Longitudinal diamagnetic effects in beam-plasma system embedded in an external magnetic field
High-current electrons beams generated in an external magnetic field in vacuum behave as a diamagnetic and force a magnetic field out of its volumes in radial direction. Under the condition of conservation of a magnetic flux the magnetic field inside of the beam decreases and increases outside. In t...
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irk-123456789-174672011-02-27T12:06:58Z Longitudinal diamagnetic effects in beam-plasma system embedded in an external magnetic field Agafonov, A.V. Динамика плазмы и взаимодействие плазма – стенка High-current electrons beams generated in an external magnetic field in vacuum behave as a diamagnetic and force a magnetic field out of its volumes in radial direction. Under the condition of conservation of a magnetic flux the magnetic field inside of the beam decreases and increases outside. In the beam-plasma systems embedded in a magnetic field (plasma filled diodes or a beam in a plasma channel) another state of the beam with the total magnetic field increased to the axis can be realized. Radial focusing of the beam is ensured by electrostatic field of an ion pivot and azimuthal self magnetic field. If the external magnetic field changes in longitudinal direction then the value of magnetic field from the region of beam injection is transferred along near axis region of the system. It looks like a “magnetic needle” and resembles “frozen field” effect but the physics is different. Different beam-plasma systems were considered by means of computer simulation. Computer simulation was performed using electromagnetic PIC code KARAT. Сильноточные электронные пучки во внешнем магнитном поле ведут себя как диамагнетик, вытесняя магнитное поле из своего объема. При условии сохранения магнитного потока это сопровождается уменьшением результирующего магнитного поля внутри пучка и увеличением его снаружи. В пучково-плазменной системе в магнитном поле (плазменный диод или плазменный канал транспортировки) возможно другое равновесное состояние пучка, в котором результирующее магнитное поле растет ближе к оси системы. Радиальная фокусировка пучка обеспечивается электростатическим полем ионного остова и собственным азимутальным магнитным полем, в то время как продольное магнитное поле имеет дефокусирующий характер. Если внешнее магнитное поле меняется вдоль оси системы, то пучок захватывает и переносит вдоль оси поле из области инжекции. Этот эффект выглядит внешне как «магнитная игла» и напоминает эффект «вмороженности» поля, но отличается по физике. При численном моделировании с помощью электромагнитного кода КАРАТ рассмотрены различные пучково-плазменные системы. Потужнострумові електронні пучки у зовнішньому магнітному полі поводяться як діамагнетик, витісняючи магнітне поле зі свого обсягу. За умови збереження магнітного потоку це супроводжується зменшенням результуючого магнітного поля усередині пучка і збільшенням його зовні. У пучково-плазмовій системі в магнітному полі (плазмовий діод або плазмовий канал транспортування) можливо інший рівноважний стан пучка, у якому результуюче магнітне поле росте ближче до вісі системи. Радіальне фокусування пучка забезпечується електростатичним полем іонного кістяка і власним азимутальним магнітним полем, у той час як подовжнє магнітне поле має дефокусуючий характер. Якщо зовнішнє магнітне поле міняється уздовж вісі системи, то пучок захоплює і переносить уздовж вісі поле з області інжекції. Цей ефект виглядає зовні як «магнітна голка» і нагадує ефект «вмерзлості» поля, але відрізняється по фізиці. При чисельному моделюванні за допомогою електромагнітного кода КАРАТ розглянуто різні пучково-плазмові системи. 2010 Article Longitudinal diamagnetic effects in beam-plasma system embedded in an external magnetic field / A.V. Agafonov // Вопросы атомной науки и техники. — 2010. — № 6. — С. 88-90. — Бібліогр.: 12 назв. — англ. 1562-6016 http://dspace.nbuv.gov.ua/handle/123456789/17467 en Національний науковий центр «Харківський фізико-технічний інститут» НАН України |
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Динамика плазмы и взаимодействие плазма – стенка Динамика плазмы и взаимодействие плазма – стенка |
