Optimal resonant asymptotics of wakefield excitation in plasma by non-resonant sequence of electron bunches
Resonant asymptotics of wakefield excitation in plasma by non-resonant sequence of relativistic electron bunch-es has been numerically simulated. It has been shown that in resonant asymptotics at optimal parameters the wake-field is excited with the maximum growth rate and the amplitude of the excit...
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irk-123456789-1946222023-11-27T21:27:38Z Optimal resonant asymptotics of wakefield excitation in plasma by non-resonant sequence of electron bunches Maslov, V.I. Bilokon, E.O. Bilokon, V.O. Levchuk, I.P. Onishchenko, I.N. Plasma electronics Resonant asymptotics of wakefield excitation in plasma by non-resonant sequence of relativistic electron bunch-es has been numerically simulated. It has been shown that in resonant asymptotics at optimal parameters the wake-field is excited with the maximum growth rate and the amplitude of the excited wakefield is the largest. Чисельно промодельована резонансна асимптотика збудження в плазмі кільватерного поля нерезонансною послідовністю релятивістських електронних згустків. Показано, що в резонансній асимптотиці при оптимальних параметрах кільватерне поле збуджується з максимальним інкрементом, а амплітуда збуджуваного кільватерного поля найбільша. Численно промоделирована резонансная асимптотика возбуждения в плазме кильватерного поля нерезонансной последовательностью релятивистских электронных сгустков. Показано, что в резонансной асимптотике при оптимальных параметрах кильватерное поле возбуждается с максимальным инкрементом, а амплитуда возбуждаемого кильватерного поля наибольшая. 2019 Article Optimal resonant asymptotics of wakefield excitation in plasma by non-resonant sequence of electron bunches / V.I. Maslov, E.O. Bilokon, V.O. Bilokon, I.P. Levchuk, I.N. Onishchenko // Problems of atomic science and technology. — 2019. — № 1. — С. 99-102. — Бібліогр.: 23 назв. — англ. 1562-6016 PACS: 29.17.+w; 41.75.Lx http://dspace.nbuv.gov.ua/handle/123456789/194622 en Вопросы атомной науки и техники Національний науковий центр «Харківський фізико-технічний інститут» НАН України |
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Plasma electronics Plasma electronics Maslov, V.I. Bilokon, E.O. Bilokon, V.O. Levchuk, I.P. Onishchenko, I.N. Optimal resonant asymptotics of wakefield excitation in plasma by non-resonant sequence of electron bunches Вопросы атомной науки и техники |
| description |
Resonant asymptotics of wakefield excitation in plasma by non-resonant sequence of relativistic electron bunch-es has been numerically simulated. It has been shown that in resonant asymptotics at optimal parameters the wake-field is excited with the maximum growth rate and the amplitude of the excited wakefield is the largest. |
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Article |
| author |
Maslov, V.I. Bilokon, E.O. Bilokon, V.O. Levchuk, I.P. Onishchenko, I.N. |
| author_facet |
Maslov, V.I. Bilokon, E.O. Bilokon, V.O. Levchuk, I.P. Onishchenko, I.N. |
| author_sort |
Maslov, V.I. |
| title |
Optimal resonant asymptotics of wakefield excitation in plasma by non-resonant sequence of electron bunches |
| title_short |
Optimal resonant asymptotics of wakefield excitation in plasma by non-resonant sequence of electron bunches |
| title_full |
Optimal resonant asymptotics of wakefield excitation in plasma by non-resonant sequence of electron bunches |
| title_fullStr |
Optimal resonant asymptotics of wakefield excitation in plasma by non-resonant sequence of electron bunches |
| title_full_unstemmed |
Optimal resonant asymptotics of wakefield excitation in plasma by non-resonant sequence of electron bunches |
