Simulation of plasma wakefield excitation by a sequence of relativistic electron bunches
Numerical simulations of plasma wakefield excitation by a long sequence of low-density relativistic electron bunches are performed with hybrid 2.5D code LCODE. For the resonant sequence, wakefields of up to 300 bunches add coherently until the wave nonlinearity comes into play.
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| Дата: | 2008 |
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Національний науковий центр «Харківський фізико-технічний інститут» НАН України
2008
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| Цитувати: | Simulation of plasma wakefield excitation by a sequence of relativistic electron bunches / K.V. Lotov, V.I. Maslov, I.N. Onishchenko, E.N. Svistun // Вопросы атомной науки и техники. — 2008. — № 6. — С. 114-116 . — Бібліогр.: 4 назв. — англ. |
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nasplib_isofts_kiev_ua-123456789-1107742025-02-10T01:32:28Z Simulation of plasma wakefield excitation by a sequence of relativistic electron bunches Чисельне моделювання збудження кільватерної хвилі в плазмі послідовністю релятивістських електронних згустків Численное моделирование возбуждения кильватерной волны в плазме последовательностью релятивистских электронных сгустков Lotov, K.V. Maslov, V.I. Onishchenko, I.N. Svistun, E.N. Plasma electronics Numerical simulations of plasma wakefield excitation by a long sequence of low-density relativistic electron bunches are performed with hybrid 2.5D code LCODE. For the resonant sequence, wakefields of up to 300 bunches add coherently until the wave nonlinearity comes into play. За допомогою гібридного 2.5-вимірного коду LCODE проведено чисельне моделювання збудження кільватерних полів у плазмі довгою послідовністю релятивістських електронних згустків невеликої густини. Для резонансного ланцюжка кільватерні поля 300 згустків додаються когерентно, поки не стає суттєвою нелінійність хвилі. С помощью гибридного 2.5-мерного кода LCODE проведено численное моделирование возбуждения кильватерных полей в плазме длинной последовательностью релятивистских электронных сгустков небольшой плотности. Для резонансной цепочки кильватерные поля 300 сгустков складываются когерентно, пока существенной не становится нелинейность волны. This work is supported by Russian Science Support Foundation, Russian President grants MD-4704.2007.2 and NSh-6046.2008.2, RFBR grant 06-02-16757, and Russian Ministry of Education grant RNP.2.2.1.1.3653. 2008 Article Simulation of plasma wakefield excitation by a sequence of relativistic electron bunches / K.V. Lotov, V.I. Maslov, I.N. Onishchenko, E.N. Svistun // Вопросы атомной науки и техники. — 2008. — № 6. — С. 114-116 . — Бібліогр.: 4 назв. — англ. 1562-6016 PACS: 29.17.+w; 41.75.Lx https://nasplib.isofts.kiev.ua/handle/123456789/110774 en Вопросы атомной науки и техники application/pdf 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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DSpace DC |
| language |
English |
| topic |
Plasma electronics Plasma electronics |
| spellingShingle |
Plasma electronics Plasma electronics Lotov, K.V. Maslov, V.I. Onishchenko, I.N. Svistun, E.N. Simulation of plasma wakefield excitation by a sequence of relativistic electron bunches Вопросы атомной науки и техники |
| description |
Numerical simulations of plasma wakefield excitation by a long sequence of low-density relativistic electron bunches are performed with hybrid 2.5D code LCODE. For the resonant sequence, wakefields of up to 300 bunches add coherently until the wave nonlinearity comes into play. |
| format |
Article |
| author |
Lotov, K.V. Maslov, V.I. Onishchenko, I.N. Svistun, E.N. |
| author_facet |
Lotov, K.V. Maslov, V.I. Onishchenko, I.N. Svistun, E.N. |
| author_sort |
Lotov, K.V. |
| title |
Simulation of plasma wakefield excitation by a sequence of relativistic electron bunches |
| title_short |
Simulation of plasma wakefield excitation by a sequence of relativistic electron bunches |
| title_full |
Simulation of plasma wakefield excitation by a sequence of relativistic electron bunches |
| title_fullStr |
Simulation of plasma wakefield excitation by a sequence of relativistic electron bunches |
| title_full_unstemmed |
