Long sequence of relativistic electron bunches as a driver in wakefield method of charged particles acceleration in plasma
Using LCODE 2.5D-simulation of wakefield excitation in plasma by a long sequence of relativistic electron bunches was performed. For the resonant sequence wakefields add coherently until the wave nonlinearity comes into play. The mechanism is found out which enables resonant excitation of the wakefi...
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Національний науковий центр «Харківський фізико-технічний інститут» НАН України
2010
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Цитувати: | Long sequence of relativistic electron bunches as a driver in wakefield method of charged particles acceleration in plasma / K.V. Lotov, V.I. Maslov, I.N. Onishchenko // Вопросы атомной науки и техники. — 2010. — № 6. — С. 103-107. — Бібліогр.: 21 назв. — англ. |
Репозитарії
Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1859853949292511232 |
|---|---|
| author | Lotov, K.V. Maslov, V.I. Onishchenko, I.N. |
| author_facet | Lotov, K.V. Maslov, V.I. Onishchenko, I.N. |
| citation_txt | Long sequence of relativistic electron bunches as a driver in wakefield method of charged particles acceleration in plasma / K.V. Lotov, V.I. Maslov, I.N. Onishchenko // Вопросы атомной науки и техники. — 2010. — № 6. — С. 103-107. — Бібліогр.: 21 назв. — англ. |
| collection | DSpace DC |
| description | Using LCODE 2.5D-simulation of wakefield excitation in plasma by a long sequence of relativistic electron bunches was performed. For the resonant sequence wakefields add coherently until the wave nonlinearity comes into play. The mechanism is found out which enables resonant excitation of the wakefield even if the bunch repetition frequency appreciably differs from the plasma frequency. Conditions for enhancement of excitation efficiency, acceleration gradient, and transformation ratio were investigated.
С использованием LCODE проведено 2.5-мерное численное моделирование возбуждения кильватерных полей в плазме длинной последовательностью релятивистских электронных сгустков. Для резонансной цепочки кильватерные поля складываются когерентно, пока существенной не становится нелинейность волны. Обнаружен механизм, который делает возможным резонансное возбуждение кильватерного поля, даже если частота следования сгустков отличается от плазменной частоты. Исследованы условия повышения эффективности возбуждения, темпа ускорения и коэффициента трансформации.
З використанням LCODE проведено 2.5-вимірне чисельне моделювання збудження кільватерних полів у плазмі довгою послідовністю релятивістських електронних згустків. Для резонансної послідовності кільватерні поля додаються когерентно, поки не стає суттєвою нелінійність хвилі. Виявлено механізм, який забезпечує резонансне збудження кільватерного поля, навіть якщо частота слідування згустків суттєво відрізняється від плазмової частоти. Досліджено умови збільшення ефективності збудження, темпу прискорення та коефіцієнта трансформації енергії.
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| first_indexed | 2025-12-07T15:42:45Z |
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PLASMA ELECTRONICS
LONG SEQUENCE OF RELATIVISTIC ELECTRON BUNCHES
AS A DRIVER IN WAKEFIELD METHOD OF CHARGED PARTICLES
ACCELERATION IN PLASMA
K.V. Lotov1, V.I. Maslov, I.N. Onishchenko
National Science Center “Kharkov Institute of Physics and Technology”, Kharkov, Ukraine;
1Budker Institute of Nuclear Physics, Novosibirsk, Russia
Using LCODE 2.5D-simulation of wakefield excitation in plasma by a long sequence of relativistic electron
bunches was performed. For the resonant sequence wakefields add coherently until the wave nonlinearity comes into
play. The mechanism is found out which enables resonant excitation of the wakefield even if the bunch repetition
frequency appreciably differs from the plasma frequency. Conditions for enhancement of excitation efficiency,
acceleration gradient, and transformation ratio were investigated.
PACS: 29.17.+w; 41.75.Lx;
1. INTRODUCTION
High gradient electric field excited in a plasma by
intense relativistic electron bunch or train of bunches
proposed in [1,2] and firstly experimentally tested in [3-5]
has already been demonstrated to offer new promising
techniques for acceleration [6], focusing [7, 8], and
deflection [9] of charged particle beams.
The bunch of the density comparable with or greater
than the plasma density n0 is required for excitation of a
high amplitude wave with the electric field of the order of
the wavebreaking limit E0=cωp/e, where m is the electron
mass, e is the elementary charge, c is the speed of light,
and ωp = √4πn0e2/m is the plasma frequency. If a high
density beam is not available, the wave can be resonantly
driven by a train of short low density electron bunches
providing the same total charge [3]. The multibunch
scheme has also been tested experimentally [3-5,10-14]
though accelerating gradients achieved so far are not so
impressive compared to single bunch experiment [6].
