Short cylindrical electron bunch dynamics and wake fields` excitation in plasma with the external magnetic field
Dynamics of the non-relativistic cylindrical electron bunch injected into the homogeneous plasma along the external magnetic field was studied using computer simulation via PIC method. The initial bunch length was equal to the wake wave length of the background plasmas. The simulation results are co...
Gespeichert in:
| Datum: | 2015 |
|---|---|
| Hauptverfasser: | , |
| Format: | Artikel |
| Sprache: | English |
| Veröffentlicht: |
Національний науковий центр «Харківський фізико-технічний інститут» НАН України
2015
|
| Schriftenreihe: | Вопросы атомной науки и техники |
| Schlagworte: | |
| Online Zugang: | http://dspace.nbuv.gov.ua/handle/123456789/112193 |
| 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: | Short cylindrical electron bunch dynamics and wake fields` excitation in plasma with the external magnetic field / M.A. Shcherbinin, I.O. Anisimov // Вопросы атомной науки и техники. — 2015. — № 4. — С. 124-128. — Бібліогр.: 10 назв. — рос. |
Institution
Digital Library of Periodicals of National Academy of Sciences of Ukraine| id |
irk-123456789-112193 |
|---|---|
| record_format |
dspace |
| spelling |
irk-123456789-1121932017-01-18T03:04:28Z Short cylindrical electron bunch dynamics and wake fields` excitation in plasma with the external magnetic field Shcherbinin, M.A. Anisimov, I.O. Новые методы ускорения заряженных частиц Dynamics of the non-relativistic cylindrical electron bunch injected into the homogeneous plasma along the external magnetic field was studied using computer simulation via PIC method. The initial bunch length was equal to the wake wave length of the background plasmas. The simulation results are compared with the case without magnetic field. It is shown that strong external magnetic field suppresses the radial bunch defocusing but moves to the further longitudinal expansion of the bunch. As a result the area of the wake wave excitation grows substantially. Periodicity of the background plasma current is determined by the excited wake wave. Досліджена динаміка нерелятивістського циліндричного електронного згустку, інжектованого в однорідну плазму вздовж силових ліній зовнішнього магнітного поля, за допомогою комп’ютерного моделювання методом крупних частинок. Початкова довжина згусткa дорівнює довжині кільватерної хвилі у фоновій плазмі. Результати моделювань порівнюються з відповідними результатами за відсутності магнітного поля. Показано, що сильне зовнішнє магнітне поля пригнічує радіальне дефокусування згусткa, але призводить до інтенсивнішого розширення згусткa в поздовжньому напрямку. У результаті область збудження кільватерної хвилі суттєво зростає. Спостерігається періодичність у просторовому розподілі струмів фонової плазми, що визначається структурою кільватерної хвилі. Представлены результаты исследования динамики нерелятивистского электронного сгустка, инжектированного в однородную плазму при воздействии внешнего магнитного поля, с помощью компьютерного моделирования методом частиц в ячейках. Начальная длина сгустка равна длине кильватерной волны в фоновой плазме. Результаты моделирований сравниваются с соответствующими результатами без магнитного поля. Показано, что сильное магнитное поле подавляет радиальную дефокусировку сгустка, но приводит к его быстрому расширению в продольном направлении. В результате область возбуждения кильватерной волны существенно возрастает. Наблюдается периодичность в пространственном распределении токов фоновой плазмы, обусловленная структурой кильватерной волны. 2015 Article Short cylindrical electron bunch dynamics and wake fields` excitation in plasma with the external magnetic field / M.A. Shcherbinin, I.O. Anisimov // Вопросы атомной науки и техники. — 2015. — № 4. — С. 124-128. — Бібліогр.: 10 назв. — рос. 1562-6016 PACS: 52.25.Xz, 52.35.Fp, 52.40.Mj http://dspace.nbuv.gov.ua/handle/123456789/112193 en Вопросы атомной науки и техники 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 |
Новые методы ускорения заряженных частиц Новые методы ускорения заряженных частиц |
| spellingShingle |
Новые методы ускорения заряженных частиц Новые методы ускорения заряженных частиц Shcherbinin, M.A. Anisimov, I.O. Short cylindrical electron bunch dynamics and wake fields` excitation in plasma with the external magnetic field Вопросы атомной науки и техники |
| description |