| title_sort |
optimal resonant asymptotics of wakefield excitation in plasma by non-resonant sequence of electron bunches |
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Національний науковий центр «Харківський фізико-технічний інститут» НАН України |
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2019 |
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Plasma electronics |
| url |
http://dspace.nbuv.gov.ua/handle/123456789/194622 |
| citation_txt |
Optimal resonant asymptotics of wakefield excitation in plasma by non-resonant sequence of electron bunches / V.I. Maslov, E.O. Bilokon, V.O. Bilokon, I.P. Levchuk, I.N. Onishchenko // Problems of atomic science and technology. — 2019. — № 1. — С. 99-102. — Бібліогр.: 23 назв. — англ. |
| series |
Вопросы атомной науки и техники |
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| fulltext |
ISSN 1562-6016. ВАНТ. 2019. №1(119)
PROBLEMS OF ATOMIC SCIENCE AND TECHNOLOGY. 2019, № 1. Series: Plasma Physics (25), p. 99-102. 99
OPTIMAL RESONANT ASYMPTOTICS OF WAKEFIELD EXCITATION
IN PLASMA BY NON-RESONANT SEQUENCE OF ELECTRON
BUNCHES
V.I. Maslov
1,2
, E.O. Bilokon
2
, V.O. Bilokon
2
, I.P. Levchuk
1
, I.N. Onishchenko
1
1
National Science Center “Kharkov Institute of Physics and Technology”, Kharkiv, Ukraine;
2
V.N. Karazin Kharkiv National University, Kharkiv, Ukraine
E-mail: vmaslov@kipt.kharkov.ua
Resonant asymptotics of wakefield excitation in plasma by non-resonant sequence of relativistic electron bunch-
es has been numerically simulated. It has been shown that in resonant asymptotics at optimal parameters the wake-
field is excited with the maximum growth rate and the amplitude of the excited wakefield is the largest.
PACS: 29.17.+w; 41.75.Lx
INTRODUCTION
As plasma in experiment is inhomogeneous and
nonstationary and properties of wakefield changes at
increase of its amplitude it is difficult to excite wake-
field resonantly by a long sequence of electron bunches
(see [1, 2]), to focus sequence (see [3-7]), to prepare
sequence from long beam (see [8-10]) and to provide
large transformer ratio (see [11-17]). In [2] the mecha-
nism has been found and in [18-21] investigated of res-
onant plasma wakefield excitation by a nonresonant
sequence of short electron bunches. The frequency syn-
chronization results by defocusing of those bunches
which fall into a wrong phase with respect to the wave.
In [6] it has been shown that nonresonant wakefield also
can effectively focuses the bunches. Here results are
presented on 2.5D numeral simulation by code LCODE
[22] of resonant asymptotics of wakefield excitation in
plasma by non-resonant sequence of relativistic electron
bunches. Under resonant asymptotics we mean the exci-
tation of the wakefield with the maximum growth rate,
when the non-resonant sequence has already self-
cleaned so that the interaction of the excited wakefield
with the bunch electrons in the acceleration phases is
negligible. Then the wakefield grows with steps.
1. MODEL OF NUMERICAL SIMULATION
We consider the wakefield excitation, when initially
the plasma density n0e is a little smaller than resonant
one n0e<nres(=m
2
me/4e
2
) (m is the repetition frequen-
cy of bunches). I.e. we consider the non-resonant case,
when m is a little larger the plasma frequency m>p.
We consider the conditions at which the largest wake-
field amplitude is excited and largest its growth rate is
obtained.
We use the cylindrical coordinate system (r, z). Time
is normalized on ωpe
-1
, distance – on c/ωpe, density on
nres, beam current Ib – on Icr=mc
3
/4e, fields – on
(4nresc
2
me)
1/2
.
Parameters are taken close to those of plasma wake-
field experiments [23].