We present results of numerical simulation of plasma
wakefield excitation by a sequence of relativistic electron
bunches, made with 2.5D quasi-static code LCODE [15]
that treats the bunches as ensembles of macro-particles
and plasma as a cold electron fluid, since particle models
cannot treat very long bunch trains due to error
accumulation. The code is quasi-static, that is, the plasma
response is calculated as a function of the co-moving
coordinate ξ = z−ct. The quasi-static approximation is
fully justified for short highly relativistic beams which
evolve slowly on the time scale of beam passage through
a plasma cross-section; in this case ξ-dependencies define
both spatial portrait of the plasma response and its
temporal evolution at a certain cross-section. In our case,
the beam is long and the dualism in interpretation of
ξ-dependencies disappears. Each bunch still interacts with
the plasma quasistatically, that is, as a rigid object
moving with the speed of light. As to the whole beam,
corresponding times and distances are to be compared
with times and distances of non-quasistatic processes. At
plasma temperatures of interest (electron-volts), both
collisions and energy drift with the group velocity occur
at times greater than the time of beam passage through a
given cross-section. Thus, quasi-static ξ-dependencies
characterize the temporal behavior of the plasma response
at a fixed point. As to the instant spatial portrait of the
system, it cannot be obtained from ξ-dependencies by
putting t constant, since the beam itself is longer than the
distance of beam evolution.
Parameters are taken close to those of plasma
wakefield experiments [3], in which electron beam
represented by a regular sequence of 6000 electron
bunches, each of energy 2 MeV, charge 0.32 nC, rms
length 2σz=1.7cm, rms radius σr=0.5cm, and rms angular
spread σθ=0.05 mrad excites wakefield in the plasma of
density np=1011 cm-3 and length of about 1m, so that the
repetition frequency of the bunches coincides with the
plasma frequency ωp (so called resonant sequence).
The multibunch scheme imposes heavy demands on
accuracy of the plasma density. We have found, however,
a robust mechanism that, at the expense of bunch
population, enables resonant excitation of the wakefield
even if the bunch repetition rate appreciably differs from
the plasma frequency. There are experimental evidences
of this effect: in KIPT experiments [3] up to 5000
bunches coherently build up plasma oscillations thus
causing a linear growth of the wakefield amplitude. To
provide this field growth without the effect of frequency
synchronization, the plasma density must be controlled to
the precision of roughly 1/5000, which is absolutely
impossible with the decaying plasma used in the
experiments.
2d3v-investigation of transformation ratio has been
carried out. The cases of bunches placing on phases and
ramping of bunches intensity, which leads to values of
transformation ratio, exceeding limiting value 2, which
follows from Wilson theorem, have been considered.
2. RESULTS OF SIMULATION
2.1. RESONANT TRAIN OF BUNCHES
We consider dynamics of first 31 bunches in the
plasma. Bunches and plasma densities in the cylindrical
coordinate system (r,z) at some z as functions of the
dimensionless time τ=ωpt are shown in Figs. 1, 2. From
Fig. 1 we see that, at the middle of the plasma, the
bunches are already focused by the wakefield, and the
focusing is non-uniform. This looks like compression of
bunches both in radial and longitudinal directions,
though, of course, at these times and beam energies,
radial relative shifts of beam particles prevail. Because of
PROBLEMS OF ATOMIC SCIENCE AND TECHNOLOGY. 2010. № 6. 103
Series: Plasma Physics (16), p. 103-107.
the complicated shape of bunches, the excited wave
(Fig. 2) looks like a nonlinear one, with the wave period
being longer near the axis. However, it is not nonlinear
yet, that is, the period of remaining wakefields will be
exactly 2π/ωp if we break the sequence after the 31-th
bunch. As the bunch sequence evolves, the wakefield also
evolves, and location of defocusing regions shifts with
respect to the bunches. For a bunch slice to be defocused,
it is sufficient to fall into the defocusing field only once
for a relatively short period of time. As a consequence, at
the end of the plasma the bunches are mostly defocused
(Fig. 3), and the wakefield is lower.