Simulation of plasma wakefield excitation by a sequence of relativistic electron bunches |
| title_sort |
simulation of plasma wakefield excitation by a sequence of relativistic electron bunches |
| publisher |
Національний науковий центр «Харківський фізико-технічний інститут» НАН України |
| publishDate |
2008 |
| topic_facet |
Plasma electronics |
| url |
https://nasplib.isofts.kiev.ua/handle/123456789/110774 |
| citation_txt |
Simulation of plasma wakefield excitation by a sequence of relativistic electron bunches / K.V. Lotov, V.I. Maslov, I.N. Onishchenko, E.N. Svistun // Вопросы атомной науки и техники. — 2008. — № 6. — С. 114-116 . — Бібліогр.: 4 назв. — англ. |
| series |
Вопросы атомной науки и техники |
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| fulltext |
SIMULATION OF PLASMA WAKEFIELD EXCITATION BY A SEQUENCE
OF RELATIVISTIC ELECTRON BUNCHES
K.V. Lotov1, V.I. Maslov, I.N. Onishchenko, E.N. Svistun2
National Science Center “Kharkov Institute of Physics and Technology”, 61108, Kharkov, Ukraine;
1 Budker Institute of Nuclear Physics, 630090, Novosibirsk, Russia;
and Novosibirsk State University, 630090, Novosibirsk, Russia;
2 V.N. Karazin Kharkov National University, 61108, Kharkov, Ukraine
Numerical simulations of plasma wakefield excitation by a long sequence of low-density relativistic electron
bunches are performed with hybrid 2.5D code LCODE. For the resonant sequence, wakefields of up to 300 bunches add
coherently until the wave nonlinearity comes into play.
PACS: 29.17.+w; 41.75.Lx
1. INTRODUCTION
The intense plasma wakefield excitation by a single dense
bunch has allowed to achieve accelerating gradient above
40 GeV/m and to double energy of 42 GeV-bunch by a
plasma afterburner of the length less than 1m [1]. The question
arises to what limit the wakefield can grow if it is excited by a
long sequence of low-density electron bunches. To address
this question, we study self-consistent dynamics of only 500
short electron bunches in the uniform plasma. Even for this
reduced number of bunches comparatively to experiments [2-
3], the problem needs huge simulation area and computation
time and can be solved only with the fluid description of
plasma.
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 [4] that
treats plasma as a cold electron fluid and the bunches as
ensembles of macro-particles. Parameters are taken close to
those of plasma wakefield experiments [2-3], 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=0.5 cm, and rms angular
spread σθ=0.05mrad 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).
2. RESULTS OF SIMULATION
To begin with, we consider dynamics of first 31
bunches in the plasma. We use the cylindrical coordinate
system (r,z) and plot plasma and beam densities at some z
as functions of the dimensionless time τ=ωpt. 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 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 beam density in the middle of the plasma (at z=50 cm from the injection point)
Fig. 2. Temporal evolution of the plasma electron density at z=50 cm
Fig. 3. Temporal evolution of the beam density near the end of the plasma (z=85 cm)
PROBLEMS OF ATOMIC SCIENCE AND TECHNOLOGY. 2008. № 6. 114
Series: Plasma Physics (14), p. 114-116.
Fig. 4 shows the dimensionless density of plasma
electrons en~ =ne/np (ne is electron density)in the middle of
the plasma after passage of 200 bunches (near the
saturation level). The wave is clearly nonlinear, with the
value of positive perturbation being almost twice greater
than the value of negative perturbation.
Fig. 4. Electron density perturbation at z=50 cm during
one period after passage of 200 bunches
For the sequence of 500 bunches (Fig.5), we observe
that 100 bunches lose their energy linearly, i.e. coherently
deposit energy in plasma wakefield excitation (Fig.6).
Fig. 5. Longitudinal momenta of 500 bunches as they
pass the middle of the plasma (z=50cm)
The next portion of bunches (up to approximately
300th bunch) continues to lose their energy and contribute
to wakefield build-up, but at a smaller rate. Subsequent
bunches fall half-and-half in deceleration and acceleration
phases of the excited wakefield, so that the wakefield
amplitude saturates at the magnitude of 3 MeV/m.
Fig. 6. 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.6 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.
