Plasma wake-field acceleration of charged particles by selfmodulated long relativistic electron bunch
- High-amplitude plasma wake-waves are excited by high-density relativistic electron bunches (REB) moving in a plasma. The wake- fields can be used to accelerate charged particles, to serve as electrostatic wigglers in freeelectron plasma lasers (FEL), and also can find many other applications. The...
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Національний науковий центр «Харківський фізико-технічний інститут» НАН України
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| Цитувати: | Plasma wake-field acceleration of charged particles by selfmodulated long relativistic electron bunch / V.I. Karas`, V.A. Balakirev, Ya.B. Fainberg, G.V. Sotnikov, I.V. Karas`, V.D. Levchenko // Вопросы атомной науки и техники. — 2000. — № 1. — С. 122-125. — Бібліогр.: 16 назв. — англ. |
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irk-123456789-816232015-05-19T03:02:05Z Plasma wake-field acceleration of charged particles by selfmodulated long relativistic electron bunch Karas, V.I. Balakirev, V.A. Fainberg, Ya.B. Sotnikov, G.V. Karas, I.V. Levchenko, V.D. Новые мeтoды ускорения заряженных частиц - High-amplitude plasma wake-waves are excited by high-density relativistic electron bunches (REB) moving in a plasma. The wake- fields can be used to accelerate charged particles, to serve as electrostatic wigglers in freeelectron plasma lasers (FEL), and also can find many other applications. The electromagnetic fields in the region occupied by the bunch control the dynamics of the bunch itself. In particular, the transverse forces cause a strong compression (pinching) of bunches having small transverse dimensions (kprb << 1, where kp = ωp/c, ωp is the plasma frequency, c is the light velocity, and rb is the radius of the bunch). This phenomenon is at the basis of operation of plasma lenses that can be used to focus ultrahigh energy particles. The longitudinal fields give rise to longitudinal modulation of an electron bunch. Specifically, an originally uniform bunch evolves into individual microbunches. This paper presents the results of 2.5-dimensional numerical simulation of both the modulation of long REB in a plasma and the excitation of wake fields by these bunches. The previous one-dimensional study has shown that the density profile modulation of a long bunch moving in plasma results in the growth of the wake wave amplitude. This is explained by the fact that the wake fields generated by microbunches being due to the evolution of the initially uniform bunch during the modulation, are coherent. The bunch modulation occurs at the plasma frequency. The present study is concerned with the REB motion, taking into account the plasma and REB nonlinearities. It is demonstrated that the radial REB dynamics exerts primary effect on both the REB self-modulation and the wake field excitation by the bunches formed. 2000 Article Plasma wake-field acceleration of charged particles by selfmodulated long relativistic electron bunch / V.I. Karas`, V.A. Balakirev, Ya.B. Fainberg, G.V. Sotnikov, I.V. Karas`, V.D. Levchenko // Вопросы атомной науки и техники. — 2000. — № 1. — С. 122-125. — Бібліогр.: 16 назв. — англ. 1562-6016 http://dspace.nbuv.gov.ua/handle/123456789/81623 533.9 en Вопросы атомной науки и техники Національний науковий центр «Харківський фізико-технічний інститут» НАН України |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine |
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Новые мeтoды ускорения заряженных частиц Новые мeтoды ускорения заряженных частиц |
| spellingShingle |
Новые мeтoды ускорения заряженных частиц Новые мeтoды ускорения заряженных частиц Karas, V.I. Balakirev, V.A. Fainberg, Ya.B. Sotnikov, G.V. Karas, I.V. Levchenko, V.D. Plasma wake-field acceleration of charged particles by selfmodulated long relativistic electron bunch Вопросы атомной науки и техники |
| description |