Fig. 1. Temporal evolution of the bunches density in the middle of the plasma (at z=50 cm from the injection point)
Fig. 2. Temporal evolution of the plasma electron density (z=50 cm)
For the sequence of 500 bunches (see Fig. 3), we
observe that 100 bunches lose their energy linearly, i.e.
coherently deposit energy in plasma wakefield excitation
(Fig. 4).
Fig. 3. Longitudinal momenta of 500 bunches as they
pass the middle of the plasma (z=50cm)
The next portion of bunches (up to approximately
300-th bunch) continues to lose their energy and
contribute to wakefield build-up, but at a smaller rate.
Subsequent bunches fall in deceleration and acceleration
phases of the excited wakefield, so that the wakefield
amplitude saturates at the magnitude of 3 MeV/m.
Fig. 4. The amplitude of the on-axis electric field as a
function of the coordinate along the plasma and the
number of bunches
The overall picture of wakefield excitation is seen
from Fig. 4 that shows the temporal growth of
longitudinal electric field Ez in different plasma cross-
sections. Near the entrance, the bunches have a perfect
Gaussian-like shape, and the field grows linearly until the
wave gets nonlinear and goes out of resonance with the
sequence. At z~50 cm, the effect of bunch pinching
comes into play, and we observe faster field growth and a
higher saturation level. The maximum electric field here
is as high as 10% of the wavebreaking limit. Near the end
of the plasma, the bunches are mostly defocused, and the
excited wakefield is low.
2.2. NONRESONANT TRAIN OF BUNCHES
Fig. 5 shows how the frequency synchronization
manifests itself if the plasma density is 5% lower than the
resonant one.
Fig. 5. Wakefield amplitude as a function of coordinate
and number of past bunches for n0 = 0.95 nres
Here we plot the on-axis amplitude of the longitudinal
electric field Ezm versus the distance z along the plasma
and the number of bunches N past through these cross-
sections. At small z, we observe beating of the field, as it
should be for a harmonic oscillator driven by a periodic
force of a slightly different frequency. Some distance
downstream, the shape of bunches changes, and we see
the linear wakefield growth composed by small equal
steps that follow with the beat frequency.
To visualize the underlying physics, we reduce the
plasma density to 75% of the resonance value and look at
the phasing of bunches with respect to the wakefield
(Fig. 6, a). Just after entering the plasma, the bunches are
fresh, and the beating is nearly periodic. The bunches at
the beginning of beating pulses are mainly in the
decelerating phase of the wave; the ones near the end are
in the accelerating phase; the bunches near the field
maximum, on the average, do not exchange energy with
the wave. In the linear wakefield considered, intervals of
104
focusing are π/2 shifted forward in time with respect to
the acceleration intervals.
105
Fig. 6. The on-axis field Ez(t) (top) and the beam density
nb(r, t) (bottom) near the entrance to the plasma at z = 0
(a) and at the distance of frequency synchronization
z = 70c/ωp (b) for n0 = 0.75 nres. Black dashes under the
beam density map in (a) indicate cross-sections of the
defocusing transverse force. The thin sinusoid in (a) is the
wakefield of the first bunch. Vertical thin lines in (a) show
the relative location of bunch centroids with respect to
the wave
The bunches near the field maximum thus fall into the
defocusing phase of the wave and quickly leave the
wakefield area (Fig. 6, b). The bunches which build up or
damp the wave (thereby defining its structure) are in the
phase of a small transverse force and preserve their shape.
Due to this fact, the wave remains unchanged until the
defocused bunches get completely destroyed. With
respect to the plasma-frequency sinusoid, all survived
bunches are in the decelerating phase, while the destroyed
bunches were in the accelerating phase. Consequently, as
the latter disappear, the plasma-frequency sinusoid
becomes the dominant mode that monotonically increases
its amplitude with each group of survived bunches. In
other words, the survived bunches form a sequence which
is strictly resonant with the plasma wave. It is particularly
remarkable that the beam rearrangement occurs
identically in all beating periods, just with a time delay.
We can estimate the time of frequency
synchronization from the linear wakefield theory [16].
For the discussed beam parameters, this time corresponds
to the distance of about 15 cm that is marked in Fig. 1 by
the arrow.
