискорення є схема, у якій використовується лазерний імпульс із круговою поляризацією. Показано, що сили радіаційного тертя можуть сприяти передачі енергії від лазерного поля до часток. Крім того, показано, що для лазерного прискорення сили радіаційного тертя значно менш істотні, ніж у циклічних прискорювачах.
Изложены некоторые результаты изучения динамики заряженных частиц в поле интенсивных электромагнитных волн. Исследованы интегралы и рассмотрены некоторые схемы лазерного ускорения. Показано, что наиболее эффективной схемой ускорения является схема, в которой используется лазерный импульс с круговой поляризацией. Показано, что силы радиационного трения могут способствовать передаче энергии от лазерного поля к частицам. Кроме того, показано, что для лазерного ускорения силы радиационного трения значительно менее существенны, чем в циклических ускорителях.
|
| issn |
1562-6016 |
| url |
https://nasplib.isofts.kiev.ua/handle/123456789/78891 |
| citation_txt |
Peculiarities of particles and field dynamics at critical intensity of electromagnetic waves (Part I) / V.A. Buts // Вопросы атомной науки и техники. — 2005. — № 1. — С. 119-121. — Бібліогр.: 3 назв. — англ. |
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2025-11-24T05:51:08Z |
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2025-11-24T05:51:08Z |
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1850841995159797760 |
| fulltext |
PECULIARITIES OF PARTICLES AND FIELD DYNAMICS AT
CRITICAL INTENSITY OF ELECTROMAGNETIC WAVES (PART I)
V.A. Buts
National Scientific Center « Kharkov Institute of Physics and Technology»,
61108, Kharkov, Ukraine, e-mail: vbuts@kipt.kharkov.ua
Some results of study of the charged particles that are moving in a field of intensive electromagnetic waves are
represented. The integrals are investigated and some schemes of laser acceleration are considered. It was revealed that
the most effective scheme of acceleration is the scheme, in which the laser pulse with circular polarization is used. Is
shown that the forces of radiating friction can promote transferring of energy from a laser field to particles. Besides is
shown, that for laser acceleration the force of radiating friction are considerably less essential, than in cyclic
accelerators.
PACS: 41.75.Jv
1. INTRODUCTION
We shall understand fields with critical intensity the
fields, at which there are qualitatively change of interaction
dynamics of particles and fields. In this section we shall
consider dynamics of particles in intensive electromagnetic
fields. The measure of intensity will be served a parameter
of a wave force /eE mcε ω= . The condition 1ε > means
that 510 /E V cm> for 10cmλ = and 1010 /E V cm> for
410 cmλ −= . In such fields the charged particles get velocity
close to velocity of light during time about one period of a
wave. The long synchronism is not necessity for an
effective exchange of energy between particles and fields In
these conditions. It means, that the resonant conditions of
particles and fields interaction cease to play a significant
role in interaction. The analytical solving of a task about
movement of particles thus encounters significant
difficulties, because there is no usual small parameter
1ε << . However in many cases it is possible to receive the
significant information on dynamics of particles, using
integrals of movement. Besides, in some enough simple
cases, it is possible to receive the analytical solutions. Such
cases are key for understanding of interaction of intensive
fields with particles. Below we shall consider such
opportunities.
2. FORMULATION OF A TASK
Let's consider the charged particle, which goes in an
external constant magnetic field 0H and in a field of an
electromagnetic wave with any polarization. The vector
0H
r
is directed along an axis z . Let wave have the
following components
e=Re E exp i k r−iwt ;
E º {E0 αx , iαy , α z }
H=Re c
w
[k E ]exp i k r−iwt ,
where α º {α x , iα y , α z } - vector of polarization.
If time measure in 1ω − , velocity in c , magnitude of a
wave vector k in / cω , a pulse in mc and to enter
dimensionless amplitude of a field 0 0 /eE mcε ω= than
one can transform the equations of motion in a kind:
( ) [ ] ( )1 Re Re ;i iHkp kP e pe p e ψω
γ γ γ
ε εΨ
= − ⋅ + + ⋅
r rrr rr r& r r
(1)
where 0 0, / ; / ;Ht e H H eH mcτ ω ω ω≡ ≡ ≡
rr .krψ τ= −
rr
From the equation (1), it is possible to find following
integral of movement
( ) [ ]Re i
Hp i e re k constψε ω γ− ⋅ + − =
rrr rr
. (2)
The movement of a particle can occur only on the
following surface
γ 2= p∣∣
2 p¿
21
(3)
The surface (3) represents hyperboloid of rotation. The
hyperboloid surface (3) is represented in a fig. 1 and 2.