Dynamics of the non-relativistic cylindrical electron bunch injected into the homogeneous plasma along the external magnetic field was studied using computer simulation via PIC method. The initial bunch length was equal to the wake wave length of the background plasmas. The simulation results are compared with the case without magnetic field. It is shown that strong external magnetic field suppresses the radial bunch defocusing but moves to the further longitudinal expansion of the bunch. As a result the area of the wake wave excitation grows substantially. Periodicity of the background plasma current is determined by the excited wake wave. |
| format |
Article |
| author |
Shcherbinin, M.A. Anisimov, I.O. |
| author_facet |
Shcherbinin, M.A. Anisimov, I.O. |
| author_sort |
Shcherbinin, M.A. |
| title |
Short cylindrical electron bunch dynamics and wake fields` excitation in plasma with the external magnetic field |
| title_short |
Short cylindrical electron bunch dynamics and wake fields` excitation in plasma with the external magnetic field |
| title_full |
Short cylindrical electron bunch dynamics and wake fields` excitation in plasma with the external magnetic field |
| title_fullStr |
Short cylindrical electron bunch dynamics and wake fields` excitation in plasma with the external magnetic field |
| title_full_unstemmed |
Short cylindrical electron bunch dynamics and wake fields` excitation in plasma with the external magnetic field |
| title_sort |
short cylindrical electron bunch dynamics and wake fields` excitation in plasma with the external magnetic field |
| publisher |
Національний науковий центр «Харківський фізико-технічний інститут» НАН України |
| publishDate |
2015 |
| topic_facet |
Новые методы ускорения заряженных частиц |
| url |
http://dspace.nbuv.gov.ua/handle/123456789/112193 |
| citation_txt |
Short cylindrical electron bunch dynamics and wake fields` excitation in plasma with the external magnetic field / M.A. Shcherbinin, I.O. Anisimov // Вопросы атомной науки и техники. — 2015. — № 4. — С. 124-128. — Бібліогр.: 10 назв. — рос. |
| series |
Вопросы атомной науки и техники |
| work_keys_str_mv |
AT shcherbininma shortcylindricalelectronbunchdynamicsandwakefieldsexcitationinplasmawiththeexternalmagneticfield AT anisimovio shortcylindricalelectronbunchdynamicsandwakefieldsexcitationinplasmawiththeexternalmagneticfield |
| first_indexed |
2025-07-08T03:31:22Z |
| last_indexed |
2025-07-08T03:31:22Z |
| _version_ |
1837047987358924800 |
| fulltext |
ISSN 1562-6016. ВАНТ. 2015. №4(98) 124
SHORT CYLINDRICAL ELECTRON BUNCH DYNAMICS
AND WAKE FIELDS` EXCITATION IN PLASMA
WITH THE EXTERNAL MAGNETIC FIELD
M.A. Shcherbinin, I.O. Anisimov
Taras Shevchenko National University of Kyiv Faculty of Radio Physics,
Electronics and Computer Systems, Kiev, Ukraine
E-mail: ioa@univ.kiev.ua
Dynamics of the non-relativistic cylindrical electron bunch injected into the homogeneous plasma along the ex-
ternal magnetic field was studied using computer simulation via PIC method. The initial bunch length was equal to
the wake wave length of the background plasmas. The simulation results are compared with the case without magnet-
ic field. It is shown that strong external magnetic field suppresses the radial bunch defocusing but moves to the fur-
ther longitudinal expansion of the bunch. As a result the area of the wake wave excitation grows substantially. Perio-
dicity of the background plasma current is determined by the excited wake wave.
PACS: 52.25.Xz, 52.35.Fp, 52.40.Mj
INTRODUCTION
The possibility of wake wave excitation in plasma
[1] or dielectric [2] environment is widely discussed.
Electron bunch or sequence of bunches [3, 9], as well as
short powerful laser pulses [4] can be used as an instru-
ment for wake wave excitation. An opportunity to con-
struct a wake wave accelerator of charge particles was
experimentally approved [5]. Another reason to study
the wake wave excitation is the possibility of inhomo-
geneous plasma diagnostics via transition radiation of
charged particles and bunches [6].
The problem is that, after the bunch injection into
plasma, a part of bunches’ electrons do not participate in
the wake wave excitation because of the radial defocus-
ing in the wake field. The strong magnetic field is able
to suppress this defocusing and improve the process of
wake wave excitation. The objective of this paper is
studying the influence of the longitudinal magnetic field
on the dynamics of short cylindrical electron bunch in
homogeneous plasma and dynamics of the background
plasma electrons, using PIC simulation via 2.5 D elec-
tromagnetic code [7].
