Simulation of plasma wakefield focusing and self-focusing of a short sequence of electron bunches depending on the bunch length, shape and distance between bunches
By using two-dimensional numerical simulation, the ratio between the effects of wakefield focusing and self-focusing during the propagation of a short sequence of electron bunches in plasma has been simulated. Cases of dominant wakefield focusing have been demonstrated. In addition, the collection d...
Gespeichert in:
| Datum: | 2022 |
|---|---|
| Hauptverfasser: | , , |
| Format: | Artikel |
| Sprache: | English |
| Veröffentlicht: |
Національний науковий центр «Харківський фізико-технічний інститут» НАН України
2022
|
| Schriftenreihe: | Problems of Atomic Science and Technology |
| Schlagworte: | |
| Online Zugang: | http://dspace.nbuv.gov.ua/handle/123456789/195882 |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Zitieren: | Simulation of plasma wakefield focusing and self-focusing of a short sequence of electron bunches depending on the bunch length, shape and distance between bunches / ПІБ // Problems of Atomic Science and Technology. — 2022. — № 6. — С. 36-39. — Бібліогр.: 14 назв. — англ. |
Institution
Digital Library of Periodicals of National Academy of Sciences of Ukraine| id |
irk-123456789-195882 |
|---|---|
| record_format |
dspace |
| spelling |
irk-123456789-1958822023-12-08T12:29:33Z Simulation of plasma wakefield focusing and self-focusing of a short sequence of electron bunches depending on the bunch length, shape and distance between bunches Bondar, D.S. Maslov, V.I. Onishchenko, I.N. Basic plasma physics By using two-dimensional numerical simulation, the ratio between the effects of wakefield focusing and self-focusing during the propagation of a short sequence of electron bunches in plasma has been simulated. Cases of dominant wakefield focusing have been demonstrated. In addition, the collection data is presented on the parameters of the bunch length, shape and distance between bunches correspond to certain ratios of wakefield focusing and self-focusing that can be used in further studies. За допомогою двовимірного чисельного моделювання змодельовано співвідношення між ефектами кільватерного фокусування та самофокусування при поширенні короткої послідовності електронних згустків у плазмі. Продемонстровані випадки домінуючого кільватерного фокусування. Крім того, представлені збірні дані про параметри довжини, форми згустку та відстані між згустками, що відповідають певним співвідношенням фокусування кільватерним полем та самофокусування, які можуть бути використані в подальших дослідженнях. 2022 Article Simulation of plasma wakefield focusing and self-focusing of a short sequence of electron bunches depending on the bunch length, shape and distance between bunches / ПІБ // Problems of Atomic Science and Technology. — 2022. — № 6. — С. 36-39. — Бібліогр.: 14 назв. — англ. 1562-6016 PACS: 29.17.+w; 41.75.Lx DOI: https://doi.org/10.46813/2022-142-036 http://dspace.nbuv.gov.ua/handle/123456789/195882 en Problems of Atomic Science and Technology Національний науковий центр «Харківський фізико-технічний інститут» НАН України |
| institution |
Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| collection |
DSpace DC |
| language |
English |
| topic |
Basic plasma physics Basic plasma physics |
| spellingShingle |
Basic plasma physics Basic plasma physics Bondar, D.S. Maslov, V.I. Onishchenko, I.N. Simulation of plasma wakefield focusing and self-focusing of a short sequence of electron bunches depending on the bunch length, shape and distance between bunches Problems of Atomic Science and Technology |
| description |
By using two-dimensional numerical simulation, the ratio between the effects of wakefield focusing and self-focusing during the propagation of a short sequence of electron bunches in plasma has been simulated. Cases of dominant wakefield focusing have been demonstrated. In addition, the collection data is presented on the parameters of the bunch length, shape and distance between bunches correspond to certain ratios of wakefield focusing and self-focusing that can be used in further studies. |
| format |
Article |
| author |
Bondar, D.S. Maslov, V.I. Onishchenko, I.N. |
| author_facet |
Bondar, D.S. Maslov, V.I. Onishchenko, I.N. |