The analysis of integrals. If (
k x=k y=0, k¿=0 ), longitudinal component of
integral assume the form:
p∣∣−k z= p∣∣,0−k z γ0≡C=const
(4)
In figure 1 the characteristic kind of hyperboloid section
2 2 21 p pγ ⊥= + +P by planes of integrals (4) is represented
at interaction of a particle with slow waves ( 1zk > ). In
figure 2 - for a case 1zk < .
p
L
p
ll
γ
Fig. 1
p
L
p
ll
γ
Fig.2
The important physical conclusions can be made from
these two figures. In particular, it is visible, that at
interaction of a particle with a fast wave ( k z1 ) the
energy of a particle is not restricted by integrals and can
reach any value. It is namely that case, at which it is
potentially possible unlimited acceleration, and possible
great transformation of energy from particles to the
wave. Using integrals (2) it is possible also to find out
many important features of movement of particles. In
Problems of Atomic Science and Technology. 2005. № 1. Series: Plasma Physics (10). P. 119-121 119
mailto:vbuts@kipt.kharkov.ua
particular, it is possible to find conditions, at which the
particles completely pass all their energy to a wave.
3. ACCELERATION OF THE CHARGED
PARTICLES IN VACUUM
If the external magnetic field is absent, the equations of
movement (1) can be solved [1]. Lets charged particles
move in vacuum and are in a field of a flat electromagnetic
wave of the large intensity. Such particles carry along a
direction of this wave propagation. Let's note the most
important features of such entrainment [1]. If the particle
originally were in rest, average velocity of a particle in a
direction of wave propagation is close to ( )2 2/ 4v c ε ε= ⋅ +
. As the result of this entrainment varies also period of a
wave, which is "perceived" by a particle: ( )2
0 1 / 4T T ε= ⋅ +
The longitudinal pulse periodically varies, but the average
size of this pulse is not equal to zero:
( )2 1 cos 2 / 2,zp zε ψ ψ τ= − = − . If the particle had the
large enough initial energy, than the dynamics can
qualitatively change. So, the period of a wave concerning a
particle becomes equal ( )2 2 2
0 / 2T T γ γ ε= ⋅ + ⋅ . The
increase of the period in this case is caused by two factors.
The first factor is caused by usual effect Doppler. Second
addend is caused by nonlinear dynamics of a particle in a
field of an intensive electromagnetic wave. The maximal
size of a longitudinal pulse in this case also essentially
grows: 2
,0 / 2z zp p ε γ= + ⋅ The energy changes in
boundaries ( )2
0 0 1 4γ γ γ +Ј Ј E . Such dynamics of
particles allows to offer the various simple schemes of
high-frequency acceleration of particles and new schemes
of excitation of short-wave radiation (see, [1-3]). However
at such schemes of acceleration the accelerated particles run
away in a cross direction. For illustration of such scattering
in figure 3 is represented dependence of a cross deviation of
particles ( 0 5zP = and 1ε = ) from their initial arrangement
concerning a phase of a wave. The presence scattering
makes this scheme of acceleration not very interesting. The
situation essentially varies at acceleration of particles by a
field of a high-frequency pulse
( ) 2
0exp iβ ψ ψ ψε ε − − + = 0
r r
having circular
polarization. In a field of such pulse all particles have
coincide trajectories. It is interesting, that the longitudinal
impulse of particles repeats the form of a pulse envelope.
In figure 4 the dependence of a longitudinal impulse of
particles on time is submitted.
Initially particles were in regular intervals located
concerning a phase of a high-frequency wave. It is visible,
that the trajectories of all particles completely coincide.
Such feature of dynamics of particles in a pulse allows to
use it for effective acceleration. Especially for acceleration
of particles having the large initial velocity.
4. INFLUENCE OF FRICTION AT LASER
ACCELERATION
At interaction electrons with intensive laser field there is a
radiation arising. This radiation, as well as the radiation in
cyclic accelerators, can limit energy, which particles can
acquire. In work [3], examining acceleration of
electrons by a field of laser radiation, the authors have
equated force of radiating friction to accelerating forces
(forces of high-frequency pressure). In result they have
found, that in a field of laser radiation the electrons can
not get energy large, than 200 МэВ ( ~ 1 kλ µ ). It is
necessary to notice that, as force of high-frequency
pressure and force of radiating friction both are
proportional 2ε , this result does not depend on intensity
of a field of laser radiation. In this sense he is universal.