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Динамика плазмы и взаимодействие плазма – стенка Динамика плазмы и взаимодействие плазма – стенка Agafonov, A.V. Longitudinal diamagnetic effects in beam-plasma system embedded in an external magnetic field |
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High-current electrons beams generated in an external magnetic field in vacuum behave as a diamagnetic and force a magnetic field out of its volumes in radial direction. Under the condition of conservation of a magnetic flux the magnetic field inside of the beam decreases and increases outside. In the beam-plasma systems embedded in a magnetic field (plasma filled diodes or a beam in a plasma channel) another state of the beam with the total magnetic field increased to the axis can be realized. Radial focusing of the beam is ensured by electrostatic field of an ion pivot and azimuthal self magnetic field. If the external magnetic field changes in longitudinal direction then the value of magnetic field from the region of beam injection is transferred along near axis region of the system. It looks like a “magnetic needle” and resembles “frozen field” effect but the physics is different. Different beam-plasma systems were considered by means of computer simulation. Computer simulation was performed using electromagnetic PIC code KARAT. |
| format |
Article |
| author |
Agafonov, A.V. |
| author_facet |
Agafonov, A.V. |
| author_sort |
Agafonov, A.V. |
| title |
Longitudinal diamagnetic effects in beam-plasma system embedded in an external magnetic field |
| title_short |
Longitudinal diamagnetic effects in beam-plasma system embedded in an external magnetic field |
| title_full |
Longitudinal diamagnetic effects in beam-plasma system embedded in an external magnetic field |
| title_fullStr |
Longitudinal diamagnetic effects in beam-plasma system embedded in an external magnetic field |
| title_full_unstemmed |
Longitudinal diamagnetic effects in beam-plasma system embedded in an external magnetic field |
| title_sort |
longitudinal diamagnetic effects in beam-plasma system embedded in an external magnetic field |
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Національний науковий центр «Харківський фізико-технічний інститут» НАН України |
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2010 |
| topic_facet |
Динамика плазмы и взаимодействие плазма – стенка |
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http://dspace.nbuv.gov.ua/handle/123456789/17467 |
| citation_txt |
Longitudinal diamagnetic effects in beam-plasma system embedded in an external magnetic field / A.V. Agafonov // Вопросы атомной науки и техники. — 2010. — № 6. — С. 88-90. — Бібліогр.: 12 назв. — англ. |
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| fulltext |
PLASMA DYNAMICS AND PLASMA WALL INTERACTION
88 PROBLEMS OF ATOMIC SCIENCE AND TECHNOLOGY. 2010. № 6.
Series: Plasma Physics (16), p. 88-90.
LONGITUDINAL DIAMAGNETIC EFFECTS IN BEAM-PLASMA SYSTEM
EMBEDDED IN AN EXTERNAL MAGNETIC FIELD
A.V. Agafonov
P.N. Lebedev Physical Institute of RAS, Moscow, Russia
High-current electrons beams generated in an external magnetic field in vacuum behave as a diamagnetic and force
a magnetic field out of its volumes in radial direction. Under the condition of conservation of a magnetic flux the
magnetic field inside of the beam decreases and increases outside. In the beam-plasma systems embedded in a magnetic
field (plasma filled diodes or a beam in a plasma channel) another state of the beam with the total magnetic field
increased to the axis can be realized. Radial focusing of the beam is ensured by electrostatic field of an ion pivot and
azimuthal self magnetic field. If the external magnetic field changes in longitudinal direction then the value of magnetic
field from the region of beam injection is transferred along near axis region of the system. It looks like a “magnetic
needle” and resembles “frozen field” effect but the physics is different. Different beam-plasma systems were considered
by means of computer simulation. Computer simulation was performed using electromagnetic PIC code KARAT.