| author_sort |
Bondar, D.S. |
| title |
Simulation of plasma wakefield focusing and self-focusing of a short sequence of electron bunches depending on the bunch length, shape and distance between bunches |
| title_short |
Simulation of plasma wakefield focusing and self-focusing of a short sequence of electron bunches depending on the bunch length, shape and distance between bunches |
| title_full |
Simulation of plasma wakefield focusing and self-focusing of a short sequence of electron bunches depending on the bunch length, shape and distance between bunches |
| title_fullStr |
Simulation of plasma wakefield focusing and self-focusing of a short sequence of electron bunches depending on the bunch length, shape and distance between bunches |
| title_full_unstemmed |
Simulation of plasma wakefield focusing and self-focusing of a short sequence of electron bunches depending on the bunch length, shape and distance between bunches |
| title_sort |
simulation of plasma wakefield focusing and self-focusing of a short sequence of electron bunches depending on the bunch length, shape and distance between bunches |
| publisher |
Національний науковий центр «Харківський фізико-технічний інститут» НАН України |
| publishDate |
2022 |
| topic_facet |
Basic plasma physics |
| url |
http://dspace.nbuv.gov.ua/handle/123456789/195882 |
| citation_txt |
Simulation of plasma wakefield focusing and self-focusing of a short sequence of electron bunches depending on the bunch length, shape and distance between bunches / ПІБ // Problems of Atomic Science and Technology. — 2022. — № 6. — С. 36-39. — Бібліогр.: 14 назв. — англ. |
| series |
Problems of Atomic Science and Technology |
| work_keys_str_mv |
AT bondards simulationofplasmawakefieldfocusingandselffocusingofashortsequenceofelectronbunchesdependingonthebunchlengthshapeanddistancebetweenbunches AT maslovvi simulationofplasmawakefieldfocusingandselffocusingofashortsequenceofelectronbunchesdependingonthebunchlengthshapeanddistancebetweenbunches AT onishchenkoin simulationofplasmawakefieldfocusingandselffocusingofashortsequenceofelectronbunchesdependingonthebunchlengthshapeanddistancebetweenbunches |
| first_indexed |
2025-07-17T00:08:56Z |
| last_indexed |
2025-07-17T00:08:56Z |
| _version_ |
1837850623700107264 |
| fulltext |
ISSN 1562-6016. Problems of Atomic Science and Technology. 2022. №6(142).
36 Series: Plasma Physics (28), p. 36-39.
https://doi.org/10.46813/2022-142-036
SIMULATION OF PLASMA WAKEFIELD FOCUSING AND SELF-
FOCUSING OF A SHORT SEQUENCE OF ELECTRON BUNCHES
DEPENDING ON THE BUNCH LENGTH,
SHAPE AND DISTANCE BETWEEN BUNCHES
D.S. Bondar1,2, V.I. Maslov1,2, I.N. Onishchenko1
1National Science Center “Kharkov Institute of Physics and Technology”, Kharkiv, Ukraine;
2V.N. Karazin Kharkiv National University, Kharkiv, Ukraine
E-mail: bondar@kipt.kharkov.ua1,2;
vmaslov@kipt.kharkov.ua1,2;
onish@kipt.kharkov.ua1
By using two-dimensional numerical simulation, the ratio between the effects of wakefield focusing and self-
focusing during the propagation of a short sequence of electron bunches in plasma has been simulated. Cases of
dominant wakefield focusing have been demonstrated. In addition, the collection data is presented on the parameters
of the bunch length, shape and distance between bunches correspond to certain ratios of wakefield focusing and self-
focusing that can be used in further studies.
PACS: 29.17.+w; 41.75.Lx
INTRODUCTION
The issues of focusing electron bunches and, in partic-
ular, relativistic electron bunches, do not lose their rele-
vance [1]. The focusing of electron bunches has been the
subject of research in a number of publications [2-11]. The
intensity of focusing of electron bunches in plasma often
significantly exceeds the intensity and degree of magnetic
focusing [12]. Two focusing effects take place in the case
of plasma. Firstly, it is well known self-focusing mecha-
nism based on the compensation of the space charge of a
bunch injected into plasma. Secondly the use of a trans-
verse plasma wakefield can additionally strengthen focus-
ing effect. Some preliminary studies of focusing by an ex-
cited wakefield has been presented in [13]. Homogeneous
focusing of electron bunches by an excited wake-field has
been studied in [6].
