Relativistic electron bunch excitation of plasma wake-field and charged particle acceleration in the presence of external magnetic field
The report is devoted to the theoretical study and numerical simulation of the excitation of wake-fields in plasma and their application for charged particle acceleration. It is shown that at a given relationship between the parameters of the "plasma bunch - magnetic field" system in the m...
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Національний науковий центр «Харківський фізико-технічний інститут» НАН України
2001
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| Cite this: | Relativistic electron bunch excitation of plasma wake-field and charged particle acceleration in the presence of external magnetic field / V.A. Balakirev, V.I. Karas’, I.V. Karas’ // Вопросы атомной науки и техники. — 2001. — № 5. — С. 57-59. — Бібліогр.: 3 назв. — англ. |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1859938069973565440 |
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| author | Balakirev, V.A. Karas’, V.I. Karas’, I.V. |
| author_facet | Balakirev, V.A. Karas’, V.I. Karas’, I.V. |
| citation_txt | Relativistic electron bunch excitation of plasma wake-field and charged particle acceleration in the presence of external magnetic field / V.A. Balakirev, V.I. Karas’, I.V. Karas’ // Вопросы атомной науки и техники. — 2001. — № 5. — С. 57-59. — Бібліогр.: 3 назв. — англ. |
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| container_title | Вопросы атомной науки и техники |
| description | The report is devoted to the theoretical study and numerical simulation of the excitation of wake-fields in plasma and their application for charged particle acceleration. It is shown that at a given relationship between the parameters of the "plasma bunch - magnetic field" system in the magnetoactive plasma owing to the hybrid space-surface character of wake-field waves excited by a relativistic electron bunch (REB), the accelerated bunch energy εmax can appear essentially higher than the exciting bunch energy even if the longitudinal REB charge density profiling is not used. With the help of 2.5 D numerical simulation of wake-fields excited by a single REB or a REB sequence it has been established the following: the ion channel is formed owing to transverse ion motion in self- consistent electromagnetic fields, this channel stabilizes REB propagation and thus serves to increase the REB excited fields; the self-modulation of a long pulsed REB is a very promising way both to obtain high rates of charged particle acceleration and to modulate the bunch and plasma densities (this gives evidence that the linear approach cannot be used to describe the plasma even in the low beam density case). These results make it possible to clarify the prospects and to evaluate the possibility of creating new-type charged particle accelerators which will have acceleration rates much higher than the conventional resonant accelerator has.
|
| first_indexed | 2025-12-07T16:10:07Z |
| format | Article |
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RELATIVISTIC ELECTRON BUNCH EXCITATION OF PLASMA
WAKE-FIELD AND CHARGED PARTICLE ACCELERATION
IN THE PRESENCE OF EXTERNAL MAGNETIC FIELD
V.A. Balakirev, V.I. Karas’, I.V. Karas’
National Science Center “Kharkov Institute of Physics and Technology”, Kharkov, Ukraine,
ira@kipt.kharkov.ua
The report is devoted to the theoretical study and numerical simulation of the excitation of wake-fields in plasma
and their application for charged particle acceleration. It is shown that at a given relationship between the
parameters of the "plasma bunch - magnetic field" system in the magnetoactive plasma owing to the hybrid space-
surface character of wake-field waves excited by a relativistic electron bunch (REB), the accelerated bunch energy
maxε can appear essentially higher than the exciting bunch energy even if the longitudinal REB charge density
profiling is not used. With the help of 2.5 D numerical simulation of wake-fields excited by a single REB or a REB
sequence it has been established the following: the ion channel is formed owing to transverse ion motion in self-
consistent electromagnetic fields, this channel stabilizes REB propagation and thus serves to increase the REB
excited fields; the self-modulation of a long pulsed REB is a very promising way both to obtain high rates of
charged particle acceleration and to modulate the bunch and plasma densities (this gives evidence that the linear
approach cannot be used to describe the plasma even in the low beam density case). These results make it possible
to clarify the prospects and to evaluate the possibility of creating new-type charged particle accelerators which will
have acceleration rates much higher than the conventional resonant accelerator has.
