PIC simulation of low-frequency modulation of supercritical electron beam at plasma assstancei
The results of simulations of virtual cathode dynamics at the presence of plasma are presented. The theoretical analysis of dynamics of the electron-ion formation is based on particle-in-cell method (PIC). Numerical calculations are carried out for the modernized experimental installation "Agat...
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Національний науковий центр «Харківський фізико-технічний інститут» НАН України
2005
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| Cite this: | PIC simulation of low-frequency modulation of supercritical electron beam at plasma assstancei / P.I. Markov, I.N. Onishchenko, G.V. Sotnikov // Вопросы атомной науки и техники. — 2005. — № 1. — С. 131-133. — Бібліогр.: 7 назв. — англ. |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1860074596478222336 |
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| author | Markov, P.I. Onishchenko, I.N. Sotnikov, G.V. |
| author_facet | Markov, P.I. Onishchenko, I.N. Sotnikov, G.V. |
| citation_txt | PIC simulation of low-frequency modulation of supercritical electron beam at plasma assstancei / P.I. Markov, I.N. Onishchenko, G.V. Sotnikov // Вопросы атомной науки и техники. — 2005. — № 1. — С. 131-133. — Бібліогр.: 7 назв. — англ. |
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| container_title | Вопросы атомной науки и техники |
| description | The results of simulations of virtual cathode dynamics at the presence of plasma are presented. The theoretical analysis of dynamics of the electron-ion formation is based on particle-in-cell method (PIC). Numerical calculations are carried out for the modernized experimental installation "Agate" with intense relativistic electron beam. It is shown that an output electron beam current has a strong temporal modulation. The modulating frequency at injection of hydrogen ions is about 300 MHz.
Представлено результати розробки чисельного 2,5-мірного електромагнітного коду для моделювання динаміки віртуального катода в присутності плазми. Чисельний код заснований на методі великих часток. Виконано тестування чисельного коду на задачі поширювання надкритичного електронного пучка в кінцевому магнітному полі для параметрів експериментальної установки Агат [4, 5]. Показано, що вихідний струм електронного пучка сильно промодульовано у часі. Частота модуляції при інжекції іонів водню складає приблизно 300 Мгц.
Представлены результаты разработки численного 2,5-мерного электромагнитного кода для моделирования динамики виртуального катода в присутствии плазмы. Численный код основан на методе крупных частиц. Выполнено тестирование численного кода на задаче распространения сверхкритического электронного пучка в конечном магнитном поле для параметров экспериментальной установки Агат [4, 5]. Показано, что выходной ток электронного пучка сильно промодулирован во времени. Частота модуляции при инжекции ионов водорода составляет примерно 300 МГц.
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PIC SIMULATION OF LOW-FREQUENCY MODULATION OF SUPER
CRITICAL ELECTRON BEAM AT PLASMA ASSISTANCE
P.I. Markov, I.N. Onishchenko, G.V. Sotnikov
NSC “Kharkov Institute of Physics and Technology”, Akademicheskaya Str.1,
61108, Kharkov, Ukraine, phone: (0572)356623, e-mail: sotnikov@kipt.kharkov.ua
The results of simulations of virtual cathode dynamics at the presence of plasma are presented. The theoretical anal
ysis of dynamics of the electron-ion formation is based on particle-in-cell method (PIC). Numerical calculations are car
ried out for the modernized experimental installation "Agate" with intense relativistic electron beam. It is shown that an
output electron beam current has a strong temporal modulation. The modulating frequency at injection of hydrogen ions
is about 300 MHz.
PACS: 02.60.Cb, 07.05.Tp
1. INTRODUCTION
Basis of a method of collective acceleration of ions is
the slow wave of a spatial charge formed by high-current
electron beam as a result of its spatial and time modula
tion. Methods of spatial [1, 2] and time [1, 3] modulations
are well-known. At use of beams with current higher than
limiting vacuum one the opportunity of time modulation
by the virtual cathode field at plasma presence opens [4].
The virtual cathode behavior at the presence of plasma
in the strong magnetic field approximation (one-dimen
sional model) in the cylindrical resonator has been inves
tigate by us earlier [5]. The numerical calculations which
have been carried out for ions of hydrogen and nitrogen,
have shown, that an electron beam current an output of
the resonator is modulated with low frequency. At injec
tion of hydrogen ions this frequency is 300~MHz and at
injection of ions of nitrogen it is 100~MHz. The reason of
modulation is the formation of a virtual anode on an input
of the resonator. Pulsations of a virtual anode result in
modulation of input and output electron beam currents.
