Dynamics and capture of space-charge dominated electron beams in crossed-fields system
Problems of nonlinear dynamics of space-charge dominated electron beams in crossed ExB-fields are discussed from the point of view of the investigation of schemes of intense electron beam formation for compact cyclic accelerators and for high-efficiency relativistic magnetrons. The review of th...
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| Дата: | 1999 |
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| Формат: | Стаття |
| Мова: | English |
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Національний науковий центр «Харківський фізико-технічний інститут» НАН України
1999
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| Назва видання: | Вопросы атомной науки и техники |
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| Цитувати: | Dynamics and capture of space-charge dominated electron beams in crossed-fields system / A.V. Agafonov // Вопросы атомной науки и техники. — 1999. — № 4. — С. 13-15. — Бібліогр.: 8 назв. — англ. |
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irk-123456789-815142015-05-18T03:02:31Z Dynamics and capture of space-charge dominated electron beams in crossed-fields system Agafonov, A.V. Problems of nonlinear dynamics of space-charge dominated electron beams in crossed ExB-fields are discussed from the point of view of the investigation of schemes of intense electron beam formation for compact cyclic accelerators and for high-efficiency relativistic magnetrons. The review of the results of computer simulations of an electron clouds formation due to nonlinear azimuthal instability inside magnetron is given. A scheme of electron storage and capture of electron beams in crossed fields is proposed. 1999 Article Dynamics and capture of space-charge dominated electron beams in crossed-fields system / A.V. Agafonov // Вопросы атомной науки и техники. — 1999. — № 4. — С. 13-15. — Бібліогр.: 8 назв. — англ. 1562-6016 http://dspace.nbuv.gov.ua/handle/123456789/81514 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 |
| description |
Problems of nonlinear dynamics of space-charge
dominated electron beams in crossed ExB-fields are
discussed from the point of view of the investigation of
schemes of intense electron beam formation for
compact cyclic accelerators and for high-efficiency
relativistic magnetrons. The review of the results of
computer simulations of an electron clouds formation
due to nonlinear azimuthal instability inside magnetron
is given. A scheme of electron storage and capture of
electron beams in crossed fields is proposed. |
| format |
Article |
| author |
Agafonov, A.V. |
| spellingShingle |
Agafonov, A.V. Dynamics and capture of space-charge dominated electron beams in crossed-fields system Вопросы атомной науки и техники |
| author_facet |
Agafonov, A.V. |
| author_sort |
Agafonov, A.V. |
| title |
Dynamics and capture of space-charge dominated electron beams in crossed-fields system |
| title_short |
Dynamics and capture of space-charge dominated electron beams in crossed-fields system |
| title_full |
Dynamics and capture of space-charge dominated electron beams in crossed-fields system |
| title_fullStr |
Dynamics and capture of space-charge dominated electron beams in crossed-fields system |
| title_full_unstemmed |
Dynamics and capture of space-charge dominated electron beams in crossed-fields system |
| title_sort |
dynamics and capture of space-charge dominated electron beams in crossed-fields system |
| publisher |
Національний науковий центр «Харківський фізико-технічний інститут» НАН України |
| publishDate |
1999 |
| url |
http://dspace.nbuv.gov.ua/handle/123456789/81514 |
| citation_txt |
Dynamics and capture of space-charge dominated electron beams in crossed-fields system / A.V. Agafonov // Вопросы атомной науки и техники. — 1999. — № 4. — С. 13-15. — Бібліогр.: 8 назв. — англ. |
| series |
Вопросы атомной науки и техники |
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AT agafonovav dynamicsandcaptureofspacechargedominatedelectronbeamsincrossedfieldssystem |
| first_indexed |
2025-07-06T06:30:27Z |
| last_indexed |
2025-07-06T06:30:27Z |
| _version_ |
1836878066240978944 |
| fulltext |
DYNAMICS AND CAPTURE OF SPACE-CHARGE DOMINATED
ELECTRON BEAMS IN CROSSED-FIELDS SYSTEM*
A.V.Agafonov
Lebedev Physical Institute of RAS, Moscow, Russia
INTRODUCTION
Theoretical and experimental investigations of
the dynamics of space-charge dominated rectilinear
beams considered as a new physic subject, are receiving
more and more attention in recent years. At the same
time, a similar but more complex subject, space charge
dominated beams in crossed ExB-fields, finds practical
applications and has been investigated over a long
period of time but without notable success in theory.
Suffice it to note that there does not yet exact a clear
theoretical description ever of the pre-generation
operation of a classical (low-voltage) magnetron or the
regime of magnetic insulation disturbance in high-
current coaxial diodes. The physics of instruments with
crossed fields is complex due to the strong nonlinearity
of the processes and the necessity to take into account
nonstationary effects.