PACS numbers: 29.17.+w, 29.27.Bd, 41.75.Jv, 41.75.Lx, 52.35.-g, 52.35.Mw, 52.38.Kd, 52.65.Rr
1 INTRODUCTION
The ideas of using collective fields for acceleration
in the plasma and noncompensated charged beams were
stated as early by Veksler (1956), Budker (1956),
Fainberg (1956). The appearance and development of
new powerful energy sources such as lasers, high-cur-
rent relativistic electron beams, super - high - power mi-
crowave generators, gave another impetus to the devel-
opment of the collective methods of charged particle ac-
celeration. As a result, Tajima and Dawson (1979) and
Chen et. al (1985), there appeared new modifications of
the method of charged particle acceleration in a plasma
by charge density waves (see reviews: Dawson (1999),
Fainberg (1987), Fainberg (1994), Fainberg (1997),
Fainberg (2000), Power et. al. (1999), Suk et al. (2001),
where it was proposed that the accelerating fields should
be excited by laser pulses and relativistic electron
bunches. The charged particle acceleration by charge
density waves in a plasma and in uncompensated
charged beams, Fainberg (1956), appears to be a most
promising trend in the collective methods of accelera-
tion. The variable part of the charge density can be
made to be very high (up to n0 , where n0 is the unper-
turbed plasma density); therefore, the accelerating fields
can reach 107 to 109 V/cm. Chen et al. (1985) have pro-
posed a modification of the Fainberg (1956) accelera-
tion method, consisting in using a train of bunches. The
experiments undertaken in Rosenzweig (1990) on wake-
field acceleration have demonstrated the importance of
three-dimensional effects. The excitation of nonlinear
stationary waves in the plasma by a periodic train of
electron bunches has been studied by Amatuni et al.
(1979), Rosenzweig (1990), where it was shown that the
electric field of the wave in the plasma increases with
γ b at commensurable plasma/beam densities.
2 2.5-D NUMERICAL MODELING OF
THE FORMATION OF A PLASMA CHAN-
NEL AND OF THE LONG REB SELF-MODU-
LATION
The excitation of wake fields is investigated with an
aid of the 2D3V axially symmetric version of the SUR
code being, in turn, a further development of the COM-
PASS code Batishchev et al. (1994a), Batishchev et al.
(1994b). Earlier, this code has been used to simulate the
induction accelerator Karas’ et. al. (1992), the modulat-
ed relativistic electron beam Batishchev et al. (1993),
and a single REB or a train of these bunches in a plasma
Batishchev et. al. (1994a), Batishchev et al. (1994b),
Karas’ et al. (1996), Karas’ et al. (1997), Karas’ et al.
(1998), Karas’ et al. (2000a).
2.1 Mathematical model and methods
The REB dynamics is described by the relativistic
Belyaev-Budker equations for the distribution functions
( )f r pα
, of plasma particles of each species and by
the Maxwell equations for the self-consistent electric E
and magnetic B fields. We assume that, initially, a cold
two - component background plasma ( m mi e = 1840 ,
where mi and me are the ion and electron masses) fills
the entire region [ ] [ ]0 0, ,L R× , where L = 100 cm
and R = 10 cm. In order to analyze the dependence of
the amplitude of the excited fields on the number of
bunches injected into plasma, we carried out series of
calculations. A finite sequence of REB, which are speci-
fied by the expression
( )0( , , )n bn r z t n R rθ= − ×
ВОПРОСЫ АТОМНОЙ НАУКИ И ТЕХНИКИ. 2001. №5.
Серия: Ядерно-физические исследования (39), с. 57-59.
57
mailto:karas@kipt.kharkov.ua
( )( ) ( )( )1 1b p p pv t z n z v t Z nθ λ θ λ× − + − − + + − .
Here n is the number of the injected bunch;
V cb b= −1 1 2γ is the bunch velocity; c is the speed
of light; the initial bunch sizes are equal to 0.4×
(0.1-0.5) cm; nb is the mean density of a relativistic
electron bunch; λ π ωp pec= 2 . The scale on
which the electric and magnetic fields vary is
m c ee peω . We assume that the plasma/bunch parti-
cles escape from the calculated region through the
z = 0 and z Z= boundary surfaces and are elastically
reflected from the r R= surface. We also assume that
cold background electrons and ions can return to the re-
gion under consideration from the buffer zones z < 0
and z Z> . The boundary conditions for the fields cor-
respond to the metal wall at the cylindrical surface
r R= and free emission of electromagnetic waves
from the right and left plasma boundaries. The weight of
the model particles was a function of the radial coordi-
nate, and the total number of these particles was about
106. All the calculations were carried out on a Pen-
tium-166 personal computer using the modified particle-
in-cell simulation algorithm.
2.2 Numerical Simulation of the formation of a plas-
ma channel due to ion redistribution
Barov and Rosenzweig (1994) pointed out that, in
the immobile - ion approximation, a channel with an
neutralized positive charge can arise in the plasma when
the background electron escape from the region through
which the REBs propagate. It has already been noted
that, in order to analyze the formation of an ion channel
in a realistic situation, we must take into account, along
with the electron motion, the ion motion in self-consis-
tent electromagnetic fields. We will show that the ion
dynamics plays a key role in the formation of an ion
channel. Figures 1 and 2 illustrate the formation of an
ion channel. The parameters of the plasma channel are
governed by the ratio between the bunch and plasma
densities and by the ratio between the bunch radius and
the collisionless skin depth.