2.3. TRASFORMATION RATIO
For plasma wakefield accelerator (PWFA) concept
three parameters are of great importance: accelerating
rate, efficiency and transformer ratio. For the simplest
case of PWFA – one-dimensional collinear along z two
“point” bunches (driver and witness) with number of
particles N1 , N2 and particle energy Ε1, Ε2 , respectively,
these parameters are defined by following relations:
accelerating rate G=dΕ2/dz; transformer ratio T = ΔΕ2/Ε1;
and efficiency η = Δ(N2Ε2)/ N1Ε1
High accelerating rate allows to reduce length of
accelerator but energy gain of accelerated bunch is
limited because the higher gradient of excited wakefield
the higher retarding field and smaller length on which
driver bunch loses its whole energy. As it has obtained in
[17] (Wilson’s theorem) for this case
T = ΔΕ2/Ε1 ≤ (2-N2/N1), (1) a
η ≤ N1/N2 (2-N2/N1). (2)
There some possibility to overcome this limit,
including the use multibunch driver. So for resonant train
of M bunches due to different stoppage distances of
various bunches, namely 1st, 2nd, 3rd,……M bunch loses
its whole energy on distance L, L/3, L/5,….L/(2M-1),
respectively, transformer ratio [17]
T≤Σ2/(2k-1)-N2/N1, i.e. T∼lnM, (3)
though wakefield increases linearly with number of
bunches M.
If bunches are placed in zeros of summarized wakefield
then T grows faster, namely linearly with M [18]. b
T≤2√M-N2/N1, (4)
because all bunches are in the equal its own decelerating
field and lose whole energy on the equal distance.
If the sequence is ramped then [18]:
T≤2M-N2/N1. (5)
We carried out 2d3v simulation of these cases and
investigated influence of focusing/defocusing of bunches
on value of transformer ratio.
For resonant (ωmod=ωp) sequence of 7 bunches of
equal intensity (IM= I0) and 8th accelerated bunch the
results are presented in Figs. 7, 8.
Fig. 7. Longitudinal electric field Ez (red) and coupling
coefficient (black) at γb=1000, Ib=0,3×10-3mc3/4e,
rb=0,3c/ωp
ωp
Fig. 8. Longitudinal momenta of bunches
From Figs. 7, 8 it follows that for the resonant train
transformer ratios, defined by field TE and by energy TΕ
are different TE≠TΕ, namely TE≈1.17, TΕ ∼ lnM [17] and
are not high enough. To enhance transformer ratio all
bunches should be in the equal decelerating field and
consequently lose its energy on the same distance and
consequently TE=TΕ. For this aim each bunch should be
placed in phase where total wakefield of previous
bunches is zero. It gives transformer ratio TΕ ∼ √M [17].
We proposed to place bunches only in phases of
wakefield zeros, where bunches experience focusing [19].
To manifest influence of focusing/defocusing of bunches
we considered mildy relativistic case γb=10. In Figs. 9,10
there are shown Ez wakefield (red), coupling coefficient
(black) and bunch density (yellow) for bunches placing in
focusing (see Fig. 9) and defocusing (Fig. 10) phases
where wakefield is zero (Ib=0,3×10-3mc3/4e, rb=0,3c/ωp).
106
Fig. 9. Focusing phases TE = 4.2, TΕ > 2√ M
Fig. 10. Defocusing phases TE = 1, TΕ < √ M
From Fig. 9 it is seen that placing bunches in focusing
zeros of wakefield results in linear increase of total
wakefield simultaneously with high transformer ratio.
Meanwhile in defocusing case (see Fig. 10) there is no
wakefield growth nor transformer ratio enhancement with
number of bunches.
Fig. 11. Dependence of TE on number of point bunches,
placed in wakefield zeros phases, where bunches are
focused: γ=1000 (black), γ=10 (blue dashed-line); 2√M
(red), M (green chain line)
Dependence of transformer ratio on number of
bunches with taking into account radial dynamic of
bunches at 2d3v simulation is shown in Fig. 11 for
bunches of equal charge and in Fig. 12 for ramped
sequence of bunches. For bunches experiencing focusing
(γ=10) transformer ratio is higher comparing to TE=2√M
for identical bunches and TE = 2M for ramped sequence.
In [14] the similar scheme of placing bunches in zeros
of Ez wakefield was proposed but additionally the train of
bunches should be profiled (e.g. ramped). For such
scheme the transformer ratio increases linearly with the
number of bunches (T=MT1), while the peak accelerating
field is only Efinal=ME1 (at the expense of the total charge
which scales as M2Q1 for R1 =2). E1 is the wake excited by
the first bunch with charge Q1. From an energy
standpoint, each bunch transfers as much energy to the
accelerating wake as the first bunch does, and the rest of
its energy is transferred through the plasma to the
subsequent bunches to prevent them from decelerating at
higher rate.