The question of the dependence of the ratio of wakefield
focusing and self-focusing (focusing of shielded bunch by
the magnetic field of its own current) on the length of se-
quence bunches and the distance between them has not been
sufficiently studied. The paper considers this issue using nu-
merical simulation by code LCODE [14].
The cylindrical coordinate system (r, z) was taken.
The time tis normalized to pe
-1, all the distances – to
cpe
-1, the density − to the unperturbed plasma electron
density n0e, the beam current Ib to mc3/e = 17 kA, the
fields – to mcωpe/e, where 𝑚 is the electron mass, 𝑒 – is
the electron charge, c – is the speed of light, ωpe – is the
plasma electron frequency. These normalisations are
used also in the figures.
We present the results of numerical simulation of plasma
wakefield excitation by a sequence of relativistic electron
bunches, obtained with the 2.5D quasistatic code LCODE
that treats the plasma as a cold electron fluid, and the
bunches as ensembles of macroparticles. The parameters
were similar to those of the plasma wakefield experiments,
in which the electron beam represented by a regular se-
quence of electron bunches excites the wakefield in the
uniform plasma. The maximum simulation time is 80.1T0,
here T0 =pe
-1. The distribution of bunches is Gaussian in
the transversal directions. The plasma ions represent the
immobile background.
Spatial step equals 0.1cT0. Time step for plasma electrons
equals 0.1T0. Time step for beam electrons equals 0.1b
1/2T0,
here b = 5 is relativistic factor of bunch electrons.
We presenttemporal dependences in selected points of
observation.
RESULTS OF NUMERICAL SIMULATION
To study the ratio between wakefield focusing and self-
focusing, we consider sequences of two bunches with differ-
ent current distributions along the bunch length (we consider
a two-dimensional simulation picture). Considering the indi-
cated simulation pattern and the fact that we assume a fixed
bunch length, we can assert that the charge of the bunch’s
changes in accordance with the indicated principles. We con-
sider sequences of two bunches, for each of which the current
is along the bunch: remains constant with a given amplitude
along the bunch; changes according to the law of cosine; in-
creases linearly along the bunch; decreases linearly along the
bunch. The length of the bunches and the distance between
them is measured in plasma wavelength . Let us first con-
sider the case of a sequence of two bunches, the current of
which is distributed uniformly along the entire length of the
bunch. Thanks to this example, we will find out the ratio of
wake focusing and self-focusing, the method for determining
this ratio. The base length of the sequence bunches in this case
was the 0.5 . The base distance between bunches is also
0.5 . Fig. 1 shows results of numerical simulation of
wakefield excitation in plasma by a sequence of two
bunches. The current distribution along the length of the
bunches is uniform (homogeneous). The following de-
scribes the logic for determining the ratio of wake focusing
and self-focusing, which were applied for other cases. In
Fig. 1 shows the radial electric force Er. When the bunch
just flies into the plasma, its space charge is not compen-
sated, since the plasma electrons have not yet had time to
scatter out from the bunch region.
mailto:bondar@kipt.kharkov.ua
mailto:vmaslov@kipt.kharkov.ua
mailto:onish@kipt.kharkov.ua
ISSN 1562-6016. Problems of Atomic Science and Technology. 2022. №6(142) 37
Fig. 1. <rb> ‒ average bunch radius; nb ‒ off axis average electron density of bunches; Hθ ‒ off axis magnetic field;
Er ‒ off-axis transverse electric field; Fr ‒ average focusing force; t = 3. Cosine current distribution of bunches
This force, due to the action of Er, pushes the bunch
electrons apart. In addition, there is another 2nd force,
which focuses the bunch by its own magnetic field Hθ of
the bunch, created by bunches current. The total force Fr
is equal to Fr = Er-Hθ.
If the bunch does not change, then its current does not
change and Hθ does not change, and Hθ is different from
zero only in the region of a bunch. Outside the bunch
(along ξ) Hθ=0. Er created by the bulk charge of the bunch
is Er=Hθ. Therefore, as seen in Fig. 1, in the head of the
bunch, where the plasma electrons have not yet had time
to scatter from the bunch Fr≈0.
By the way, Hθ acts only on the bunch, Hθ does not act
on plasma electrons. And Er acts on plasma electrons.
