Self-sustaining secondary emission in magnetron guns, beam modulation and feedbacks
This paper reports on computer simulations of an electron cloud formation inside a smooth-bore magnetron. Preliminary results were published in [1-3]. Computer simulations have been performed using 2.5D and 3D electromagnetic PIC code KARAT [4] for the magnetron diode (MD) with parameters close to e...
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| Published in: | Вопросы атомной науки и техники |
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| Date: | 1999 |
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| Language: | English |
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Національний науковий центр «Харківський фізико-технічний інститут» НАН України
1999
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| Cite this: | Self-sustaining secondary emission in magnetron guns, beam modulation and feedbacks / A.V. Agafonov, V.M. Fedorov, V.P. Tarakanov // Вопросы атомной науки и техники. — 1999. — № 4. — С. 11-13. — Бібліогр.: 5 назв. — англ. |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1859641582930624512 |
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| author | Agafonov, A.V. Fedorov, V.M. Tarakanov, V.P. |
| author_facet | Agafonov, A.V. Fedorov, V.M. Tarakanov, V.P. |
| citation_txt | Self-sustaining secondary emission in magnetron guns, beam modulation and feedbacks / A.V. Agafonov, V.M. Fedorov, V.P. Tarakanov // Вопросы атомной науки и техники. — 1999. — № 4. — С. 11-13. — Бібліогр.: 5 назв. — англ. |
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| container_title | Вопросы атомной науки и техники |
| description | This paper reports on computer simulations of an electron cloud formation inside a smooth-bore magnetron. Preliminary results were published in [1-3]. Computer simulations have been performed using 2.5D and 3D electromagnetic PIC code KARAT [4] for the magnetron diode (MD) with parameters close to experimental [5], 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.
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| first_indexed | 2025-12-07T13:22:42Z |
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SELF-SUSTAINING SECONDARY EMISSION IN MAGNETRON GUNS,
BEAM MODULATION AND FEEDBACKS*
A.V.Agafonov*, V.M.Fedorov, V.P.Tarakanov
*Lebedev Physical Institute of RAS, Moscow, Russia,
IVTAN, Moscow, Russia
INTRODUCTION
This paper reports on computer simulations of an
electron cloud formation inside a smooth-bore
magnetron. Preliminary results were published in [1−3].
Computer simulations have been performed using 2.5D
and 3D electromagnetic PIC code KARAT [4] for the
magnetron diode (MD) with parameters close to
experimental [5], 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.
DYNAMICS OF SECONDARY EMISSION BEAM
IN MD
The main parameters of MD are: radius of the
anode rA = 0.53 cm, radius of the cathode rK = 0.33 cm;
external longitudinal magnetic field B0 = 2.5 kG (B0/Bcr
≅ 1.15, ωec/2π = 7 GHz, period of cyclotron rotation
0.14 ns); the voltage rise time to maximum value of V0m
= 12 kV was varied from 2 to 10 ns; maximum emission
current of the primary beam Iem = 3 A. For given voltage
and geometry of MD the Child-Langmuir current
through the MD without a magnetic field equals
approximately ICL ≅ 240 A (here and below currents and
charge densities correspond to linear values per cm of
length in the longitudinal direction). Electrotechnical
parameters are τL/R = 0.25 ns, τRC = 0.24 ns, where C is
the capacitance of MD. Drift velocity of electrons in
crossed fields is veθ = cE0/B0 = 2.4×109 cm/s, if the
electric field is estimated as VAK/dAK.
The process of electron cloud formation inside
an axisymmetrical MD under the condition of
homogeneous initial emission of low current primary
beam from a cathode starts due to inevitable presence of
electric field fluctuations in rotating flow of electrons
stored inside the gap for the time of the growth of the
external voltage. Weak azimuthal instability is
amplified by nonuniform secondary emission and a
feedback on the surface of the cathode. Under
conditions of conservation of full energy and
momentum a part of the electrons lose energy under the
action of the field and drifts to larger radii towards the
anode. Another part of the electrons increases its energy
and returns to the cathode with an energy exceeding the
threshold value for secondary emission. In view of
indicated reasons, the emission of secondary electrons is
nonuniform. This effect leads to an intensification of the
cathode back-bombardment process and to fast and
effective growth of secondary electrons inside MD. The
secondary-emission current exceeds the primary-beam
current by more than an order of magnitude and
subsequently exerts a determining action on the
operation of the MD. The MD passes over to a
condition of self-sustaining emission and the primary
beam could be switched off. After the transient process,
a stable formation consisting of several bunches is
formed in this geometry. Electron clouds rotate as a
whole with approximately constant angular frequency.