1. SIMULATION PARAMETERS
Simulation is carried out for the following parame-
ters: length of the cylindrical camera is 1.5 m; it’s radius
is 0.2 m; bunch is injected along it’s axis. Plasma densi-
ty is 5⋅108 cm-2, ion and electron temperatures are 0.2
and 2 eV, respectively. The bunch initial radius is 2 cm;
it’s initial velocity is 3⋅107 m/s; and its duration is 6 ns.
Langmuir frequency of the background plasma is
ωp=12.5⋅108 s-1, magnetic field B=1 mT (electron cyclo-
tron frequency ωc=1.5⋅107 s-1), plasma frequency for
bunch electrons ωb=2.5⋅108 s-1. Parameters of bunch and
plasma were chosen so that the bunch initial length is
approximately equal to the wake wave length in the
background plasma (unlike [8]).
2. DYNAMICS OF ELECTRON BUNCH
While the electron bunch enters plasma, its forefront
excites the wake wave, so the bunch moves in the wake
field [9]. Consequently the bunch is substantially de-
formed during its’ passage through plasma.
Fig. 1 presents the distribution of electron bunch
density in the systems’ half cross section in absence (a)
and in presence (b) of the external magnetic field.
Figs. 2, 3 demonstrate the corresponding distributions of
the velocity components of the bunch electrons.
a
b
Fig. 1. Distribution of the electron bunch density for
B=0 (a) and B=1 mT (b) for various time points
In absence of the external magnetic field one can ob-
serve the substantial longitudinal focusing of the bunch
(see Fig. 1,a, Fig. 2,a). Also almost all the bunch elec-
ISSN 1562-6016. ВАНТ. 2015. №4(98) 125
trons are defocused in the radial direction (see Fig. 2,b).
When the bunch reaches the collector, its' density be-
comes significantly smaller compared to the initial val-
ue (see Fig. 1,a). The length of a bunch is not changed
significantly.
a
b
Fig. 2. Distributions of longitudinal (in the reference
frame axes connected with the bunch) (a), and radial (b)
velocity components of the bunch electrons, B=0
The longitudinal magnetic field suppresses the radial
defocusing of the bunch (see Fig. 1,b). Radial expansion
of the bunch (see Fig. 3,b) moves to the appearance of
the azimuthal component of Lorenz forth and corre-
sponding velocity component (see Fig. 3,c). Azimuthal
velocity of electrons moves to the appearance of Lorenz
force, directing particles towards the system axis.
From the radial velocities` distribution (see Fig. 3,b)
one can see that at the beginning of the bunch motion
different parts of bunch move in the different directions:
away from systems’ axis and towards it. It results in the
different directions of the azimuthal rotation (see
Fig. 3,c). After the bunch focusing the larger part of
bunches’ electrons moves synchronously from the sys-
tem axis and towards it (see Fig. 3,b). At the later stages
the motion becomes similar to the stochastic dynamics.
But the bunch longitudinal focusing is significantly
suppressed due to the magnetic field (see Fig. 1,b) be-
cause the bunch density remains large and Coulomb
repulsion is not decreased significantly during the bunch
motion.
The backward part of the bunch moves in the accel-
erating electric field of the wake wave (see Fig. 3,a) and
forms the density maximum in the middle of the bunch.
The front part of a bunch substantially expands in the
longitudinal direction during the bunch motion, so the
total bunch length approximately doubles compared to
the initial value.
a
b
c
Fig. 3. Distributions of longitudinal (in the reference
frame axes connected with the bunch) (a), radial (b)
and azimuthal (c) velocity components of the bunch
electrons, B=1 mT
ISSN 1562-6016. ВАНТ. 2015. №4(98) 126
From Fig. 3,a one can see that in the late time points
the front part of the bunch remains faster than other
parts: electrons of the bunch front part do not take part
in interaction with wake wave field, and front part is
permanently accelerated due to longitudinal expansion
of the bunch.
One can notice a small tail with the larger density af-
ter the bunch. This tail appears because the bunch length
is not precisely equal to the length of Langmuir wave in
plasma.
a
b
Fig. 4. Time dependence of the deformation index
for B=0 (a) and B=1 mT (b)
Fig. 4 shows the time dependences of the defor-
mation index σ without (a) and with (b) the magnetic
field:
( ) ( )
( )
2
0
0
2
0
0
2 , ,
2 ,
r
r
dz rdr n r t n r t
dz rdrn r t
π
σ
π
∞
−∞
∞
−∞
−
=
∫ ∫
∫ ∫
,
where ( ),n r t and ( )0 ,n r t are the spatial distribution
of the bunch density and the same distribution in the
given bunch current approximation, respectively [10].