Plasma electrons under the action of Er scatter with time
to the sides, and thus charge screening of the bunch arises
with time. In Fig. 1 to the middle of the bunch, charge
screening occurs and Er = 0 is reached. Focusing is car-
ried out only because of the Hθ and Er = Hθ.
Here, one can say, only self-focusing occurs, that is,
only focusing by its own magnetic field. Further along
the bunch, the plasma electrons diverge by inertia due to
the momentum received from the space charge. And this
discrepancy by inertia means the appearance of a wake
field Er of the opposite sign from repulsive to focusing.
Here only self-focusing occurs (only focusing by
bunches) own magnetic field. Further along the bunch,
the plasma electrons diverge by inertia due to the mo-
mentum received from the space charge. And this dis-
crepancy by inertia means the appearance of a wake field
𝐸𝑟 of the opposite sign from repulsive to focusing.
As seen in Fig. 1, Er=Hθ is reached by the end of the 1st
bunch. So, Fr=2Hθ. From Er=Hθ, one can conclude that
by the end of the 1st bunch, the ratio of self-focusing and
wake focusing is 50/50%.
From Er=Hθ, one can conclude that by the end of the 1st
bunch, the ratio of self-focusing and wake focusing is
50/50%. As can be seen from Fig. 1, the heads of all
bunches, except for the 1st one, are defocused, and the
tails are focused.
Fig. 2 shows the excitation of the wake field by a se-
quence of bunches, the current distribution in which
changes according to the cosine law.
Fig. 2. <rb> ‒ average bunch radius (red line); nb ‒ off
axis average electron density of bunches (blue line);
Hθ ‒ off axis magnetic field (brown line); Er ‒ off axis
transverse electric field (light blue line); Fr ‒ average
focusing force (yellow line); t=3.
Cosine current distribution of bunches
For Fig. 1, it is easy to calculate the ratio of self-focus-
ing and wakefield focusing in accordance with the graph.
However, it is clear that absolute values are not important
for determining the ratio. Only their ratios make sense.
For all other figures, the ratios were put on using graph-
ical data.
For the graphs in Fig. 1. Fr
self-focus ≈ Hθ = 0.00175. At the
end of the first bunch the ratio of focusing power to self-
focusing Fr/Fr
self-focus = 2.3. Fr
wake/Fr
self-focus ≈ 1.3, where
Fr
wake = Fr - Fr
self-focus. Thus, the approximate ratio of
wakefield focusing and self-focusing is 50/50%, as pre-
dicted, taking into account all the features and errors of
numerical simulation. For the second bunch
Fr/Fr
self-focus ≈ 4.46, Fr
wake/Fr
self-focus = 3.46. Thus, it is ob-
vious that a change in the bunch current profile from uni-
form to one that changes according to the cosine law
leads to an increase in the ratio of wakefield focusing to
self-focusing, and an increase in the influence of wake
focusing in the process.
38 ISSN 1562-6016. Problems of Atomic Science and Technology. 2022. №6(142)
In Fig. 3 the process of excitation of the wakefield was
shown by a sequence of bunches with a linearly increas-
ing current distribution. It can be seen that according to
the data in Fig. 3, there is no wakefield focusing in the
region of the first bunch.
Fig. 3. <rb> ‒ average bunch radius (red line); nb ‒ off
axis average electron density of bunches (blue line);
Hθ ‒ off axis magnetic field (brow nline); Er ‒ off axis
transverse electric field (light blue line); Fr ‒ average
focusing force (yellow line); t=3.
Linear growth of current distribution of bunches
In the case of the second bunch of the sequence, the
following relation are observed: Fr
wake/Fr
self-focus = 1.5.
Fig. 4 shows the process of excitation of the wakefield
by a sequence of two bunches, the current (and charge)
of which decreases linearly. In this case, it is obvious that
for both bunches, the predominant wakefield focusing of
the bunches is observed. In this case, the heads of the
bunches are defocused, while the tails of the bunches are
subject to wake focusing. In the case of rectangular
bunches (see Fig. 1), the bunch tails are also mostly fo-
cused. A similar result is also observed in the case of
bunches, the current of which is distributed according to
the cosine law. The absence of focusing as such (only in-
homogeneous with an amplitude less than the maximum)
is observed only for the first bunch of the sequence for
the distribution of the growing bunch current. For Fig. 5,
the distance between bunches is used in the case of a se-
quence of two bunches as the distance between the end
of the first bunch and the beginning of the second bunch.