Fig. 12. Dependence of TE on number of bunches for
ramped sequence:
γ=1000 (black), γ=10 (blue dashed-line); 2M (red)
Fig. 13 shows an example of a case where 4 drive
bunches with l=λp/2 whose charges scale as
15:45:75:105 pC drive a 110 MV/m wake when they are
placed 1.5λp apart. The wake amplitude is small given the
total charge provided, but the transformer ratio is almost
quadrupled.
Fig. 13. Ramped bunch train distribution for maximum
transformer ratio. The drive bunches are separated by 1.5
plasma wavelengths
2.4. PLASMA-BASED AFTERBURNER
DESIGN FOR ILC
An afterburner from 100 to 500 GeV for International
Linear Collider can be designed by extending the ramped
bunches scheme within the limits of linear regime; an
exact design will have to account for the nonlinear effects
at ILC. A small witness bunch can gain 400 GeV (per
particle) by sampling a ~15 GV/m accelerating wakefield
over ~27 m of plasma. This wakefield can be excited by a
train of 4 ramped drive bunches if the plasma density is
increased to np=2×1017 cm-3
and the beam charge is
increased 5 times, while the focused beam size is
σr~10 μm. The total charge is 1.2 nC and needs to be
distributed as 75:225:375:525 pC while the bunches are
separated by 1.5λp =112 μm. Finally, in this model, if the
witness bunch only loads the wake by 30% in order to
minimize the energy spread, its charge would have to be
0.3Qtotal/T=0.3×1.2nC/8=45 pC [20]. If the same amount
of charge was distributed into 4 identical equidistant
bunches (or one single drive bunch), then the maximum
accelerating wakefield could be 4 times higher,
~60 GV/m, but the fourth drive bunch would lose all its
energy in less than 2 m in the plasma, thus limiting the
possible energy gain of the witness particles to 120 GeV.
107
However, using the 4 ramped bunches, the transformer
ratio in principle can be close to R=8 and the decelerating
wakefield inside any drive bunch is only (15 GV/m)/R =
1.875 GV/m.
This example demonstrates the advantages of using
transformer ratio enhancement techniques in plasma
accelerators [21].
CONCLUSIONS
1. It is shown that sequence of only about 300 relativistic
electron bunches contributes to wakefield growth until the
wave nonlinearity comes into play. For experiment [3] the
maximal wakefield of the order of 3 MV/m, i.e., 10% of
the wavebreaking limit, is achieved in the middle of the
plasma length. The electron density perturbation up to
60% is observed.
2. The effect of frequency synchronization makes
possible resonant wakefield excitation by very long bunch
train: requirement of sharp frequency matching removed.
3. It was proposed and simulated the way to increase
transformer ratio by means of placing bunches in those
zeros of WF where they are focusing by radial component
of WF.
4. PWFA based on multi-bunch driver has a perspective
as a concept of creating more compact collider
comparatively to conventional ones.
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Article received 07.10.10
ДЛИННАЯ ПОСЛЕДОВАТЕЛЬНОСТЬ РЕЛЯТИВИСТСКИХ ЭЛЕКТРОННЫХ СГУСТКОВ
КАК ДРАЙВЕР В КИЛЬВАТЕРНОМ МЕТОДЕ УСКОРЕНИЯ ЗАРЯЖЕННЫХ ЧАСТИЦ В ПЛАЗМЕ
К.В. Лотов, В.И. Маслов, И.Н. Онищенко
С использованием LCODE проведено 2.5-мерное численное моделирование возбуждения кильватерных
полей в плазме длинной последовательностью релятивистских электронных сгустков. Для резонансной
цепочки кильватерные поля складываются когерентно, пока существенной не становится нелинейность волны.
Обнаружен механизм, который делает возможным резонансное возбуждение кильватерного поля, даже если
частота следования сгустков отличается от плазменной частоты. Исследованы условия повышения
эффективности возбуждения, темпа ускорения и коэффициента трансформации.
ДОВГА ПОСЛІДОВНІСТЬ РЕЛЯТИВІСТСЬКИХ ЕЛЕКТРОННИХ ЗГУСТКІВ ЯК ДРАЙВЕР
В КІЛЬВАТЕРНОМУ МЕТОДІ ПРИСКОРЕННЯ ЗАРЯДЖЕНИХ ЧАСТИНОК У ПЛАЗМІ
К.В. Лотов, В.І. Маслов, І.М. Онищенко
З використанням LCODE проведено 2.5-вимірне чисельне моделювання збудження кільватерних полів у
плазмі довгою послідовністю релятивістських електронних згустків. Для резонансної послідовності кільватерні
поля додаються когерентно, поки не стає суттєвою нелінійність хвилі. Виявлено механізм, який забезпечує
резонансне збудження кільватерного поля, навіть якщо частота слідування згустків суттєво відрізняється від
плазмової частоти. Досліджено умови збільшення ефективності збудження, темпу прискорення та коефіцієнта
трансформації енергії.
