Selforganisation and dynamics peculiarities of intense electron beams in compact crossed fields systems
The review of the results of computer simulations of electron flow self-organisation inside magnetically isolated coaxial diodes (magnetron gun) is given. Magnetron guns of usual and inverted polarities are considered.
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irk-123456789-790082015-03-25T03:02:40Z Selforganisation and dynamics peculiarities of intense electron beams in compact crossed fields systems Agafonov, A.V. Tarakanov, V.P. Fedorov, V.M. The review of the results of computer simulations of electron flow self-organisation inside magnetically isolated coaxial diodes (magnetron gun) is given. Magnetron guns of usual and inverted polarities are considered. 2001 Article Selforganisation and dynamics peculiarities of intense electron beams in compact crossed fields systems / A.V. Agafonov, V.P. Tarakanov, V.M. Fedorov // Вопросы атомной науки и техники. — 2001. — № 5. — С. 160-162. — Бібліогр.: 6 назв. — англ. 1562-6016 PACS number: 29.17.+w http://dspace.nbuv.gov.ua/handle/123456789/79008 en Вопросы атомной науки и техники Національний науковий центр «Харківський фізико-технічний інститут» НАН України |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine |
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The review of the results of computer simulations of electron flow self-organisation inside magnetically isolated coaxial diodes (magnetron gun) is given. Magnetron guns of usual and inverted polarities are considered. |
| format |
Article |
| author |
Agafonov, A.V. Tarakanov, V.P. Fedorov, V.M. |
| spellingShingle |
Agafonov, A.V. Tarakanov, V.P. Fedorov, V.M. Selforganisation and dynamics peculiarities of intense electron beams in compact crossed fields systems Вопросы атомной науки и техники |
| author_facet |
Agafonov, A.V. Tarakanov, V.P. Fedorov, V.M. |
| author_sort |
Agafonov, A.V. |
| title |
Selforganisation and dynamics peculiarities of intense electron beams in compact crossed fields systems |
| title_short |
Selforganisation and dynamics peculiarities of intense electron beams in compact crossed fields systems |
| title_full |
Selforganisation and dynamics peculiarities of intense electron beams in compact crossed fields systems |
| title_fullStr |
Selforganisation and dynamics peculiarities of intense electron beams in compact crossed fields systems |
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Selforganisation and dynamics peculiarities of intense electron beams in compact crossed fields systems |
| title_sort |
selforganisation and dynamics peculiarities of intense electron beams in compact crossed fields systems |
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Національний науковий центр «Харківський фізико-технічний інститут» НАН України |
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2001 |
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http://dspace.nbuv.gov.ua/handle/123456789/79008 |
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Selforganisation and dynamics peculiarities of intense electron beams in compact crossed fields systems / A.V. Agafonov, V.P. Tarakanov, V.M. Fedorov // Вопросы атомной науки и техники. — 2001. — № 5. — С. 160-162. — Бібліогр.: 6 назв. — англ. |
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Вопросы атомной науки и техники |
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2025-07-06T03:08:10Z |
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2025-07-06T03:08:10Z |
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SELFORGANISATION AND DYNAMICS PECULIARITIES
OF INTENSE ELECTRON BEAMS IN COMPACT
CROSSED FIELDS SYSTEMS
A.V. Agafonov, V.P. Tarakanov1, V.M. Fedorov1
Lebedev Physical Institute,
Leninsky pr. 53, Moscow, Russia, 119991
agafonov@sci.lebedev.ru,
1 Joint Institute of High Temperatures of RAS,
Izorskaya 13/19, Moscow, Russia, 127412
karat@tarak.msk.su
The review of the results of computer simulations of electron flow self-organisation inside magnetically isolated
coaxial diodes (magnetron gun) is given. Magnetron guns of usual and inverted polarities are considered.
PACS number: 29.17.+w
1 INTRODUCTION
The main reasons of the self-organisation process
and development of regular space structures of the flows
inside magnetron guns are: non-linear azimuthal in-
stability of the flow under condition of strong non-uni-
form secondary self-sustaining emission and pure ther-
mionic emission, and the dominant influence of a feed-
back on the emitting surface on the dynamics of elec-
tron curls. The dynamics of intense electron flows in
systems with curvature radius of electrodes compared
with the amplitude of "bethatron" oscillations differs
from usual systems. Several examples are shown includ-
ing the storage of particles inside the gap, the develop-
ment of dense electron curls, the utilisation of such sys-
tems for generation of high-frequency oscillations [1 –
5].