2. RESULTS OF NUMERICAL SIMULATION
We first consider the wakefield excitation in a plas-
ma of length 1.67 m by first 28 bunches of finite length
(at half-height) b=0.2 (Fig. 1). One can see that 11-th
and 12-th bunches are similar to the first bunch, and
they just lead to the next increase in the amplitude of the
wakefield (Fig. 2). From Fig. 2 one can see that after
point, where the maximum wakefield amplitude is
reached (Fig. 3), it grows approximately by step. This
means that the intermediate bunches are defocused and
do not interact with the wakefield. At the same time,
bunches, which excite the wakefield, at the point of
reaching maximum amplitude have parameters close to
those which they had at the point of their injection.
Fig. 1. Temporal evolution of the beam density at γb=5; (ne-nres)/nres=-0.15, b=0.2, Ib=0.526·10
-3
, z=1.33m
Fig. 2. The on-axis wakefield excitation Ez (red), <E>=∫dr r Eznb/∫dr rnb (black) and density of bunches on the axis
nb=nb(r=0) (yellow) as a function of the time τ for γb=5, b=0.2, Ib=0.526·10
-3
, z=1.33m by train of 28 bunches in
the nonresonant case (ne-nres)/nres=-0.15
mailto:vmaslov@kipt.kharkov.ua
100 ISSN 1562-6016. ВАНТ. 2019. №1(119)
Fig. 3. The amplitude of Ez as a function of the coordi-
nate along the plasma at γb=5; (ne-nres)/nres=-0.15,
b=0.2, Ib=0.526·10
-3
From Fig. 3 one can see that the maximum ampli-
tude of excited wakefield is reached at a depth, equal
z=83 cm. This depth corresponds to approximately 8
wavelengths. At this depth, the electrons of the bunches
from the accelerating phases have been defocused such
strongly that their interaction with wakefield can be
neglected. At the same time, the radii of the decelerated
bunches are approximately initial (Fig. 4).
In the vicinity of the injection point, both the heads
of the first bunches at the beginning of each wakefield
beating, and the tails of the last bunches at the end of
each beginning are under the action of a radial force of
approximately equal Fr≈0 (Figs. 5, 6). And the tails of
the first bunches at the beginning of each beating and
the head of the last bunches at the end of each beating
are under the effect of a weak focusing force (see Figs.
5, 6).
Fig. 4. Ez2=Ez(r=rb) (red), the radial wake force Fr (dark blue), nb2=nb(r=rb) (yellow), and radius of bunches rb
(blue) as a function of the time for γb=5; (n0e-nres)/nres=-0.15, b=0.2, Ib=0.526·10
-3
, z=1.33m
Fig. 5. Ez2 (red), Fr (dark blue), nb2 (yellow) and rb (blue) as a function of the time for γb=5; (n0e-nres)/nres=-0.15,
b=0.1, Ib=1.05·10
-3
, z=0.05m. 1-st bunches in the beginning of each beating are shown by arrows
Fig. 6. Ez2 (red), Fr (dark blue), nb2 (yellow), and rb (blue) of Nb=20 bunches as a function of the time for γb=5;
(n0e-nres)/nres=-0.35, b=0.05, Ib=1.56·10
-3
, z=1.0m. 4 bunches, which excite wakefield, are shown by arrows
ISSN 1562-6016. ВАНТ. 2019. №1(119) 101
Taking into account that all beats at the beginning
are the same and identical, the impression is that there is
a symmetry between the behavior of the bunches at the
beginning and at end of each beating. However, this
symmetry is quickly violated, because with an increase
of the wakefield amplitude, the beats are shortened.
Thus, the bunches at the ends of the beats, which were
in Fr ≈ 0, get into the final Fr.