PACS: 52.40.Mj
1. INTRODUCTION
High-current electron beams in an external
longitudinal magnetic field behave as a diamagnetic and
force a magnetic field out of its volume. It leads to
decreasing of the full magnetic field inside of the beam
and to increasing of the field outside if the wall chamber
conductivity is high enough. The last condition
corresponds to the conservation of the magnetic flux in
the cross section of the chamber. For charged beams a
degree of the diamagnetism cannot exceed 100% [1]. The
equilibrium with closed magnetic field lines, i.e. with
different directions of full magnetic field inside and
outside of the beam was called E-layers (project
“Astron”) [2, 3]. Such equilibrium was created
experimentally only under condition of electrostatic
neutralisation of a beam space charge [4]. The coaxial
chamber with additional potential difference between the
electrodes can be used to create charged E-layer [5]. From
another side, to reach essentially increasing of the full
magnetic field, an inverse diode with magnetic isolation
can be used [6]. For both last examples the voltage plays a
role of the beam ions space charge neutralising.
Another type of the equilibrium can be created when
a high-current electron beam is injected in the plasma
with comparative density placed in a longitudinal
magnetic field (plasma filled diodes, plasma channels).
This type resembles two above-mentioned states with
additional electrostatic field. Right analogy with these
vacuum states consists in the presence of a radial focusing
field in an ion pivot. In this case the role of internal
electrode plays near axis ion pivot. The pivot arises when
a space charge of the beam pushes out plasma electrons
from its volume. As the result full magnetic field
increases to the axis of the beam-plasma system
embedded in a constant longitudinal magnetic field and
exceeds this initial external field several times [7, 8].
Several peculiarities arise because the combination of the
external beam and plasma fields cannot be observed in
vacuum systems. Beam electrons are confined always
inside plasma column if the density of the plasma exceeds
the density of the beam, but it is not enough for current
neutralisation. This situation practically does not depend
on the value of the external magnetic field and allows
using spatially inhomogeneous external magnetic field.
Very interesting effect arises in this case. The longitudinal
magnetic field created by the beam pierces the external
one. It looks like a “magnetic needle”. Actually, it can be
considered as a transformation of the usual transverse
diamagnetic effect in the axially homogeneous system to
the axially inhomogeneous one. The beam “captures” the
field in the area of generation or injection and tries to
“drag” it through external magnetic field. To demonstrate
the effect different external magnetic field configurations
were considered by means of computer simulation
performed by electromagnetic PIC code KARAT [9].
Following results are presented for the geometry of
the plasma filled diode shown in Fig. 1. Such diodes are
used to produce high-current low-energy electron beams
for surface material modifications [10-12]. An electron
beam is generated in the thin double-layer near the
cathode formed just after the beginning of an accelerating
voltage pulse. The relatively low applied voltage is
localized in this layer making possible the beginning of
the explosive emission from the cathode surface.
Fig1. Configuration of the diode
The space between 0.6 cm radius cathode and 1 cm
radius anode fills plasma with 3×1013 cm-3 density and
0.6 cm radius. The plasma is homogeneous in radial and
axial directions. The applied voltage rises to 100 kV in
1 ns and stays constant at this level. It is supposed that an
emission of a beam begins immediately after the
accelerating field arises. A time delay between the
beginning of the voltage pulse and emission of the beam
does not influence essentially on the final results. To
simplify simulations at the first step, plasma ions are
considered as a background, i.e. ions have infinite mass.
The current of the beam is defined as a current limited by
space charge under the condition of zero accelerating field
at the cathode surface.
2. THE MAIN RESULTS
2.1. THE DIOD WITHOT AN EXTERNAL FIELD
Fig. 2 shows the dynamics of the beam current emitted
from the cathode (b, 1 E), the beam (b, 1 A), and the
plasma electron (g,1 A) currents to the cathode. Beam
(b, 2 A) and plasma electron (g, 2 A) currents reaching
the anode in the bounds of initial plasma channel radius
are given in Fig. 3. The beam current on the anode is
about 15 kA and exceeds Alven current IA = 17βγ ≈
11 kA. The average density of the beam electrons is
about 5×1012 cm-3.