Fig. 1: Stable configuration of secondary emission flow
(top), primary flow in saturated working regime of the
cathode (middle) and primary space-charge-limited flow
(bottom).
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
anode across the external magnetic field exceeding the
critical magnetic field of magnetic insulation. This
feedback is conditioned by right phasing of a part of
ВОПРОСЫ АТОМНОЙ НАУКИ И ТЕХНИКИ. 1999. № 4.
Серия: Ядерно-физические исследования (35), с. 11-13.
11
secondary emitted electrons by rotating crossed E×B-
field. These electrons are captured inside rotating
modulated electron flow and stay inside the gap for
many revolutions around the cathode, maintaining its
azimuthal and time structures. Another part of
secondary emitted electrons can stay inside the gap only
for a small time comparable with the period of cyclotron
motion because they are forced to return to the cathode
by the radial component of rotating crossed E×B-field,
which changes its direction during the rotation of the
flow as a whole.
The regime of self-sustaining secondary
emission in MD is characterized by the average radial
component of electric field on the cathode surface,
which is close but not equal to zero. At given azimuth of
the cathode surface it oscillates with a frequency equal
to the average rotating frequency of the flow as a whole
times the number of bunches, and with amplitudes
varying from -10 up to 30 − 40 kV/cm.
Note that strong azimuthal instability and large
azimuthal modulation with leakage current to the anode
occurred only if the current of primary beam is small in
comparison with the full current of self-sustaining
secondary emission. Fig.1 (top) shows stable
configuration of electron flow inside the MD with
secondary emission cathode.
Fig. 2: Dynamics of store of electrons inside the gap for
the above mentioned cases
Fig.2 (top) shows dynamics of store of primary
Ne0 and secondary Nes electrons inside MD. The time
behavior of radial electric field near the surfaces of the
cathode is shown in the top of Fig.3.
DYNAMICS OF PRIMARY AND MIXED BEAMS
IN MD
Investigation of the instability of pure primary
beam of different currents up to space-charge limited
current homogeneously emitted from a cathode of MD
(an MD without secondary emission) shows that under
condition of space-charge limited current no azimuthal
instability occurs. Deep azimuthal modulation of the
flow and leakage current to the anode arises only if the
condition of saturated regime (normal component of
electric field does not equal zero) of a cathode is
satisfied. The behavior is conditioned by the same
feedback on the emitting surface 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 cathode, but
oscillates with large amplitude.
Fig. 3: Behavior of the radial electric field near the
surface of the cathode for the aforementioned cases.
In the middle of Fig.1 stable configuration of the
flow of primary electrons inside the MD without
secondary emission and the cathode operating in
saturated regime is shown. The bottom figure shows
stable configuration for the case of space-charge limited
current of primary electrons. In the middle and in the
bottom pictures of Fig.2 dynamics of store of primary
N0 inside MD are shown for aforementioned cases.
ВОПРОСЫ АТОМНОЙ НАУКИ И ТЕХНИКИ. 1999. № 4.
Серия: Ядерно-физические исследования (35), с. 11-13.
11
The time behavior of radial electric field near
the surfaces of the cathode for aforementioned cases is
shown in Fig.3. In the case when the current of primary
beam is comparable with the current of secondary-
emission beam the behavior of the electron flow for
later time is similar to the case of space charge limited
primary beam. The charge of primary beam emitted
homogeneously from the cathode influenced the
character of secondary emission and smoothes over a
nonuniformity of secondary emission. Secondary-
emission current increases initially and then drops to a
value, which provides the fall of radial electric field on
the cathode surface to 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.
3D COMPUTER SIMULATION
Presented above results obtained for 2-
dimensional r-θ geometry of the system. Results of 3D
calculations have confirmed all main physical
mechanisms and conclusions of 2D calculation. The
transverse leakage current drops sharply when
BO/Bcr ≥ 1.4 and longitudinal leakage current prevail.