PHYSICAL PROCESSES IN DEVICES WITH
CROSSED FIELDS
The physical characteristics of the processes
under consideration are partially presented in works [1
-- 7]. Usually, to describe electron flow in so-called
magnetron diodes (MD), one uses stationary models of
Brillouin flow, in which it is not possible to describe the
escape of particles from an emitting surface, or kinetic
dual-velocity flow, in which it is possible [1]. For
system in which extraction of the electron beam in the
axial direction is absent, the applicability of such
analytical models is complicated by the influence of the
pre-history of flow formation. In particular, we can
immediately note that for such systems the increase of
voltage on the MD should lead to capture of some of
the emitted particles in acceleration gap which circulate
around the cathode without returning to it. Hence, the
value of the radial electric field on the cathode surface
depends not only on emission current but also on the
magnitude of accumulated circulating charge in the
acceleration gap.
Dividing the flow into two components, namely,
one circulating during many turns and maintaining
information on possible nonuniformities, and the other
emitting from the cathode and retuning to the cathode
during a time of the order of a period of cyclotron
rotation, leads to conditions arising for the development
of azimuthal instability of the flow. However, without
the provision of a number of additional conditions, this
instability causes only weak azimuthal modulation of
the flow and is not accompanied by the development of
leakage current at the anode across an external
magnetic field exceeding the threshold value for
magnetic insulation.
Strong azimuthal modulation of flow
accompanied by the development of leakage current at
the anode, i.e., passing over of azimuthal instability to a
strongly nonlinear regime in which an exchange of
energy and momentum occurs between particles and the
rotating self-consistent crossed E×B-field, can occur in
two cases. First, if emission current is not too large and
information about the developing structural flow is not
carried to the cathode by the returning flow of
electrons. Second, if feedback exists on the emitting
surface of the cathode providing proper phasing of
emitted particles that increases the degree of azimuthal
variation of flow and, accordingly, discards part of the
emitted particles not in proper phase.
Instability is saturated at a level of leakage
currents at the anode, which can amount to several
percent of ICL (Child-Langmuir current). Then, electron
flow constitutes a self-organizing, regular (in the
azimuthal direction), rotating structure of dense electron
bunches. Such a structure rotates with approximately
the same angular velocity and exists for a long time.
Dynamic equilibrium is established between the current
of emitted particles and return current to the cathode
and current to the anode. The special feature of this
dynamic equilibrium is the long presence of emitted
particles in the acceleration gap, which considerably
exceeds the period of cyclotron rotation [1 − 4].
Feedback on the emitting surface, promoting the
development of strong azimuthal instability, is
particularly effective when using a cathode with
secondary emission of electrons. The sharp nonuniform
character of secondary emission, depending in turn on
flow structure, leads to the formation of alternating
radial electric field at a given cathode azimuth due to
rotation of the modulated flow as a whole. The average
radial electric field at the cathode can be close to zero.
At the same time, the emission of particles in improper
phases is simply suppressed by the negative value of the
field, and the emission of particles in proper phases is
sharply increased due to boundary effects [5, 6]. The
type of operation of a MD with a secondary-emission
cathode depends on the maximal voltage and rate of
voltage rise on the gap. For low voltages, characteristic
for classical magnetrons, a regular azimuthal structure
of flow arises on the flat top of a pulse and is
maintained over a long period of time.
For higher voltages (above approximately
100 kV), the regular structure is formed on the long
leading edge of the voltage, and when passing over to
the flat top there begins a debunching of the original
structure and formation of a new one, with a different
number of azimuthal variations, if the voltage does not
exceeds a certain maximal value. Exceeding this
maximum in the process of rising voltage results in
disruption of the self-maintenance regime of secondary
emission. The physical feature of such a regime is that,
at high voltage and accumulation of a large space
charge in dense bunches, the energy spectrum of
electrons returning to the cathode is significantly shifted
ВОПРОСЫ АТОМНОЙ НАУКИ И ТЕХНИКИ. 1999. № 4.
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in the direction of larger energies and exceeds that is
optimal for maximal yield of secondary electrons.
Practically, such systems represent a new class
of flows with a variable number of particles. The
growth of azimuthal instability in such a system is
possible only under conditions when accumulated
information in the flow is no carried to the electrodes.
In particular, for uniform emission of a primary beam
with current comparable with the current of secondary
emission, instability develops weakly.
A demonstrative example is the development of
instability in pure primary beam emitting uniformly in
azimuth. The results of computer simulations show that
in a regime of current limited by space charge,
azimuthal instability does not develop at all. However,
it does become strong and accompanied by significant
leakage current if it turns out that the cathode is
operating in a regime of saturation. Then, the normal
component of the electric field at the cathode differs
from zero and the development of weak azimuthal
instability increases as in the case of nonuniform
secondary emission due to proper phasing of emitted
particles. The difference will respect to the case of
nonuniform secondary emission is only that the radial
electric field at the cathode surface is not alternating,
i.e., there is no direct suppression of emission from the
cathode. However, large oscillation of field due to
azimuthal bunching of beam promotes bunching of
some of the electrons with proper phases relative to the
rotating E×B-field, which are in the gap for a long time.