Fig. 2. Dynamics of currents at the cathode
Fig. 3. Dynamics of currents reaching the anode
Self longitudinal magnetic field of the beam fluctuates at
the level of tens Gauss.
2.2. THE DIOD IN HOMOGENEOUS FIELD
Fig. 4 and Fig.5 show initial (t = 0 ns) and final (t =
12 ns) distributions of the longitudinal magnetic fields.
The magnetic field influence weakly on the beam
dynamics and the value of the beam current reaching the
anode is similar to the previous case (see Fig. 3).
Magnetic field at the axis of the diode equals
approximately 7 kGs (Fig. 5) and several times exceeds
the external one (2 kGs). Here it is necessary to note, that
the modification of the magnetic field concentrates near
the axis, and this modification is latent if the field out of
plasma channel changes insignificantly in comparison
with the given external field.
Fig. 4. Initial distribution of magnetic field
Fig. 5. Final distribution of magnetic field
2.3. THE DIOD WITH PLASMA DENSITY
GRADIENT IN THE HOMOGENEOUS FIELD
To confirm the main influence of plasma ions on the
effect discussed above the results for the diode with
plasma gradient are given in this section. Initial density of
the plasma decreases from 3×1013 cm-3 near the cathode
to 3×1012 cm-3 near the anode (Fig. 6). Initial distribution
of the magnetic field is chosen similar to the previous
case (see Fig. 4). Fig. 7 shows the final distribution of the
full magnetic field at the moment t = 12 ns.
Fig. 6. Initial distribution of plasma density
Fig. 7 Final distribution of magnetic field
It is obvious from Fig. 6 and Fig. 7 that the form of the
full magnetic field at the axis follows the profile of the
89
90
plasma ion density. Essential modification of the initial
magnetic field concentrates near the axis.
Beam current reaching the anode decreases to
approximately 8 kA due to decreasing the plasma density
to the anode in comparison with previous cases.
3. CONCLUSIONS
The new effect of the transportation of a magnetic field
by a high-current electron beam from the area of the beam
generation or injection through an external magnetic field
inside a plasma channel was demonstrated be means of
computer simulation.
The work is supported by the RFBR under grant 09-02-
00715.
REFERENCES
1. A.V. Agafonov, V.S. Voronin, K.N. Pazin, A.N. Lebedev.
High-Current Electron Beam Transportation in Magnetic
Field// JTF. 1974, v. 44, p. 1909-1916 (in Russian).
2. N.C. Christofilos. Astron Thermonuclear Reactor//
Proc. of the 2nd United Nations International
Conference on Peaceful Uses of Atomic Energy.
Geneva: United Nations, 1958, p. 279-290.
3. N.C. Christofilos. Minimum-B properties of
Relativistic Electron Coils// Phys. Fluids. 1966, v. 9, p.
1425-1427.
4. M.L. Andrews, H. Davitian, H.H. Fleschmann, et al.
Generation of Astron-type E-layers using Very High-
Current Electron Beams // Phys.Rev.Lett. 1971, v.27,
p. 1428-1431.
5. A.V. Agafonov. Charged Е-layer // Plasma Physics.
1976, v. 2, p. 57-62 (in Russian).
6. A.V. Agafonov. High-Current Electron Beam
Equilibrium of Θ-pinch Type in an Inverse Magnetic
Isolation Coaxial Diode // Plasma Physics. 1982, v. 8,
p. 925-930 (in Russian).
7. A.V.Agafonov, V.P. Tarakanov. Paramagnetic States
of High-Current Electron Beams in a Beam-Plasma
Systems// Problems of Atomic Science and Technology.
Series “Plasma Physics” (12). 2006, N 6, p. 169-171.