In the case of a uniform distribution of each bunch with
changing both the bunch lengths and the distance be-
tween the bunches the ratio of wakefield focusing and
self-focusing for the second bunch does not exceed 3.2
and reaches a minimum, equal to 1.15, both at bunch
lengths and at a distance between bunches equal to the
wavelength.
Fig. 4. <rb> ‒ average bunch radius (red line); nb ‒ off
axis average electron density of bunches (blue line);
Hθ ‒ off axis magnetic field (brown line); Er ‒ off axis
transverse electric field (light blue line); Fr ‒ average
focusing force (yellow line); t=3.
Linear decrease of current distribution of bunches
In the case of linearly decreasing and cosine current
profiles, only wakefield focusing in the region of bunch
tails is predominantly observed due to the features of
these distributions. Closer to the tails of the bunches, the
amplitude of the intrinsic current of the bunch ap-
proaches 0. For a linearly increasing distribution, the sit-
uation is similar, except that the ratio is more inhomoge-
neous on the graph, and a maximum is reached at a bunch
length of 0.8. Fig. 5 shows the relationship between
wakefield focusing and self-focusing as a function of the
distance between the bunches and the length of the
bunches. From the analysis of the data, it is obvious that,
regardless of the shape of the bunches, especially with an
increase in their length and especially in the region of the
second bunch of the sequence.
It is possible to identify areas in which only self-focusing
predominates.
.
Fig. 5. Dependence of the ratio of wakefield focusing and self-focusing as a function of the lengths and distance be-
tween the bunches for a uniform (left fig.) and linearly increasing (right fig.) bunch current distribution
ISSN 1562-6016. Problems of Atomic Science and Technology. 2022. №6(142) 39
In addition, there are optimal ratios of the length of the
bunches and the distance between them, at which the maxi-
mum ratio of wakefield focusing and self-focusing is ob-
served. In addition, there are obvious cases in which, almost
regardless of the length and distance between the bunches,
the same ratio between wakefield focusing and self-focusing
is observed. In particular, such cases are considered in Fig.
5 for uniform bunches. For example, in Fig. 5 (right) shows
the results for a linearly increasing current density of relativ-
istic electron bunches. An extremum can be observed at a
bunch length of 0.75 of the plasma wavelength. In this case,
at different distances between the bunches, the ratio of wake
focusing and self-focusing for the first bunch is about 0.375
and for the second bunch about 1.8. The data obtained from
figures can be applied in further studies.
CONCLUSIONS
The ratio between the effects of wakefield focusing and
self-focusing during the propagation of a short sequence of
electron bunches in plasma has been simulated. It is shown
that the intensity of focusing strongly depends on the shape
of the bunches, their lengths, the distance between the
bunches, and their number. For most parameters, the inten-
sity of the wakefield focusing exceeds the intensity of self-
focusing. In particular, for the end of second relativistic elec-
tron bunch, the current of which is distributed uniformly
along the bunch and which follows through the period of the
plasma wave after the first bunch, the intensity of wakefield
focusing exceeds the intensity of self-focusing more than in
three times.
In the case of a uniform distribution of each bunch with
changing both the bunch lengths and the distance between
the bunches the ratio of wakefield focusing and self-focus-
ing for the second bunch does not exceed 3.2 and reaches a
minimum, equal to 1.15, both at bunch lengths and at a dis-
tance between bunches equal to the wavelength. For the
middle of the second bunch, the current of which decreases
linearly along the bunch, the intensity of wakefield focusing
exceeds the intensity of self-focusing in two times.
REFERENCES
1. I.N. Onishchenko. Investigation of plasma lenses in
NSC KIPT // Problems of Atomic Science and Technology.
Series “Plasma Physics” (82). 2012, v. 6, p. 129-133.
2. Ya.B. Fainberg, N.I. Ayzatsky, V.A. Balakirev, et al.
Focusing of Relativistic Electron Bunches at the Wake-
field Excitation in Plasma // Proc. Particle Accelerator
Conference. 1997, v. 1, p. 651-653.