- High-amplitude plasma wake-waves are excited by high-density relativistic electron bunches (REB) moving in a plasma. The wake- fields can be used to accelerate charged particles, to serve as electrostatic wigglers in freeelectron plasma lasers (FEL), and also can find many other applications. The electromagnetic fields in the region occupied by the bunch control the dynamics of the bunch itself. In particular, the transverse forces cause a strong compression (pinching) of bunches having small transverse dimensions (kprb << 1, where kp = ωp/c, ωp is the plasma frequency, c is the light velocity, and rb is the radius of the bunch). This phenomenon is at the basis of operation of plasma lenses that can be used to focus ultrahigh energy particles. The longitudinal fields give rise to longitudinal modulation of an electron bunch. Specifically, an originally uniform bunch evolves into individual microbunches. This paper presents the results of 2.5-dimensional numerical simulation of both the modulation of long REB in a plasma and the excitation of wake fields by these bunches. The previous one-dimensional study has shown that the density profile modulation of a long bunch moving in plasma results in the growth of the wake wave amplitude. This is explained by the fact that the wake fields generated by microbunches being due to the evolution of the initially uniform bunch during the modulation, are coherent. The bunch modulation occurs at the plasma frequency. The present study is concerned with the REB motion, taking into account the plasma and REB nonlinearities. It is demonstrated that the radial REB dynamics exerts primary effect on both the REB self-modulation and the wake field excitation by the bunches formed. |
| format |
Article |
| author |
Karas, V.I. Balakirev, V.A. Fainberg, Ya.B. Sotnikov, G.V. Karas, I.V. Levchenko, V.D. |
| author_facet |
Karas, V.I. Balakirev, V.A. Fainberg, Ya.B. Sotnikov, G.V. Karas, I.V. Levchenko, V.D. |
| author_sort |
Karas, V.I. |
| title |
Plasma wake-field acceleration of charged particles by selfmodulated long relativistic electron bunch |
| title_short |
Plasma wake-field acceleration of charged particles by selfmodulated long relativistic electron bunch |
| title_full |
Plasma wake-field acceleration of charged particles by selfmodulated long relativistic electron bunch |
| title_fullStr |
Plasma wake-field acceleration of charged particles by selfmodulated long relativistic electron bunch |
| title_full_unstemmed |
Plasma wake-field acceleration of charged particles by selfmodulated long relativistic electron bunch |
| title_sort |
plasma wake-field acceleration of charged particles by selfmodulated long relativistic electron bunch |
| publisher |
Національний науковий центр «Харківський фізико-технічний інститут» НАН України |
| publishDate |
2000 |
| topic_facet |
Новые мeтoды ускорения заряженных частиц |
| url |
http://dspace.nbuv.gov.ua/handle/123456789/81623 |
| citation_txt |
Plasma wake-field acceleration of charged particles by selfmodulated long relativistic electron bunch / V.I. Karas`, V.A. Balakirev, Ya.B. Fainberg, G.V. Sotnikov, I.V. Karas`, V.D. Levchenko // Вопросы атомной науки и техники. — 2000. — № 1. — С. 122-125. — Бібліогр.: 16 назв. — англ. |
| series |
Вопросы атомной науки и техники |
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2025-07-06T06:49:52Z |
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| fulltext |
ВОПРОСЫ АТОМНОЙ НАУКИ И ТЕХНИКИ 2000. №1.
Серия: Плазменная электроника и новые методы ускорения (2), с. 122-125.
122
UDK 533.9
PLASMA WAKE-FIELD ACCELERATION OF CHARGED PARTICLES
BY SELFMODULATED LONG RELATIVISTIC ELECTRON BUNCH
V.I.Karas', V.A.Balakirev, Ya.B.Fainberg, G.V.Sotnikov, I.V.Karas',
V.D.Levchenko*
National Science Center "Kharkov Institute of Physics and Technology", Ukraine
*) Keldysh Institute of Applied Mathematics, RAS, Moscow, Russia
- High-amplitude plasma wake-waves are excited by high-density relativistic electron bunches (REB) moving in a
plasma. The wake- fields can be used to accelerate charged particles, to serve as electrostatic wigglers in free-
electron plasma lasers (FEL), and also can find many other applications.