Computer simulations have been performed using
the electromagnetic PIC code KARAT [6] for magnet-
ron diodes (MD) with different parameters, and with an
external voltage source V0(t) connected to MD via an
RL-circuit. The yield of secondary electrons from the
cathode takes into account the dependence of the yield
on the energy of electrons and the angle between the
direction of electron velocity and the perpendicular to
the cathode surface, and also the threshold of secondary
emission.
2 SELF-SUSTAINING SECONDARY EMIS-
SION IN MD
The regime of self-sustaining secondary emission in
MD is characterised by the average radial component of
electric field on the cathode surface, which is close but
not equal to zero. At the given azimuth of the cathode
surface it oscillates with a frequency equals to the aver-
age rotating frequency of the flow as a whole times the
number of bunches.
Feedback on the emitting surface, promoting the de-
velopment of a strong azimuthal instability, is particu-
larly effective when using a cathode with secondary
emission of electrons. The sharp non-uniform character
of secondary emission, depending in turn on the 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 suppressed by the negative value of the field, and the
emission of particles in proper phases is sharply in-
creased.. The type of operation of a MD with a sec-
ondary-emission cathode depends on the maximal volt-
age and rate of a voltage rise on the gap. For low volt-
ages, 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 az-
imuthal variations. If the voltage exceeds a certain max-
imal value in the process of rising voltage it 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 elec-
trons returning to the cathode is significantly shifted in
the direction of larger energies and exceeds that is opti-
mal for maximal yield of secondary electrons. The sharp
drop in the secondary emission current leads to elimi-
nation of the "mismatched" part of the electron flow,
and the particles remaining in the gap form, in the main,
form captured circulating flow.
The feedback on the surface of the cathode exerts
the dominant influence on the growth of the instability
and on arising of a transverse leakage current to the an-
ode across the external magnetic field exceeding the
critical magnetic field of magnetic insulation.
3 PRIMARY BEAM AND MIXED SECOND-
ARY AND PRIMARY BEAMS OF COMPAR-
ABLE CURRENTS IN MD
ВОПРОСЫ АТОМНОЙ НАУКИ И ТЕХНИКИ. 2001. №5.
Серия: Ядерно-физические исследования (39), с. 160-162.
160
Investigation of instability of the pure primary beam
of different currents up to the space-charge limited cur-
rent homogeneously emitted from a cathode of MD (an
MD with a thermionic cathode without secondary emis-
sion) shows that under condition of space-charge lim-
ited current no azimuthal instability occurs. Deep azi-
muthal modulation of the flow and leakage current to
the anode arises only if the condition of saturated re-
gime (normal component of the electric field does not
equal zero) of a cathode is satisfied. The behaviour is
conditioned by the same feedback on the emitting sur-
face providing additional correct azimuthal modulation
of emitted particles similar to the case of secondary
emission. The difference is that the radial electric field
does not change its direction on the surface of the cath-
ode, but oscillates with a large amplitude.
In the case when the current of primary beam is
comparable with the current of the secondary-emission
beam the behaviour of the electron flow for later time is
similar to the case of the space-charge limited primary
beam. The charge of the primary beam emitted homo-
geneously from the cathode influenced the character of
secondary emission and smoothes over a non-uniformity
of secondary emission due to additional suppression of
the radial electric field on the cathode surface. Second-
ary-emission current increases initially and then drops
to a value that provides together with the primary beam
the fall of the radial electric field on the cathode surface
close to zero. Azimuthal modulation of the flow and
leakage current to the anode do not exist in this case.
However, they arise for a time if the current of primary
beam decreases approximately by an order of its initial
value.
4 CAPTURE AND ACCUMULATION
OF ELECTRONS IN MD
The conditions for possible interruption of the sec-
ondary 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 realise a process of accumulation and capture
of the 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 bethatron-type systems. Such systems can
also be used as injectors for classic accelerators.
It is possible to store an electron flow having a num-
ber of particles at the level of 1012 per centimetre of
length axially in a compact system with crossed fields.
In this case, the lateral dimensions are several centi-
metres, the voltage is at the level of 100 - 200 kV and
the external magnetic field is about of 3 kGs. For sub-
sequent acceleration of captured flow, one can use a
bethatron field and cut electrodes that do not hinder the
formation of electron flow nor the penetration of an ex-
ternal longitudinal magnetic field.