Now we consider behavior of 1st, 20th, 100th, and
300th bunches in detail (Figs. 7-9). The 1st bunch
propagates through the plasma with no change; it is
shown mainly for reference.
a
b
c
d
Fig. 7. Evolution of the bunch shape in plasma; 1st (a),
20th (b), 100th (c), and 300th (d) bunch at seven instants
as they move through the plasma
a
b
c
d
Fig. 8. Phase space portraits of the 1st (a), 20th (b),
100th (c), and 300th (d) bunch at the seven instants
115
The 20th and 100th bunches (ones at the stage of field
growth) are decelerated by the excited plasma wakefield,
and the deceleration rate is highest at bunch centers. This
phasing of the wave is very natural: the plasma wave
which provides the highest deceleration rate grows faster
than any other wave and eventually becomes the
dominant one. Once a bunch is completely in the
decelerating phase, its front half is defocused and lost on
the walls. For 20th and 100th bunches this happens near
the end of the plasma and causes the observed decrease of
the field amplitude there.
a
b
c
d
Fig. 9. Radial momenta of the 1st (a), 20th (b), 100th (c),
and 300th (d) bunch at the seven instants
The 300th bunch evolves differently. From the very
beginning, it propagates in the developed wakefield and is
strongly compressed as a whole. Reasons for this kind of
phasing are not clear yet. When passing through regions
of high Ez, the bunch loses much of its energy and reduces
the average longitudinal velocity. This backward shift
could be favorable for transverse confinement of the
bunch, but instead we observe transverse widening in all
cross-sections of the bunch. Probably, this happens due to
large transverse momenta (Fig. 9) acquired by bunch
particles in regions of strong focusing. These momenta
are sufficient for beam particles to escape radially when
the bunch enters the low wakefield region near plasma
exit.
3. CONCLUSION
It is shown that sequence of only about 300 relativistic
electron bunches contributes to wakefield growth. 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.
ACKNOWLEDGEMENTS
This work is supported by Russian Science Support
Foundation, Russian President grants MD-4704.2007.2
and NSh-6046.2008.2, RFBR grant 06-02-16757, and
Russian Ministry of Education grant RNP.2.2.1.1.3653.
REFERENCES
1. I. Blumenfeld, C.E. Clayton, F.-J. Decker et al. Energy
doubling of 42 GeV electrons in a metre-scale plasma
wakefield accelerator // Nature, Letters. 15 February,
2007, v.445, p.741-744.
2. А.К. Berezin, Ya.B. Fainberg, V.A. Kiselev et al.
Wakefield excitation in plasma by relativistic electron
beam, consisting regular chain of short bunches //
Fizika Plasmy. 1994, v. 20, N 7-8, p. 663-670.
3. V.A.Kiselev, A.F.Linnik, V.I.Mirny, et al.,
Experiments on resonator concept of plasma wakefield
accelerator driven by a train of relativistic electron
bunches // Problems of Atomic Science and Technology,
Series: “Plasma Electronics and New Methods of
Acceleration” (41). 2008, N 6, p.73-76.
4. K.V.Lotov, Simulation of ultrarelativistic beam
dynamics in plasma wake-field accelerator // Phys.
Plasmas. 1998, v. 5, N3, p. 785-791.
Article received 17.10.08
ЧИСЛЕННОЕ МОДЕЛИРОВАНИЕ ВОЗБУЖДЕНИЯ КИЛЬВАТЕРНОЙ ВОЛНЫ В ПЛАЗМЕ
ПОСЛЕДОВАТЕЛЬНОСТЬЮ РЕЛЯТИВИСТСКИХ ЭЛЕКТРОННЫХ СГУСТКОВ
К.В.Лотов, В.И.Маслов, И.Н.Онищенко, Е.Н.Свистун
С помощью гибридного 2.5-мерного кода LCODE проведено численное моделирование возбуждения
кильватерных полей в плазме длинной последовательностью релятивистских электронных сгустков небольшой
плотности. Для резонансной цепочки кильватерные поля 300 сгустков складываются когерентно, пока
существенной не становится нелинейность волны.
ЧИСЕЛЬНЕ МОДЕЛЮВАННЯ ЗБУДЖЕННЯ КІЛЬВАТЕРНОЇ ХВИЛІ В ПЛАЗМІ
ПОСЛІДОВНІСТЮ РЕЛЯТИВІСТСЬКИХ ЕЛЕКТРОННИХ ЗГУСТКІВ
К.В.Лотов, В.І.Маслов, І.М.Онищенко, О.М.Свистун
За допомогою гібридного 2.5-вимірного коду LCODE проведено чисельне моделювання збудження
кільватерних полів у плазмі довгою послідовністю релятивістських електронних згустків невеликої густини.
Для резонансного ланцюжка кільватерні поля 300 згустків додаються когерентно, поки не стає суттєвою
нелінійність хвилі.
116
1. INTRODUCTION
2. RESULTS OF SIMULATION
ACKNOWLEDGEMENTS
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