The electromagnetic fields in the region occupied by the bunch control the dynamics of the bunch itself. In
particular, the transverse forces cause a strong compression (pinching) of bunches having small transverse
dimensions ( k rp b <<1 , where k cp p= ω , ωp is the plasma frequency, c is the light velocity, and rb is the
radius of the bunch). This phenomenon is at the basis of operation of plasma lenses that can be used to focus ultra-
high energy particles. The longitudinal fields give rise to longitudinal modulation of an electron bunch. Specifically,
an originally uniform bunch evolves into individual microbunches.
This paper presents the results of 2.5-dimensional numerical simulation of both the modulation of long REB in a
plasma and the excitation of wake fields by these bunches. The previous one-dimensional study has shown that the
density profile modulation of a long bunch moving in plasma results in the growth of the wake wave amplitude. This
is explained by the fact that the wake fields generated by microbunches being due to the evolution of the initially
uniform bunch during the modulation, are coherent. The bunch modulation occurs at the plasma frequency. The
present study is concerned with the REB motion, taking into account the plasma and REB nonlinearities. It is
demonstrated that the radial REB dynamics exerts primary effect on both the REB self-modulation and the wake
field excitation by the bunches formed.
1. Introduction
The charged particle acceleration by charge density
waves in a plasma and in uncompensated charged beams
appears to be a most promising trend in the collective
methods of acceleration [1-3]. The variable part of the
charge density can be made to be very high (up to n0 ,
where n0 is the unperturbed plasma density); therefore,
the accelerating fields can reach 107 to 109 V/cm. Chen
et al [4] have proposed a modification of the Fainberg
acceleration method [1], consisting in using a train of
bunches. In [5], Katsouleas has considered electron
bunches with different profiles, namely, a bunch with a
slow build-up in the density and its very quick fall-off,
and also the bunch with the Gaussian-type distribution
for different rise and fall-off times. It was established in
[5] that the use of these nonsymmetric bunches instead
of symmetric ones can provide the accelerating field
Eac value to be many times (10 to 20) higher than the
retarding field Est value. The so-called transformation
coefficient T E Eac st ac b= = −∆γ γ 1 is equal to
2πN , where N corresponds to the number of
wavelengths along the bunch length. The excitation of
nonlinear stationary waves in the plasma by a periodic
train of electron bunches has been studied in refs. [6, 7],
where it was shown that the electric field of the wave in
the plasma increases with γ (γ is the relativistic factor
of the beam) at commensurable plasma and beam
densities. The experiments undertaken in refs. [7, 8] on
wake-field acceleration has demonstrated the importance
of three-dimensional effects.
Here, we consider two different regimes with high
amplitudes of plasma wake fields that are employed in
the accelerator physics. The first regime makes use of an
extended short beam, then the high-amplitude waves
excited by this beam and having high-gradient
longitudinal electric fields can be used to accelerate
other bunches. In the second case, a strong focusing can
be attained with a long narrow beam, making use of its
intrinsic magnetic field which is unbalanced because of
space charge compensation by the plasma.
Apart from the transverse forces, the bunch particles are
also influenced by powerful longitudinal forces on the
side of electric wake fields. The longitudinal fields will
give rise to a longitudinal modulation of the electron
bunch, i.e., to a splitting of an originally uniform bunch
into microbunches with a modulation period
λ π ωp pc n= = × −2 3 36 106
0
1 2. cm. In particular,
in the plasma with a particle density of 1016 cm-3 the
modulation period is 0.3 mm. The effect of longitudinal
REB modulation by wake fields can be used for
developing plasma modulators of dense electron beams.
It is pertinent to note one more feature of this
phenomenon. Since the modulation frequency is
coincident with the plasma frequency, the wake fields of
microbunches are then combined coherently. Therefore,
the electron bunch modulation will involve an increase
in the amplitude of the wake field behind the bunch.
This effect opens up a possibility of using long-pulse
electron bunches to excite intense wake fields in a
plasma. It is particularly remarkable that the effect of
longitudinal modulation at a plasma frequency takes
place for a long laser pulse, too [9].