Peaks on the curves correspond to maximal focusing of
the bunch. After the lapse of time the graph (see
Fig. 4,a) levels off at the value of 1.0, that means that all
the bunch particles are pulverized far from the axis.
In the presence of magnetic field the first peak on
the graph corresponds to the bunch focusing due to
plasma-beam interaction, and the second peak is a result
of the further radial focusing of the bunch due to the
magnetic field.
3. THE ELECTRIC FIELD OF EXCITED
WAKE WAVE
Figs. 5, 6 show the distributions of radial and longi-
tudinal components of electric field in plasma. Area of
the strong electric field is significantly larger in longitu-
dinal direction for system with presence of longitudinal
magnetic field in comparison with the case without field
[8]. The electric field magnitude of the wake wave be-
comes higher in the presence of magnetic field. The
reason is the higher bunch density at the late time point
in plasma with the external magnetic field (see Fig. 1).
a
b
Fig.5. Spatial distribution of radial (a) and longitudinal
(b) components of electric field for B=0
a
b
Fig. 6. Spatial distribution of radial (a) and longitudinal
(b) components of electric field for B=1 mT
ISSN 1562-6016. ВАНТ. 2015. №4(98) 127
One can see the difference in the shape of the con-
stant phase areas of wake wave in both cases. Thus,
areas of the constant phase of wake wave field is dis-
placed in the direction of bunches motion further from
the systems’ axis. It can be seen that the value of this
displacement changes with the distance from injector.
The wake wave is excited mostly by the densest part of
the bunch. And the shape of this part is changed during
its passage through the system (see Fig. 1,a).
In the presence of magnetic field the slope of the
densest part of the bunch changes its sign during the
motion along the plasma system (see Fig. 1,b). Conse-
quently the slope of the constant phase areas also
changes the sign (Fig. 7).
Presence of the external magnetic field does not af-
fect substantially on the radius of the area filled by the
excited wake wave.
4. CURRENTS IN THE BACKGROUND
PLASMA
Figs. 7, 8 show spatial distributions of radial and
longitudinal components of the current density in the
background plasma. These distributions are determined
by the wake wave field.
a
b
Fig. 7. Spatial distribution of radial (a) and longitudinal
(b) components of the current density in the background
plasma for B=0
Without magnetic field radial and longitudinal cur-
rents are of the same order, but radial current density is
larger (see Fig. 7).
a
b
Fig. 8. Spatial distribution of radial (a) and longitudinal
(b)components of the current density in the background
plasma for B=1 mT
The strong longitudinal magnetic field moves to the
significant increase of the longitudinal current while the
order of the radial current value remains constant. The
azimuthal current density is much smaller relatively to
the other components. Consequently the background
plasma electrons move mainly along the magnetic field.
CONCLUSIONS
1. External longitudinal magnetic field, directed
along the systems’ axis, suppresses the radial defocus-
ing of the bunch but provokes its lengthening.
2. Strong external magnetic field moves to the for-
mation of the second maximum (and probably the next
maxima) on the time dependence of the deformation
index caused by the radial bunch focusing.
3. Strong external magnetic field leads to the contin-
uous acceleration of the bunch forefront by the electric
field of the bunch space charge. Direction of the azi-
muthal velocity of the bunch electrons depends on their
initial radial velocity caused by the wake field.
4. Magnetic field causes the expansion of the wake
field excitation area due to the radial defocusing sup-
pressing. Peculiarities of the wake field structure are
caused by motion of the densest part of the bunch.
ISSN 1562-6016. ВАНТ. 2015. №4(98) 128
5. Structure of the currents in background plasma is
determined by the wake field. Magnetic field results in
the significant increase of the longitudinal component of
the current density.
REFERENCES
1. M.J. Hogan, T.O. Raubenheimer, A. Seryi, P. Muggli,
T. Katsouleas, C. Huang, W. Lu, W. An, K.A. Marsh,
W.B. Mori, C.E. Clayton and C. Joshi. Wake gen-
eration and energy transfer relating to the transport
of intense relativistic particle beams in an under-
dense plasma // New J. Phys. 2010, v. 12, p. 055030.
2. A. Tremaine, J. Rosenzweig, and P. Schoessow.
Electromagnetic wake fields and beam stability in
slab-symmetric dielectric structures // Phys. Rev. E.
1997, v. 56, p. 7204.
3. A. Bazzania, M. Giovannozzic, P. Londrillob,
S. Sinigardia, G. Turchettia. Case studies in space
charge and plasma acceleration of charged beams //
C. R. Mecanique. 2014, v. 342, p. 647.
4. T. Tajima, J.M. Dawson. Laser Electron Accelerator
// Phys. Rev. Lett. 1979, v. 43, p. 267.