It is shown that the effective sizes of the plasma
channel and its depth increase monotonically with time
and in the direction against the z-axis. Also it is shown
that substantial variations of electron density are associ-
ated only with the wake-field wave and have not perma-
nent component contrary to ion density distribution [1].
2.3 Self-modulation of a long relativistic elec-
tron bunch
The present results show that the nonlinear picture in
the plasma-REB system drastically differs from both the
initial picture corresponding to the rigid REB and the
one by the scenario following from the one-dimensional
numerical modulation (cf. Balakirev et al. (1996)). This
supports in full measure the conclusion given in ref.
Rosenzweig (1990) about the necessity of taking into
complete account the three-dimensional effects and the
nonlinear behavior of both the plasma and the bunch.
Fig. 1. 2-D distribution of the longitudinal electric
field zE for the instances of time t pe= −60 1ω and
t pe= −100 1ω .
The spatial density distributions of REB and plasma
electrons obtained for the instances of time t pe= −60 1ω
and t pe= −100 1ω show that the density ratio n nb 0
(the initial value being 0.018) reaches 0.04 as early as at
t pe= −60 1ω . At t pe= −100 1ω , the highest beam particle
density becomes commensurable with the plasma densi-
ty, i.e., a very strong modulation of beam particle densi-
ty is observed. The spatial distributions of the longitudi-
nal Ez and transverse Er electric fields show that the
Ez and Er amplitudes grow owing to the enhancement
in the density modulation. At t pe= −100 1ω the highest
longitudinal-field amplitude reaches 0 8. m c ee peω ,
and the highest transverse-field amplitude is equal to
0 4. m c ee peω . It is essential that the amplitude
growth occurs only within a moderate REB length.
Therefore, there is little point in using the REB of the
length greater than that corresponding to the highest
longitudinal-field amplitude, otherwise no increase in
the excited wake field will be attained.
58
Fig. 2. 2-D distribution of the plasma electron den-
sity .el Q for the instances of time t pe= −60 1ω and
t pe= −100 1ω .
The undertaken numerical experiments have demon-
strated that the nonlinear dynamics of the particles of
plasma components and bunches results in the following
effects: (i) the transverse dimension of bunches varies
within a very wide range; (ii) close to the axis of the
system, an ion channel is formed, which is a contributo-
ry factor for the stabilization of bunch propagation and
the growth of bunch-generated fields; (iii) an essential
increase in the amplitudes of excited electric fields takes
place in the case of a long bunch as a result of its self–
modulation [2]. However, bunches of optimum length
should be used, since any excess of the optimum length
of the bunch fails to provide, even at self-modulation,
the growth in the amplitudes of excited electric fields.
3 WAKE-FIELDS IN MAGNETOACTIVE
PLASMAS
We attained the characteristic radial distribution of
the longitudinal electric-field component at the follow-
ing plasma and waveguide parameters: 6.3He
pe
ω
ω
= ,
23.3pea
c
ω
= , 2.4b
a
= , 4.6bγ = . The wake hybrid
wave frequency is here equal to 0.35 ωpe. It is shown
that for the radius
r
a
= 0.8 the magnitude of the longitu-
dinal electric-field component has a deep maximum cor-
responding to the energy transformation coefficient
( )
max
0
37z
E
z r
ER
E =
= = .
Note that a great value of the transformation coeffi-
cient corresponds to a significant ( ER times) excess of
the maximum energy obtained by the accelerated bunch
as compared to the energy of the bunch exciting the
wake field, because the energy transformation coeffi-
cient RE is equal to the ratio of the amplitude of the
electric field accelerating the guided bunch to the ampli-
tude of the electric field decelerating the bunch that ex-
cites the accelerating wake field. So, it has been demon-
strated that a multiple excess of the accelerated bunch
energy εmax over the energy of the exciting. REB is pos-
sible in a magnetoactive plasma at a certain relationship
between the parameters of the “plasma - bunch - mag-
netic field” system (owing to a hybrid volume - surface
character of REB-excited wake-fields), even without us-
ing the REBs contoured in the longitudinal direction, a
namely: ( )2
max 1E bmc Rε γ= − [3].
The work was performed with the help the State
Fundamental Research Foundation in Ukraine project
# 02.07/213.
REFERENCES
1. V.I.Karas', I.V.Karas', V.D.Levchenko, Yu.S.Sigov,
Ya.B.Fainberg. 2.5 – Dimensional Numerical Mod-
eling of the Formation of a Plasma Channel due to
Ion Redistribution during he Propagation of a Finite
Sequence of REB through High-density and Low-
Density Plasmas // Plasma Physics Report. 1997,
v. 23, # 4, p. 285-289.