3. J.S.T. Ng, P. Chen, H. Baldis, et al. Observation of
Plasma Focusing of a 28.5 GeV Positron Beam // Phys.
Rev. Lett. 2001, v. 87(24), p. 244801.
4. C.E. Clayton, B.E. Blue, E.S. Dodd, et al. Transverse
Envelope Dynamics of a 28.5-GeV Electron Beam in a
Long Plasma // Phys. Rev. Lett. 2002, v. 88(15), p. 154801.
5. R.R. Kniaziev, T.C. Marshall, G.V. Sotnikov.
Transport of bunches in a dielectric wakefield accelerator
using an array of plasma cells // Problems of Atomic
Science and Technology. Series “Nuclear Physics
Investigations” (100). 2015, v. 6, p. 42-46.
6. V.I. Maslov, I.N. Onishchenko, I.P. Yarovaya. Plasma
wakefield excitation, possessing of homogeneous
focusing of electron bunches // Problems of Atomic
Science and Technology. Series “Plasma Physics” (83).
2013, v. 1, p. 134-136.
7. M.C. Thompson, H. Badakov, J.B. Rosenzweig, et al.
Observations of low-aberration plasma lens focusing of
relativistic electron beams at the underdense threshold //
Phys. Plasmas. 2010, v. 17, p. 073105.
8. V. Maslov, I. Levchuk, D. Bondar, I. Onishchenko.
Homogeneous Focusing Field for Short Relativistic
Electron Bunches in Plasma // Problems of Atomic
Science and Technology. Series “Nuclear Physics
Investigations” (127). 2020, v. 3, p. 68-72.
9. V. Maslov, I. Levchuk, D. Bondar, I. Onishchenko.
Homogeneous Focusing Field for Short Relativistic Elec-
tron Bunches in Plasma // Problems of Atomic Science
and Technology. Series “Nuclear Physics Investiga-
tions” (127). 2020, v. 3, p. 62-67.
10. V. Maslov, D. Bondar, I. Levchuk, I. Onishchenko.
Improvement of Properties of Self-Injected and
Accelerated Electron Bunch by Laser Pulse in Plasma,
Using Pulse Precursor // EEJP. 2019, v. 2, p. 64-66.
11. D. Bondar, V. Maslov, I. Levchuk, I. Onishchenko.
Transformer ratio enhancement at wakefield excitation in
blowout regime in plasma by electron bunch with semi-
gaussian charge distribution // East European Journal of
Physics. 2018, v. 5(2), p. 72-77.
12. G. Hairapetian, P. Devis, C. Joshi, et al. Transverse
dynamic of a short relativistic electrons bunch in a plasma
lens // Phys. Plasma. 1995, v. 2(6), p. 2555-2561.
13. D.S. Bondar, V.I. Maslov, I.N. Onishchenko, et al.
Plasma lens for electron and positron beams // Problems
of Atomic Science and Technology. Series “Plasma
Electrons and New Methods of Accelerations” (134).
2021. v. 4, p. 70-73.
14. K.V. Lotov. Simulation of Ultrarelativistic Beam
Dynamics in Plasma Wakefield Accelerator // Phys.
Plasmas. 1998. v. 5(3), p. 785-791.
Article received 12.10.2022
.
МОДЕЛЮВАННЯ КІЛЬВАТЕРНОГО ФОКУСУВАННЯ ТА САМОФОКУСУВАННЯ КОРОТКОЇ
ПОСЛІДОВНОСТІ ЕЛЕКТРОННИХ ЗГУСТКІВ У ЗАЛЕЖНОСТІ ВІД ДОВЖИНИ, ФОРМИ
ЗГУСТКІВ ТА ВІДСТАНІ МІЖ НИМИ
Д.С. Бондар, В.І. Маслов, І.М. Оніщенко
За допомогою двовимірного чисельного моделювання змодельовано співвідношення між ефектами кільва-тер-
ного фокусування та самофокусування при поширенні короткої послідовності електронних згустків у плазмі. Про-
демонстровані випадки домінуючого кільватерного фокусування. Крім того, представлені збірні дані про параме-
три довжини, форми згустку та відстані між згустками, що відповідають певним співвідношенням фокусування
кільватерним полем та самофокусування, які можуть бути використані в подальших дослідженнях.
|