2. Physical model and equations
Previously in [10], a theoretical study has been made
123
into the process of modulation of long electron bunches
in a plasma by longitudinal wake fields. Results were
reported there for one-dimensional numerical simulation
of nonlinear dynamics of bunch modulation. It was
demonstrated in ref. [10] that the particle modulation of
a long bunch moving in the plasma causes an increase in
the wake wave amplitude. This effect is accounted for
by coherent combining of fields excited by
microbunches, into which the bunch is split in the course
of modulation. The bunch is modulated at a plasma
frequency. The investigation of the one-dimensional
approximation is justified in the case of great transverse
dimensions ( 2 1π λrb p >> ).
The present report deals with the 2.5-dimensional
numerical simulation of wake fields by long REB.
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 COMPASS
code [11]. Earlier, this code has been used to simulate
the induction accelerator [12], the modulated relativistic
electron beam [13], and a single REB or a train of these
bunches in a plasma [11, 13-16].
The dynamic of REB is described by the relativistic
Belyaev-Budker equations for the distribution functions
( )f r pα
! !, of the 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 back-ground 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.
The scale on which the electric and magnetic fields vary
is m c ee pω . We assume that the plasma and bunch
particles escape from the computation 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 computation region from the buffer zones
z < 0 and z Z> . The boundary conditions for the
fields corresponds 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 coordinate, and the total number of these particles
was about 106. All the calculations were carried out on a
PentiumII-400 personal computer using the modified
particle-in-cell simulation algorithm.
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.
3. Results and discussion
Figures 1 to 3 show spatial distributions of the electric
charge density of electrons el.Q, longitudinal electric
field dfld zE , longitudinal current density of electrons
el.Jhz, respectively, for the instants of time t p= −60 1ω
(a) and t p= −100 1ω (b).
Fig. 1.
Fig. 2.
It is seen from Fig. 1 that the longitudinal electric field
rapidly grows reaching 08. m c ee pω . Note that the
124
original beam particle density was only 6% of the
plasma electron density. The radial electric field Er
also grows, but it reaches a somewhat lower value
0 4. e pmc eω . It is significant that: (i) the finite length
of the initial bunch is responsible for the formation of
the growing electric field; (ii) the electric field has a
rather high amplitude near the axis, this being due to
microbunch pinching; (iii) the evolution of the
instability, giving rise to microbunches, leads to some
decrease in the phase velocity of the perturbed wake
wave.
From Fig. 2 it is seen that the electric charge density
distributions of plasma electrons el Q. are similar to the
spatial distributions of the longitudinal electric field
Ez . The highest density value is attained for the 8th
microbunch and is 4 5 0. n . It is of importance to note
that the maximum of the beam particle charge density
corresponds to the 5th microbunch rather than to the 8th
microbunch and is equal to 16 0. n , this being two orders
of magnitude higher than the initial beam particle
density value in the long bunch.
Fig. 3.
The spatial distribution of the longitudinal current
density of plasma electrons el Jhz. (Fig.3) also
correlates rigidly with the longitudinal electric field Ez
distribution. Here attention must be given to the peak
current value for the 8th microbunch, which is two
orders of magnitude higher than the initial longitudinal
current value of REB particles.
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. [10]). This supports in full
measure the conclusion given in ref. [7] about the
necessity of taking into complete account the three-
dimensional effects and the nonlinear behavior of both
the plasma and the bunch.
4. Conclusion
The spatial density distributions of REB and plasma
electrons obtained for the instances of time t p= −60 1ω
and t p= −100 1ω show that the density ratio n nb 0
(the initial value being 0.018) reaches 0.04 as early as at
t p= −60 1ω . At t p= −100 1ω , the highest beam particle
density becomes commensurable with the plasma
density, i.e., a very strong modulation of beam particle
density is observed.
The spatial distributions of the longitudinal Ez and
transverse Er electric fields show that the Ez and Er
amplitudes grow owing to the enhancement in the
density modulation. At t p= −100 1ω the highest
longitudinal-field amplitude reaches 08. m c ee pω ,
and the highest transverse-field amplitude is equal to
0 4. m c ee pω . 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.
The undertaken numerical experiments have
demonstrated 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
contributory 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. 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.
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