2. V.I.Karas', V.A.Balakirev, Ya.B.Fainberg,
I.V.Karas', E.A.Kornilov, V.D.Levchenko,
Yu.S.Sigov, G.V.Sotnikov. Nonlinear Phenomena
and Self-Organization Structures in Plasmas //
J. Tekh.Phys. 2000, v. 41, # 1, p. 293-305.
3. V.A.Balakirev, I.V.Karas', G.V.Sotnikov. Wake-
field Excitation by a Relativistic Electron Bunch in a
Magnetized Plasma // Plasma Physics Report. 2000,
v. 26, # 10, p. 948-951.
ВОПРОСЫ АТОМНОЙ НАУКИ И ТЕХНИКИ. 2001. №5.
Серия: Ядерно-физические исследования (39), с. 59-59.
59
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| id | nasplib_isofts_kiev_ua-123456789-78982 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1562-6016 |
| language | English |
| last_indexed | 2025-12-07T16:10:07Z |
| publishDate | 2001 |
| publisher | Національний науковий центр «Харківський фізико-технічний інститут» НАН України |
| record_format | dspace |
| spelling | Balakirev, V.A. Karas’, V.I. Karas’, I.V. 2015-03-24T15:51:26Z 2015-03-24T15:51:26Z 2001 Relativistic electron bunch excitation of plasma wake-field and charged particle acceleration in the presence of external magnetic field / V.A. Balakirev, V.I. Karas’, I.V. Karas’ // Вопросы атомной науки и техники. — 2001. — № 5. — С. 57-59. — Бібліогр.: 3 назв. — англ. 1562-6016 PACS numbers: 29.17.+w, 29.27.Bd, 41.75.Jv, 41.75.Lx, 52.35.-g, 52.35.Mw, 52.38.Kd, 52.65.Rr https://nasplib.isofts.kiev.ua/handle/123456789/78982 The report is devoted to the theoretical study and numerical simulation of the excitation of wake-fields in plasma and their application for charged particle acceleration. It is shown that at a given relationship between the parameters of the "plasma bunch - magnetic field" system in the magnetoactive plasma owing to the hybrid space-surface character of wake-field waves excited by a relativistic electron bunch (REB), the accelerated bunch energy εmax can appear essentially higher than the exciting bunch energy even if the longitudinal REB charge density profiling is not used. With the help of 2.5 D numerical simulation of wake-fields excited by a single REB or a REB sequence it has been established the following: the ion channel is formed owing to transverse ion motion in self- consistent electromagnetic fields, this channel stabilizes REB propagation and thus serves to increase the REB excited fields; the self-modulation of a long pulsed REB is a very promising way both to obtain high rates of charged particle acceleration and to modulate the bunch and plasma densities (this gives evidence that the linear approach cannot be used to describe the plasma even in the low beam density case). These results make it possible to clarify the prospects and to evaluate the possibility of creating new-type charged particle accelerators which will have acceleration rates much higher than the conventional resonant accelerator has. The work was performed with the help the State Fundamental Research Foundation in Ukraine project # 02.07/213. en Національний науковий центр «Харківський фізико-технічний інститут» НАН України Вопросы атомной науки и техники Relativistic electron bunch excitation of plasma wake-field and charged particle acceleration in the presence of external magnetic field Возбуждение кильватерных плазменных волн релятивистскими электронными сгустками и ускорение заряженных частиц при наличии внешнего магнитного поля Article published earlier |
| spellingShingle | Relativistic electron bunch excitation of plasma wake-field and charged particle acceleration in the presence of external magnetic field Balakirev, V.A. Karas’, V.I. Karas’, I.V. |
| title | Relativistic electron bunch excitation of plasma wake-field and charged particle acceleration in the presence of external magnetic field |
| title_alt | Возбуждение кильватерных плазменных волн релятивистскими электронными сгустками и ускорение заряженных частиц при наличии внешнего магнитного поля |
| title_full | Relativistic electron bunch excitation of plasma wake-field and charged particle acceleration in the presence of external magnetic field |
| title_fullStr | Relativistic electron bunch excitation of plasma wake-field and charged particle acceleration in the presence of external magnetic field |
| title_full_unstemmed | Relativistic electron bunch excitation of plasma wake-field and charged particle acceleration in the presence of external magnetic field |
| title_short | Relativistic electron bunch excitation of plasma wake-field and charged particle acceleration in the presence of external magnetic field |
| title_sort | relativistic electron bunch excitation of plasma wake-field and charged particle acceleration in the presence of external magnetic field |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/78982 |
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