This gives an advantage to the first bunches at the
beginning of each beating and the hope to find the opti-
mum, taking into account that all bunches get a large
defocusing impulse, and the 1st bunches at the begin-
ning of each beating get a small focusing impulse. Op-
timal case corresponds to the case when the accelerated
bunches are defocused as far as possible from the region
of interaction with the wakefield Ez. In this case, the
decelerating bunches does not have time to be signifi-
cantly defocused, because they get into the phases of
small Fr. And the remaining bunches get into the phases
of large Fr. It can be assumed that the optimal case (the
maximum amplitude of the wakefield and the maximum
its growth rate) corresponds to the case when many
bunches have already defocused, and those that lead to
the growth of the wakefield were initially primarily fo-
cused, and then expanded to approximately the initial
radius.
Since bunches at a large distance are expanded both
in the defocusing and in the focusing fields, then the
wakefield is excited effectively by the bunches which
are under Fr≈0. If the bunches are very thin discs, then
we can assume that the optimal case corresponds to the
case when many bunches have already defocused, and
those that lead to the stepwise growth of the wakefield
have an initial radius, since they are in Fr0 (see Fig. 6).
It is also important, under what radial forces are the
bunches when they move through the plasma. Those
bunches that intensively excite the wakefield are not
always in the focusing field during moving. They can
move under the action of an alternating field, which
varies in the vicinity of Fr0. I.e. they can first be under
the action of a small focusing field Fr>0, then in Fr≈0,
then under the action of a small defocusing field Fr<0.
There is a fundamental difference between resonant
and nonresonant regimes. Namely, in the resonance
case, only the 1st bunch is focused, while the remaining
heads of bunches are defocused, and the tails of bunches
are focused. In the nonresonant case m>p, all the
bunches on the fronts of the beats are focused, and the
remaining comparatively short bunches are strongly
defocused.
CONCLUSIONS
So, it has been shown by numerically simulated that
in resonant asymptotics of wakefield excitation in plas-
ma by non-resonant sequence of relativistic electron
bunches at optimal parameters the wakefield is excited
with the maximum growth rate and the amplitude of the
excited wakefield is the largest. Up to resonant asymp-
totics the non-resonant sequence has already self-
cleaned so that the interaction of the excited wakefield
with the bunch electrons in the acceleration phases is
negligible. Then the wakefield grows approximately
with steps.
REFERENCES
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Article received 12.09.2018
ОПТИМАЛЬНАЯ РЕЗОНАНСНАЯ АСИМПТОТИКА ВОЗБУЖДЕНИЯ КИЛЬВАТЕРНОГО ПОЛЯ
В ПЛАЗМЕ НЕРЕЗОНАНСНОЙ ПОСЛЕДОВАТЕЛЬНОСТЬЮ ЭЛЕКТРОННЫХ СГУСТКОВ
В.И. Маслов, Э.О. Билоконь, В.О. Билоконь, И.П. Левчук, И.Н. Онищенко
Численно промоделирована резонансная асимптотика возбуждения в плазме кильватерного поля нерезо-
нансной последовательностью релятивистских электронных сгустков. Показано, что в резонансной асимп-
тотике при оптимальных параметрах кильватерное поле возбуждается с максимальным инкрементом, а ам-
плитуда возбуждаемого кильватерного поля наибольшая.
ОПТИМАЛЬНА РЕЗОНАНСНА АСИМПТОТИКА ЗБУДЖЕННЯ КІЛЬВАТЕРНОГО ПОЛЯ
В ПЛАЗМІ НЕРЕЗОНАНСНОЮ ПОСЛІДОВНІСТЮ ЕЛЕКТРОННИХ ЗГУСТКІВ
В.І. Маслов, Е.О. Білоконь, В.О. Білоконь, І.П. Левчук, І.М. Онiщенко
Чисельно промодельована резонансна асимптотика збудження в плазмі кільватерного поля нерезонанс-
ною послідовністю релятивістських електронних згустків. Показано, що в резонансній асимптотиці при оп-
тимальних параметрах кільватерне поле збуджується з максимальним інкрементом, а амплітуда збуджува-
ного кільватерного поля найбільша.
mailto:elyabilokon@gmail.com
mailto:elyabilokon@gmail.com
|