Serious assumption at this simulation was the guess of
the one-dimensional electrons and ions motion. Though at
the presence of an electron beam effect of an ion stream
space charge on its transversal dynamics is strongly atten
uated, the account non-one-dimensionality motions of
electrons and ions can qualitatively and quantitatively
change the physical processes happening in a virtual cath
ode at low-energy ions presence.
With the purpose of more precise description and in
terpretation of results of experimental researches we de
signed a 2.5-dimensional electromagnetic code. Results of
the numerical calculations which have been carried out
with the help of a 2.5-dimensional electromagnetic code,
virtual cathode featuring self-consistent dynamics in plas
ma in the cylindrical drift chamber are given below.
2. A STATEMENT OF PROBLEM
The algorithm of numerical model is based on a PIC
method [7]. The geometry of calculated system is depict
ed on Fig. 1. A statement of problem is following.
The relativistic electronic beam having ring cross-sec
tion, is injected through the left end (1) of drift cham
ber (2). The right end (3) of drift chamber can be both
opened (emitter), and closed (resonator). The beam width
is ∆ = −2 1r r , where 1r and 2r are interior and exterior ra
diuses of the beam. The beam current is bI . At the input
end of the drift chamber (at 0z = ) the beam is monoener
getic, transversal components of electron velocities are
equal to zero. In the drift space there is an exterior mag
netic field with a finite value 0H of its intensity, directed
along the longitudinal z axis of the drift chamber.
Fig. 1. Geometry of calculated system
3. RESULTS OF NUMERICAL SIMULATION
The algorithm described above has been implemented
as a complex of C ++ programs. For numerical calcula
tions we take the parameters of experimental installation
"Agat" [4, 5]: radius of the drift chamber is 2.5cmR = ,
inner and outer beam radiuses are 1 1.5cmr = and
2 1.7cmr = , respectively, electron beam energy is
280keVbeU = , intensity of an external magnetic field is
0 8kOeH = . For simulation we choose a drift chamber
length 7.5cmL = . The left-hand (input) end of the drift
chamber is closed by a metal (conductive) grid, transpar
ent for particles. The right end is opened in a free space.
For the specified transverse sizes of the drift chamber and
an electron beam energy the limiting vacuum current [6]
is 3.76 kA.
For plasma simulating a low-energy hydrogen ions
( )28keVbeU = were injected in a system. The ion cur
rent ( )92 AiI = has been taken from a reason that the un
perturbed electron and ion densities were approximately
equal. The initial cross sizes of an ion stream and electron
beam has been chosen equal.
Problems of Atomic Science and Technology. 2005. № 1. Series: Plasma Physics (10). P. 131-133 131
mailto:sotnikov@kipt.kharkov.ua
At injection of the ion stream in a vacuum cylindrical
waveguide its transported current as well as an electron
beam one, is limited by value [8]:
( ) 3 22 32
2
1 1
2 2
2 2 1 2
1
1 2 ln 2 ln
i
ci
M cI
e r rR
r r r r
γ −
=
+ +
−
,
where ( )21i ieU M cγ = + and M is an ion mass.
For hydrogen ions flow the space charge limiting cur
rent is 3.12 AciI = .
Dynamics of processes at joint injection of an electron
beam and a hydrogen ion stream occurs under the follow
ing plan. For times about 1.67 ns on a distance of around
1.4ч1.6 cm from the left-hand end of the drift chamber
the VC is forming. In spite of the fact that the number of
ions in system at this time point is small and vircator pa
rameters are practically completely determined by elec
trons, VC position is shifted deeper into the drift chamber
in comparison with a case when the ion stream in the drift
chamber is absent.
Hydrogen ions are accelerated in longitudinal electric
field of VC and, having arriving at VC, take essential ef
fect on its dynamics. At this time the ions number in the
region from an input in the drift chamber up to the VC is
already enough great also they are partly compensate an
electrons space charge. As a result the VC position starts
to move deep into the drift chamber, and the input elec
tron beam current grows.
Such coordinated motion of ion stream forward front
and VC position is prolonged down to VC arriving at out
put end of the drift chamber. At VC motion at some time
moments reflected electrons are completely disappear. At
these instants an output electron current is equal to an in
jected current. However, the bunch of electrons, having
small longitudinal velocity, does not destroy completely.
VC motion leads to prolonging of hydrogen ions ener
gy increasing. The highest possible hydrogen ions energy
observed in numerical experiment at output end of the
drift chamber approximately in 2.5 times exceed initial
electrons energy.
When VC reaches the right end of the drift chamber
an output electron beam current sharply increases.
Simultaneously with the process of VC motion deep
into drift chamber and ions acceleration on its front there
is also a process of electromagnetic wave excitation by
high-current REB described above at the analysis of VC
dynamics at ions absence. An excited wave modulates an
electron beam and destroys its laminar flow.