5. I. Blumenfeld, C.E. Clayton, F.J. Decker, M.J. Hogan,
C. Huang. Measurement of the Decelerating Wake
in a Plasma Wakefield Accelerator // Nature. 2007,
v. 445, p. 741.
6. I.O. Anisimov, K.I. Lyubich. Plasma-object
diagnostics via resonant transitional radiation from
an electron bunch // J. Plasma Phys. 2001, v. 66,
p. 157.
7. Yu.M. Tolochkevych, T.Eu. Litoshenko, I.O. Anisimov.
2.5D relativistic electromagnetic PIC code for simu-
lation of beam interaction with plasma in axial-
symmetric geometry // Problems of Atomic Science
and Technology. Series “Plasma Electronics and
New Acceleration Methods”. 2010, № 4, р. 47-50.
8. M.A. Shcherbinin, I.O. Anisimov. Influence of the
external magnetic field on the cylindrical electron
bunch injected into plasma // Problems of Atomic
Science and Technology. Series “Plasma Physics”.
2014, № 6, p. 116-119.
9. T. Katsouleas. Physical mechanisms in the plasma
wake-field accelerator // Physical Review A, March
1986, v. 3, № 3, p. 2056-2065.
10. I.O. Anisimov, Yu.M. Tolochkevich. Dynamics of
One-dimensional Electron Bunch with the Initially
Rectangular Density Profile Injected Into Homoge-
neous Plasma // Ukrainian Journal of Physics. 2009,
v. 54, № 5, p. 454-460.
Article received 30.04.2015
ДИНАМИКА КОРОТКОГО ЦИЛИНДРИЧЕСКОГО ЭЛЕКТРОННОГО СГУСТКА
И ВОЗБУЖДЕНИЕ КИЛЬВАТЕРНЫХ ВОЛН В ПЛАЗМЕ В ПРИСУТСТВИИ ВНЕШНЕГО
МАГНИТНОГО ПОЛЯ
Н.А. Щербинин, И.А. Анисимов
Представлены результаты исследования динамики нерелятивистского электронного сгустка, инжектиро-
ванного в однородную плазму при воздействии внешнего магнитного поля, с помощью компьютерного мо-
делирования методом частиц в ячейках. Начальная длина сгустка равна длине кильватерной волны в фоно-
вой плазме. Результаты моделирований сравниваются с соответствующими результатами без магнитного
поля. Показано, что сильное магнитное поле подавляет радиальную дефокусировку сгустка, но приводит к
его быстрому расширению в продольном направлении. В результате область возбуждения кильватерной
волны существенно возрастает. Наблюдается периодичность в пространственном распределении токов фо-
новой плазмы, обусловленная структурой кильватерной волны.
ДИНАМІКА КОРОТКОГО ЦИЛІНДРИЧНОГО ЕЛЕКТРОННОГО ЗГУСТКА ТА ЗБУДЖЕННЯ
КІЛЬВАТЕРНИХ ХВИЛЬ У ПЛАЗМІ ПРИ ЗОВНІШНЬОМУ МАГНІТНОМУ ПОЛІ
М.А. Щербінін, І.О. Анісімов
Досліджена динаміка нерелятивістського циліндричного електронного згустку, інжектованого в однорі-
дну плазму вздовж силових ліній зовнішнього магнітного поля, за допомогою комп’ютерного моделювання
методом крупних частинок. Початкова довжина згусткa дорівнює довжині кільватерної хвилі у фоновій
плазмі. Результати моделювань порівнюються з відповідними результатами за відсутності магнітного поля.
Показано, що сильне зовнішнє магнітне поля пригнічує радіальне дефокусування згусткa, але призводить до
інтенсивнішого розширення згусткa в поздовжньому напрямку. У результаті область збудження кільватер-
ної хвилі суттєво зростає. Спостерігається періодичність у просторовому розподілі струмів фонової плазми,
що визначається структурою кільватерної хвилі.
http://www.seas.ucla.edu/plasma/journals_files/files/conference%20proceedings/2004_Blue.pdf
http://www.seas.ucla.edu/plasma/journals_files/files/conference%20proceedings/2004_Blue.pdf
http://www.seas.ucla.edu/plasma/journals_files/files/conference%20proceedings/2004_Blue.pdf
http://www.seas.ucla.edu/plasma/journals_files/files/conference%20proceedings/2004_Blue.pdf
Introduction
|