CONCLUSION
Emphasized is the dominant influence of a
feedback on dynamics of electron beam modulation and
on arising transverse leakage current to the anode across
the external magnetic field exceeding the critical
magnetic field of magnetic insulation. The instability
arises due to an energy and a momentum exchange
between particles and rotating crossed azimuthally
modulated E×B-fields. Strong azimuthal instability
exists if the current of primary beam is much less then
the secondary emission current. If these currents are
comparable, the instability is weak and decays in time
due to the absence of strong azimuthal inhomogeneity
of secondary emission current. In the case of the
emission of primary beam alone deep modulation and
leakage current arises only if the condition of saturated
regime of a cathode is satisfied. Such behavior is
conditioned by a feedback on the emitting surfaces
which provides additional correct azimuthal modulation
of electron flow by rotating crossed ExB-field and
amplifies the instability.
REFERENCES
1. Agafonov A.V., Fedorov V.M., Tarakanov V.P. Proc.
of 1997 Particle Accelerator Conf., Vancouver, Canada.
1997, v. 2, 1299 -- 1301.
2. Agafonov A.V. Proc. of the 2nd Sarantsev's seminar.
Dubna, JINR, 1998. D9-98-153, 105 -- 109.
3. Agafonov A.V., Fedorov V.M., Tarakanov V.P. Proc.
of the 12th Intern. Conference on High-Power Particle
Beams. Israel, Haifa, 1998.
4. Kotetashwily P.V., Rybak P.V., Tarakanov P.V.
Institute of General Physics, Moscow, Preprint N 44,
1991.
5. Jepsen R.L. and Muller M.V. J. Appl. Phys. 1951, v.
22, 1196 - 1207.
ВОПРОСЫ АТОМНОЙ НАУКИ И ТЕХНИКИ. 1999. № 4.
Серия: Ядерно-физические исследования (35), с. 11-13.
11
|
| id | nasplib_isofts_kiev_ua-123456789-81513 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1562-6016 |
| language | English |
| last_indexed | 2025-12-07T13:22:42Z |
| publishDate | 1999 |
| publisher | Національний науковий центр «Харківський фізико-технічний інститут» НАН України |
| record_format | dspace |
| spelling | Agafonov, A.V. Fedorov, V.M. Tarakanov, V.P. 2015-05-17T16:03:13Z 2015-05-17T16:03:13Z 1999 Self-sustaining secondary emission in magnetron guns, beam modulation and feedbacks / A.V. Agafonov, V.M. Fedorov, V.P. Tarakanov // Вопросы атомной науки и техники. — 1999. — № 4. — С. 11-13. — Бібліогр.: 5 назв. — англ. 1562-6016 https://nasplib.isofts.kiev.ua/handle/123456789/81513 This paper reports on computer simulations of an electron cloud formation inside a smooth-bore magnetron. Preliminary results were published in [1-3]. Computer simulations have been performed using 2.5D and 3D electromagnetic PIC code KARAT [4] for the magnetron diode (MD) with parameters close to experimental [5], 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. en Національний науковий центр «Харківський фізико-технічний інститут» НАН України Вопросы атомной науки и техники Self-sustaining secondary emission in magnetron guns, beam modulation and feedbacks Самоподдерживающаяся вторичная эмиссия в магнетронных пушках, модуляция пучка и обратные связи в системе Article published earlier |
| spellingShingle | Self-sustaining secondary emission in magnetron guns, beam modulation and feedbacks Agafonov, A.V. Fedorov, V.M. Tarakanov, V.P. |
| title | Self-sustaining secondary emission in magnetron guns, beam modulation and feedbacks |
| title_alt | Самоподдерживающаяся вторичная эмиссия в магнетронных пушках, модуляция пучка и обратные связи в системе |
| title_full | Self-sustaining secondary emission in magnetron guns, beam modulation and feedbacks |
| title_fullStr | Self-sustaining secondary emission in magnetron guns, beam modulation and feedbacks |
| title_full_unstemmed | Self-sustaining secondary emission in magnetron guns, beam modulation and feedbacks |
| title_short | Self-sustaining secondary emission in magnetron guns, beam modulation and feedbacks |
| title_sort | self-sustaining secondary emission in magnetron guns, beam modulation and feedbacks |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/81513 |
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