On Fig. 2 plots of currents of electron and ion beams
currents are given. Minimums on curves of input and out
put electron currents correspond to complete destruction
of the laminar electron beam propagation. At this instant
there is enough considerable current on a wall of the drift
chamber (a curve 3). As against to only electronic system,
at an ion stream presence, the modulation of an output
current becomes much deeper. It is concerned with deeper
modulation of an input current owing to ions presence. At
the time moments, relevant to a laminar flow, the maxi
mum transferred current is higher, and at the time points
of complete destruction of a laminar flow the minimum
transferred current is lower, since reflected back electrons
are broken much more weaker and the reverse electron
current is higher.
It is necessary to note, that the mechanism of low-fre
quency modulation described in [5], connected with virtu
al anode oscillations is also present at given numerical
simulation. But, firstly, it has not time to affect at the car
ried out estimated times and, secondly, the depth of mod
ulation caused by virtual anode oscillations is much low
er, than the modulation of an electron current caused by
transverse electron beam motion.
4. CONCLUSION
Additional injection of hydrogen ions into the waveg
uide where for an electron beam the condition of super
criticality is holding, leads to gradual shift of a virtual
cathode position deep into drift chamber. This process is
continues until the virtual cathode is expels out from the
simulated system. During all this time hydrogen ions are
accelerated at the virtual cathode front and their peak en
ergy exceeds initial energy of an electron beam approxi
mately in 2,5 times. Further the virtual cathode moving
deep into of the drift chamber is recommenced in the sys
tem. Thus, process of a virtual cathode origination and its
motion along the drift chamber is periodically iterated. At
the same time with this process there is the periodic mod
ulation of an electron beam by excited electromagnetic
wave. Both specified mechanisms leads to strong time
modulation of an output electron beam current. The mod
ulating frequency at injection of hydrogen ions is about
300 MHz.
This work is supported by the STCU grant № 1569.
REFERENCES
[1] A.G. Lymar' , N.A. Khizhnyak, V.V. Belikov//
VANT. Ser: Fizika Vysokih Energij I Atomnogo
Jadra. 1973, No. 3(5), p. 78–81.
[2] Yu.V. Tkach, Ya.B. Fainberg, E.A. Lemberg // Pisma
v ZhETF (28). 1978, No 9, p. 580-584 (in Rusian).
132
Fig. 2. Plots of electron and ion beams currents of in a
time dependence: 1) — an input current; 2) — an out
put current; 3) — a current on a drift chamber wall;
4) — an input ion current; 5) — an output ion current;
6) — the limiting vacuum electron current
[3] A.N. Lebedev, K.N. Pazin// Atomnaja Energija (41).
1976, No. 4, p. 244.
[4] V.A. Balakirev, A.M. Gorban', I.I. Magda et. al.//
Fizika plazmy (23). 1997, No 4, p. 350–354 (in Ru
sian).
[5] P.I. Markov, I.N. Onishchenko, G.V. Sotnikov
// Problems of Atomic Science and Technology. Se
ries: Plasma Physics. (9), 2003, No 1, p. 111-114.
[6] R.B. Miller. An Introduction to the Intense Charged
Particle Beams. NewYork: Plenum Press, 1982.
[7] Yu.A. Berezin, V.A. Vshyvkov. Metod chastits v di
namike razregennoj plazmy. Novosibirsk: Nauka,
1980, p. 98.
МОДЕЛИРОВАНИЕ МЕТОДОМ КРУПНЫХ ЧАСТИЦ НИЗКОЧАСТОТНОЙ МОДУЛЯЦИИ
СВЕХКРИТИЧЕСКОГО ЭЛЕКТРОННОГО ПУЧКА В ПРИСУТСТВИИ ПЛАЗМЫ
П.И. Марков , И.Н. Онищенко, Г.В. Сотников
Представлены результаты разработки численного 2,5-мерного электромагнитного кода для моделирования
динамики виртуального катода в присутствии плазмы. Численный код основан на методе крупных частиц. Вы
полнено тестирование численного кода на задаче распространения сверхкритического электронного пучка в ко
нечном магнитном поле для параметров экспериментальной установки Агат [4, 5]. Показано, что выходной ток
электронного пучка сильно промодулирован во времени. Частота модуляции при инжекции ионов водорода со
ставляет примерно 300 МГц.