0 5 10 15 20 25 -1,2
-0,8
-0,4
0,0
0,4
0,8
1,2 X
τ
Fig.3
0 20 40 60 80 100 0,0
0,1
0,2
0,3
0,4
0,5
0,6 Pz
τ
Fig.4
In the present section we shall show, that the forces of
friction, including forces of radiating friction, can
promote transfers of energy from an external laser field
to accelerating particles. Besides will be shown that the
restriction on the maximal size of energy in 200 MeV,
which can get particles in a field of laser radiation,
generally is absent. Let particle move in a field of a
homogeneous flat electromagnetic wave, which is
propagates in vacuum along an axis z and has only two
components: ,x yE H . The equation of the charged
particle movement with taking into account the force of
friction looks like:
1
f
dp qE v H F
dt c
= + ⋅ +
r r r rr . (5)
This equation differs from investigated in [1] only by
presence of force of friction. If this force is absent, the
variable zI p constγ≡ − = is integral of the equation
(5). If the force of friction is present, the size I already
ceases to be integral. Let's consider that the force of
friction can be presented as /fF pµ γ= −
r r
, here
constµ = . Then for definition I from (5) it is possible
to receive the following equation:
2
dI I
d
µµ
τ γ γ
= − + . (6)
The general solution of the equation (6) is possible to
write down as:
2
0
exp( ) exp( )I d
τ µ τ
γ
= − ⋅ ⋅ + ⋅∫ , (7)
120
Pz
Tn
0 1250 2500 3750 5000
0
12.5
25
37.5
50
Fig.5
where exp( ) exp( / )d
τ
µ τ γ± ≡ ± ∫ . Thus, the size of integral
I tend to size 1/γ . The characteristic time in inverse
proportion to parameter µ . From formula (5) is possible to
estimate and maximal size of a longitudinal pulse, which
the particle can achieve: 2~ /zp ε µ . Let's consider now
force of high-frequency friction.. We shall be limited to a
case of relativistic movement ( 1ε ≥ ). In our case we have
only two components of an electromagnetic field ( ,x yE H )
. Taking into account, that x yE H= , and also, that the
four-vector of velocity in our designations looks like
( ), , ( , )k
nu p u pγ γ= = −r r
, the force of radiating
friction can be presented by the following expression.
2 2 2cos ( )
p
F If
ω
ε ψ
γ
= − ⋅ ⋅ ⋅ ⋅
Ω
r
r
,
Where «frequency» 3 2 233 / 2 1,8 10e mc eΩ = = ⋅ сек-1.
It is easy to see that in this case the size of integral is
decreases, though not so fast as in the previous case. The
point 1/I γ= is a stable stationary point. In a fig. 5 the
dependence of a longitudinal pulse on time is submitted at
presence of force of friction ( 35, 5 10ε µ −= = ⋅ ). In a fig. 6
the dependence of a longitudinal pulse on time is submitted
at the following values of parameters:
3
,05, 5 10 , 20zpε µ −= = ⋅ = . From this figure it is
visible, that the energy of a particle already large than 200
МeV. Let's compare laser acceleration to acceleration in the
cyclic accelerator. The expression for capacity of radiation
in the accelerator can be presented as:
2 2 42 / 3W e c K γ= ⋅ ⋅ ⋅ ,
where K - curvature of an orbit. In case of laser
acceleration K grows proportionally to square energy (
2~ 1/K γ ). Therefore capacity of radiation does not
vary with growth of energy and problem connected to
growth of radiating losses, does not arise.
REFERENCES
1. V.A. Buts, A.V. Buts. Dynamics of the charged
particles in a field of an intensive cross
electromagnetic wave // JETPh, 1996, 110, N. 3
(9), p. 818-831.
2. A.V. Buts , V.A. Buts. Acceleration of plasma by a
field of laser radiation // Electromagnetic waves
and electronic systems. 2001, N 6, p. 50-56.
3. N.B. Baranova, M.O. Skalli, B.Ya. Zeldovich
Acceleration of the charged particles by laser
beams // JETPh.(105). 1994, N. 3, p. 469-486 .
ОСОБЕННОСТИ ДИНАМИКИ ЧАСТИЦ И ПОЛЕЙ ПРИ КРИТИЧЕСКИХ НАПРЯЖЕННОСТЯХ
ЭЛЕКТРОМАГНИТНЫХ ВОЛН (ЧАСТЬ I)
В.А. Буц
Изложены некоторые результаты изучения динамики заряженных частиц в поле интенсивных
электромагнитных волн. Исследованы интегралы и рассмотрены некоторые схемы лазерного ускорения.
Показано, что наиболее эффективной схемой ускорения является схема, в которой используется лазерный
импульс с круговой поляризацией. Показано, что силы радиационного трения могут способствовать
передаче энергии от лазерного поля к частицам. Кроме того, показано, что для лазерного ускорения силы
радиационного трения значительно менее существенны, чем в циклических ускорителях.
ОСОБЛИВОСТІ ДИНАМІКИ ЧАСТОК І ПОЛІВ ПРИ КРИТИЧНИХ НАПРУЖЕНОСТЯХ
ЕЛЕКТРОМАГНІТНИХ ХВИЛЬ (ЧАСТИНА I)
В.O. Буц
Викладено деякі результати вивчення динаміки заряджених часток у полі інтенсивних електромагнітних
хвиль. Досліджено інтеграли і розглянуто деякі схеми лазерного прискорення. Показано, що найбільш
ефективною схемою прискорення є схема, у якій використовується лазерний імпульс із круговою
поляризацією. Показано, що сили радіаційного тертя можуть сприяти передачі енергії від лазерного поля до
часток. Крім того, показано, що для лазерного прискорення сили радіаційного тертя значно менш істотні,
ніж у циклічних прискорювачах.
121
Pz
T0 3750 1.5 104
0
150
300
450
600
Fig.6
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