8. A.V .Agafonov, V.P. Tarakanov. Computer Simulation
of Low-Energy High-Current Electron Beam Dynamics
in a long Plasma Diodes// Problems of Atomic Science
and Technology. Series “Nuclear Physics
Investigations”(49). 2008, N 3, p. 136-138.
9. V.P. Tarakanov. User's Manual for Code KARAT /
Springfield, VA, Berkeley Research Associates Inc.
1992, p. 127.
10. G.E. Ozur, D.S. Nazarov, L.B. Proskurovsky.
Generation of Low Energy High-Current Electron
Beams in the Gun with Plasma Anode//Izvestija
VUZ’ov. Physics. 1994, N 3, p. 100-107.
11. A.V. Agafonov, V.A. Bogachenkov, E.G. Krastelev.
High-Current Low-Energy Electron Beam Generation
in a Plasma System// Problems of Atomic Science and
Technology. Series “Nuclear Physics Investigations”
(47). 2006, N. 3, p. 49-51.
12. A.V. Agafonov. Low Impedance Plasma Systems for
Generation of Low Energy High-Current Electron
Beams// Physics of Elementary Particles and Atomic
Nuclei Letters. 2006, v. 3, N 7(138), p. 19-26.
Article received 13.09.10
ПРОДОЛЬНЫЕ ЭФФЕКТЫ ДИАМАГНЕТИЗМА В ПУЧКОВО-ПЛАЗМЕННОЙ СИСТЕМЕ
ВО ВНЕШНЕМ МАГНИТНОМ ПОЛЕ
А.В. Агафонов
Сильноточные электронные пучки во внешнем магнитном поле ведут себя как диамагнетик, вытесняя
магнитное поле из своего объема. При условии сохранения магнитного потока это сопровождается
уменьшением результирующего магнитного поля внутри пучка и увеличением его снаружи. В пучково-
плазменной системе в магнитном поле (плазменный диод или плазменный канал транспортировки) возможно
другое равновесное состояние пучка, в котором результирующее магнитное поле растет ближе к оси системы.
Радиальная фокусировка пучка обеспечивается электростатическим полем ионного остова и собственным
азимутальным магнитным полем, в то время как продольное магнитное поле имеет дефокусирующий характер.
Если внешнее магнитное поле меняется вдоль оси системы, то пучок захватывает и переносит вдоль оси поле из
области инжекции. Этот эффект выглядит внешне как «магнитная игла» и напоминает эффект
«вмороженности» поля, но отличается по физике. При численном моделировании с помощью
электромагнитного кода КАРАТ рассмотрены различные пучково-плазменные системы.
ПОДОВЖНІ ЕФЕКТИ ДІАМАГНЕТИЗМУ В ПУЧКОВО-ПЛАЗМОВІЙ СИСТЕМІ
У ЗОВНІШНЬОМУ МАГНІТНОМУ ПОЛІ
О.В. Агафонов
Потужнострумові електронні пучки у зовнішньому магнітному полі поводяться як діамагнетик, витісняючи
магнітне поле зі свого обсягу. За умови збереження магнітного потоку це супроводжується зменшенням
результуючого магнітного поля усередині пучка і збільшенням його зовні. У пучково-плазмовій системі в
магнітному полі (плазмовий діод або плазмовий канал транспортування) можливо інший рівноважний стан
пучка, у якому результуюче магнітне поле росте ближче до вісі системи. Радіальне фокусування пучка
забезпечується електростатичним полем іонного кістяка і власним азимутальним магнітним полем, у той час як
подовжнє магнітне поле має дефокусуючий характер. Якщо зовнішнє магнітне поле міняється уздовж вісі
системи, то пучок захоплює і переносить уздовж вісі поле з області інжекції. Цей ефект виглядає зовні як
«магнітна голка» і нагадує ефект «вмерзлості» поля, але відрізняється по фізиці. При чисельному моделюванні
за допомогою електромагнітного кода КАРАТ розглянуто різні пучково-плазмові системи.
REFERENCES
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