МОДЕЛЮВАННЯ ЗА ДОПОМОГОЮ МЕТОДУ ВЕЛИКИХ ЧАСТОК НИЗЬКОЧАСТОТНОЇ
МОДУЛЯЦІЇ СИЛЬНОСТРУМОВОГО РЕЛЯТИВІСТСЬКОГО ЕЛЕКТРОННОГО ПУЧКА В
ПРИСУТНОСТІ ПЛАЗМИ
П.І. Марков , І.М. Онищенко, Г.В. Сотников
Представлено результати розробки чисельного 2,5-мірного електромагнітного коду для моделювання ди
наміки віртуального катода в присутності плазми. Чисельний код заснований на методі великих часток. Ви
конано тестування чисельного коду на задачі поширювання надкритичного електронного пучка в кінцевому
магнітному полі для параметрів експериментальної установки Агат [4, 5]. Показано, що вихідний струм
електронного пучка сильно промодульовано у часі. Частота модуляції при інжекції іонів водню складає при
близно 300 Мгц.
|
| id | nasplib_isofts_kiev_ua-123456789-78895 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1562-6016 |
| language | English |
| last_indexed | 2025-12-07T17:12:38Z |
| publishDate | 2005 |
| publisher | Національний науковий центр «Харківський фізико-технічний інститут» НАН України |
| record_format | dspace |
| spelling | Markov, P.I. Onishchenko, I.N. Sotnikov, G.V. 2015-03-22T10:36:52Z 2015-03-22T10:36:52Z 2005 PIC simulation of low-frequency modulation of supercritical electron beam at plasma assstancei / P.I. Markov, I.N. Onishchenko, G.V. Sotnikov // Вопросы атомной науки и техники. — 2005. — № 1. — С. 131-133. — Бібліогр.: 7 назв. — англ. 1562-6016 PACS: 02.60.Cb, 07.05.Tp https://nasplib.isofts.kiev.ua/handle/123456789/78895 The results of simulations of virtual cathode dynamics at the presence of plasma are presented. The theoretical analysis of dynamics of the electron-ion formation is based on particle-in-cell method (PIC). Numerical calculations are carried out for the modernized experimental installation "Agate" with intense relativistic electron beam. It is shown that an output electron beam current has a strong temporal modulation. The modulating frequency at injection of hydrogen ions is about 300 MHz. Представлено результати розробки чисельного 2,5-мірного електромагнітного коду для моделювання динаміки віртуального катода в присутності плазми. Чисельний код заснований на методі великих часток. Виконано тестування чисельного коду на задачі поширювання надкритичного електронного пучка в кінцевому магнітному полі для параметрів експериментальної установки Агат [4, 5]. Показано, що вихідний струм електронного пучка сильно промодульовано у часі. Частота модуляції при інжекції іонів водню складає приблизно 300 Мгц. Представлены результаты разработки численного 2,5-мерного электромагнитного кода для моделирования динамики виртуального катода в присутствии плазмы. Численный код основан на методе крупных частиц. Выполнено тестирование численного кода на задаче распространения сверхкритического электронного пучка в конечном магнитном поле для параметров экспериментальной установки Агат [4, 5]. Показано, что выходной ток электронного пучка сильно промодулирован во времени. Частота модуляции при инжекции ионов водорода составляет примерно 300 МГц. This work is supported by the STCU grant № 1569. en Національний науковий центр «Харківський фізико-технічний інститут» НАН України Вопросы атомной науки и техники Plasma electronics PIC simulation of low-frequency modulation of supercritical electron beam at plasma assstancei Моделювання за допомогою методу великих часток низькочастотної модуляції сильнострумового релятивістського електронного пучка в присутності плазми Моделирование методом крупных частиц низкочастотной модуляции свехкритического электронного пучка в присутствии плазмы Article published earlier |
| spellingShingle | PIC simulation of low-frequency modulation of supercritical electron beam at plasma assstancei Markov, P.I. Onishchenko, I.N. Sotnikov, G.V. Plasma electronics |
| title | PIC simulation of low-frequency modulation of supercritical electron beam at plasma assstancei |
| title_alt | Моделювання за допомогою методу великих часток низькочастотної модуляції сильнострумового релятивістського електронного пучка в присутності плазми Моделирование методом крупных частиц низкочастотной модуляции свехкритического электронного пучка в присутствии плазмы |
| title_full | PIC simulation of low-frequency modulation of supercritical electron beam at plasma assstancei |
| title_fullStr | PIC simulation of low-frequency modulation of supercritical electron beam at plasma assstancei |
| title_full_unstemmed | PIC simulation of low-frequency modulation of supercritical electron beam at plasma assstancei |
| title_short | PIC simulation of low-frequency modulation of supercritical electron beam at plasma assstancei |
| title_sort | pic simulation of low-frequency modulation of supercritical electron beam at plasma assstancei |
| topic | Plasma electronics |
| topic_facet | Plasma electronics |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/78895 |
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