After formation in a MD of electron flow with regu-
lar 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 stabilising effect on the exist-
ence of such a flow. A further increase in voltage results
in the detachment of the flow from the cathode. The re-
turn 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 with a
large number of particles.
5 SECONDARY EMISSION IN INVER-
TED MD
It was very desirable to use inverse MD instead of
usual MD to store more number of particles as the sur-
face of the cathode is larger for the same transversal di-
mension of the MD and the current can be increased.
Unfortunately, for a set of parameters the beam in the
inverse MD is unstable. The example of interesting
structures is shown in Fig. 1.
Fig. 1. The example of a periodic structure in the inver-
ted magnetron diode of small aspect ratio.
The circulating beam consists of several well spaced
intense bunches. The voltage at inverse MD is 160 kV
and is rising, the peak current of each bunch is about of
2 kA and the full number of particles inside the gap is as
greater as 4×1012 per centimetre of axial length. This
structure is changed with the variation of the voltage
and the most part of particles could be lost at the elec-
trodes.
As a rule, when analysing the non-stationary dynam-
ics of intense beams in such devices, the external circuit
is not considered. The regime of operation, for that or
ВОПРОСЫ АТОМНОЙ НАУКИ И ТЕХНИКИ. 2001. №5.
Серия: Ядерно-физические исследования (39), с. 161-162.
161
other reasons, is chosen from the condition of aperiodic
charging of a capacitance, which diode represents. At
the same time, inclusion of an external RLC-circuit with
a source of voltage V0(t) in the scheme of calculation is
necessary. This is particularly so when modelling non-
stationary processes.
The instability of the electron flow in inverse MD
with intense spikes of secondary emission current from
external cathode of large surface can be used to generate
RF-oscillation, i.e., inverse MD with the external circuit
can be used as a modulator. The modulator works on the
dynatron effect inside vacuum inverse coaxial diode
with magnetic isolation supplied by an external pulsed
high-voltage source connected to the modulator through
RL-circuit. Under conditions of permanent emission of
primary electron beam from an external electrode (cath-
ode) and the growth of the voltage at the diode the stor-
age of primary electrons arises inside the gap. Oscilla-
tions of the voltage due to oscillating regime of diode
charging and/or azimuthal instability of rotating electron
flow stimulates back-bombardment flow electrons to the
cathode and leads to power spikes of secondary emis-
sion current exceeding primary one. As the result, the
amplitude of oscillations in quasi-resonant circuit grows
and the system can turn to self-supporting oscillations.
In the usual magnetron diode, where the inner elec-
trode serves as the cathode, these oscillations promote
rapid growth of the secondary-emission process.
However, characteristics of the beam insignificantly dif-
fer from the case of aperiodic charging. In an inverted
magnetron diode, where the outer electrode serves as
the cathode, these oscillations can increase and develop
into self-sustaining regime in a certain range of para-
meters.
The difference in the behaviour of direct and inver-
ted-polarity diodes is that in a certain range of paramet-
ers the beam in an inverted diode is strongly unstable
with respect small voltage variations and the large cath-
ode surface permits briefly drawing from it large sec-
ondary-emission currents, thereby securing deeper mod-
ulation of the voltage on the diode. After withdrawing
the charge in the gap, the diode again begins to charge
and if the emission of the primary beam is continuos the
process is repeated.
Results of calculation for a magnetron diode with
anode radius ra = 0.66 cm and cathode radius
rc = 1.06 cm are presented below. The diode is immersed
in a magnetic field B0 = 3 kGs. By way of example, here
was chosen a trapezoidal form of external voltage pulse.
The rise time and fall of V0(t) was 8 ns and the flat top
had a duration of 8 ns. The chosen coefficient of sec-
ondary emission was the standard for a metal [1]. The
voltage amplitude at the external source was 50 kV.
Fig. 2. Behaviour of the voltage on the inverted diode.
6 CONCLUSION
Problems of non-linear dynamics of space-charge
dominated electron beams in crossed E×B-fields are dis-
cussed from the point of view of the investigation of
schemes of intense electron beam formation for com-
pact cyclic accelerators, for high-efficiency relativistic
magnetrons, and for electron guns. The review of the
results of computer simulations of different processes
inside usual polarity and inverted polarity magnetron di-
odes is given.
Work is supported by RFFI under
grant 00-02-16182.
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