1. INTRODUCTION
2. RESULTS OF SIMULATION
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| id | nasplib_isofts_kiev_ua-123456789-17472 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1562-6016 |
| language | English |
| last_indexed | 2025-12-07T15:42:45Z |
| publishDate | 2010 |
| publisher | Національний науковий центр «Харківський фізико-технічний інститут» НАН України |
| record_format | dspace |
| spelling | Lotov, K.V. Maslov, V.I. Onishchenko, I.N. 2011-02-26T21:46:28Z 2011-02-26T21:46:28Z 2010 Long sequence of relativistic electron bunches as a driver in wakefield method of charged particles acceleration in plasma / K.V. Lotov, V.I. Maslov, I.N. Onishchenko // Вопросы атомной науки и техники. — 2010. — № 6. — С. 103-107. — Бібліогр.: 21 назв. — англ. 1562-6016 https://nasplib.isofts.kiev.ua/handle/123456789/17472 Using LCODE 2.5D-simulation of wakefield excitation in plasma by a long sequence of relativistic electron bunches was performed. For the resonant sequence wakefields add coherently until the wave nonlinearity comes into play. The mechanism is found out which enables resonant excitation of the wakefield even if the bunch repetition frequency appreciably differs from the plasma frequency. Conditions for enhancement of excitation efficiency, acceleration gradient, and transformation ratio were investigated. С использованием LCODE проведено 2.5-мерное численное моделирование возбуждения кильватерных полей в плазме длинной последовательностью релятивистских электронных сгустков. Для резонансной цепочки кильватерные поля складываются когерентно, пока существенной не становится нелинейность волны. Обнаружен механизм, который делает возможным резонансное возбуждение кильватерного поля, даже если частота следования сгустков отличается от плазменной частоты. Исследованы условия повышения эффективности возбуждения, темпа ускорения и коэффициента трансформации. З використанням LCODE проведено 2.5-вимірне чисельне моделювання збудження кільватерних полів у плазмі довгою послідовністю релятивістських електронних згустків. Для резонансної послідовності кільватерні поля додаються когерентно, поки не стає суттєвою нелінійність хвилі. Виявлено механізм, який забезпечує резонансне збудження кільватерного поля, навіть якщо частота слідування згустків суттєво відрізняється від плазмової частоти. Досліджено умови збільшення ефективності збудження, темпу прискорення та коефіцієнта трансформації енергії. en Національний науковий центр «Харківський фізико-технічний інститут» НАН України Плазменная электроника Long sequence of relativistic electron bunches as a driver in wakefield method of charged particles acceleration in plasma Длинная последовательность релятивистских электронных сгустков как драйвер в кильватерном методе ускорения заряженных частиц в плазме Довга послідовність релятивістських електронних згустків як драйвер в кільватерному методі прискорення заряджених частинок у плазмі Article published earlier |
| spellingShingle | Long sequence of relativistic electron bunches as a driver in wakefield method of charged particles acceleration in plasma Lotov, K.V. Maslov, V.I. Onishchenko, I.N. Плазменная электроника |
| title | Long sequence of relativistic electron bunches as a driver in wakefield method of charged particles acceleration in plasma |
| title_alt | Длинная последовательность релятивистских электронных сгустков как драйвер в кильватерном методе ускорения заряженных частиц в плазме Довга послідовність релятивістських електронних згустків як драйвер в кільватерному методі прискорення заряджених частинок у плазмі |
| title_full | Long sequence of relativistic electron bunches as a driver in wakefield method of charged particles acceleration in plasma |
| title_fullStr | Long sequence of relativistic electron bunches as a driver in wakefield method of charged particles acceleration in plasma |
| title_full_unstemmed | Long sequence of relativistic electron bunches as a driver in wakefield method of charged particles acceleration in plasma |
| title_short | Long sequence of relativistic electron bunches as a driver in wakefield method of charged particles acceleration in plasma |
| title_sort | long sequence of relativistic electron bunches as a driver in wakefield method of charged particles acceleration in plasma |
| topic | Плазменная электроника |
| topic_facet | Плазменная электроника |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/17472 |
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