It also promotes the return of electrons in improper
phases (and, accordingly, not matched with the field)
back to the cathode in significantly less time. In the
case of uniform space charge limited emission,
information about the development of weak instability
comes to the cathode by returning particles. The density
of those close to the cathode is high and only a small
number of them can exist in the flow for a long time.
CAPTURE AND ACCUMULATION
OF BEAM IN CROSSED FIELDS
The conditions for possible interruption of
secondary emission current for the aforementioned
reasons or, for example, by increasing the external
voltage, which is accompanied also by the initial
discarding of a part of the flow and its subsequent
detachment from the cathode, require special attention.
This is because they permit to realize a process of
accumulation and capture of electron beam in crossed
fields which circulates so that electrons cannot return to
the cathode nor reach the anode.
The number of particles in a captured circulating
beam can be sufficiently large for possible subsequent
acceleration, including with high-frequency cycles, for
example, in betatron-type systems. Such systems can
also be used as injectors for classic accelerators.
Below, the example is given which illustrate the
possibility of accumulating an electron flow having a
number of particles at the level of 1012 per centimeter of
length axially in a compact system with crossed fields.
In this case, the lateral dimensions are several
centimeters, the voltage is at the level of 100 − 200 kV
and the external magnetic field is about of 3 kG.
Computer simulations were performed using
electromagnetic PIC-code KARAT [8] in two-
dimensional r - θ-geometry. Examples of calculations
demonstrating physical features of processes in 2D and
3D-geometries are presented in an accompanying report
[7]. For subsequent acceleration of captured flow, one
can use a betatron field and cut electrodes that do not
hinder the formation of electron flow nor the
penetration of an external longitudinal magnetic field.
The main idea consists in the following. After
formation in a MD of electron flow with regular
structure, total charge in the system still remains less
than the limiting value and can be increased by raising
the voltage on the MD. Growth of voltage leads to re-
bunching of flow and change of azimuthal structure due
to feedback disruption. During this process, azimuthal
modulation of flow disappears and the flow becomes
close to uniform in azimuth. Significant momentum
spread of particles has a stabilizing effect on the
existence of such a flow. A further increase in voltage
results in the detachment of the flow from the cathode.
The return bombardment of the cathode ceases,
secondary emission current disappears, and leakage
current at the anode is practically absent, i.e., there
forms between the electrodes of the MD a captured
circulating flow. Fig. 1 shows azimuthal structures of
flows at different instants.
Fig. 1: Configurations of flow at t = 8 ns and t = 20 ns.
ВОПРОСЫ АТОМНОЙ НАУКИ И ТЕХНИКИ. 1999. № 4.
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Fig. 2: Averaged densities at t = 8 ns and t = 20 ns
The distribution of density along the radius,
averaged over the azimuth, is presented in Fig. 2 for
these two instants. The dynamics of accumulation of
particles and voltage profile are shown in Fig. 3.
Fig. 3: Dynamics of accumulations of secondary
electrons and the form of the voltage.
CONCLUSION
Problems of nonlinear dynamics of space-charge
dominated electron beams in crossed ExB-fields are
discussed from the point of view of the investigation of
schemes of intense electron beam formation for
compact cyclic accelerators and for high-efficiency
relativistic magnetrons. The review of the results of
computer simulations of an electron clouds formation
due to nonlinear azimuthal instability inside magnetron
is given. A scheme of electron storage and capture of
electron beams in crossed fields is proposed.
REFERENCES
1. Agafonov A.V., Voronin V.S. Proc. of 1997 Particle
Accelerator Conf., Vancouver, Canada. 1997, v. 2,
1302 − 1304.
2. Agafonov A.V., Fedorov V.M., Tarakanov V.P.
Ibid., v. 2, 1299 − 1301.
3. Agafonov A.V., Krastelev E.G. Ibid., v. 3, 3141 −
3143.
4. Agafonov A.V., Fedorov V.M., Tarakanov V.P. Proc.
of the 15th Intern. Conf. on Linear Accelerators,
Ukraina, Alushta, 1997, v. 1, 137 − 139.
5. Agafonov A.V., Fedorov V.M., Tarakanov V.P. Proc.
of 12th International Conference on High-Power
Particle Beams, Haifa, Israel, 1998.
6. Agafonov A.V., Lebedev A.N., Voronin V.S. Proc.
of the 1995 Particle Accelerator Conf., Dallas,
USA. 1995, v. 5, 3269 − 3271.
7. Agafonov A.V., Fedorov V.M., Tarakanov V.P.//
Problems of Atomic Science and Techn. 1999. v.
4. Issue: Nuclear Physics Researches. (35), P. .
8. Kotetashwily P.V., Rybak P.V., Tarakanov P.V.
Institute of General Physics, Moscow, Preprint
N 44, 1991.
ВОПРОСЫ АТОМНОЙ НАУКИ И ТЕХНИКИ. 1999. № 4.
Серия: Ядерно-физические исследования (35), с. 13-15.
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