Anomalous electron transport in the low pressure DC discharge in crossed fields

A.A. Bizyukov, I.A. Bizyukov, A.E. Kashaba, E.V. Romashchenko*, K.N. Sereda
and N.D. Sereda
Kharkiv National University, Department of plasma physics, 31 Kurchatov Ave., Kharkiv, 61108, Ukraine
* East-Ukrainian National University, 1 Vatutin Str., Lugansk, Ukraine
Abstract. The interaction of HF electric field with a drifting electron stream of the discharge in crossed fields is
investigated. It is shown that in this case in the region of hydrodynamic resonance the character of electron transport
across the magnetic field is altered from diffusive to vortical. It results in local increase of the electron velocity across H
and, local decrease of the average electron density and the ionization frequency. The important time and spatial scales are
given in analytical form and general picture of the dynamic of electrons is obtained by numerical calculations.
Keywords: crossed fields, anomalous electron transport.
PACS: 51.10.+y, 52.25.Fi.
At present there is a widely-spread tendency to use plasma-dynamic systems (such like anode layer accelerators,
magnetron spray systems, ion pumps and pressure sensors based on magnetron and Penning discharges) both in
fundamental scientific researches and various technological applications [1]. These plasma-dynamic systems are
based on a static current discharge in low-pressure transverse electrical and magnetic fields. Such systems ensure
wide opportunities to obtain and control charged particles flux parameters. A characteristic feature of such systems
is spatial charge layer formation, in which almost the entire voltage drop on a discharge and the main generating and
accelerating processes of charged particles are concentrated [2]. The energy distributing function experimental
researches of ions, which come out of transverse magnetic field discharges (out of an anode layer accelerator, for
instance [3]), have shown that particular features like local “lapses” and “humps” were observed in unstable regimes
of discharge on the ion energy distributing function. The like particular features were observed by introducing RF
discharge rate to the discharge gap with the help of antennae. The emergence of RF electric fields in the anode
discharge layer explains the anomalies in the ion distributing function.
The present work is devoted both to the theoretical study of a low pressure discharge ion dynamics in a strong
transverse magnetic field in a drift approach involving RF electrical fields and to the determination of the physical
mechanism of the fine ionization structure emergence.
The influence of the external electrical fields on the motion of electrons has been viewed in a layer’s drift model
(fig.1) taking into account the conditions and scales of a discharge in a transverse magnetic field. They are
characteristic for the conditions of experiments in the Hall ion source introducing RF-field with the help of an
antenna on the cathode [3].
The equations of motions for electrons. The particles which due to collisions manage to get to the hydrodynamic resonance zone from the cathode
boundary of the anode layer reaching the separatrix pass this zone without collisions and move only due to collisions
on the anode side of the layer. Thus in the vicinity of the hydrodynamic resonance there takes place an anomalous
(collisionless) transfer of electrons across the magnetic field due to the interaction with the RF-field of a wave. Thus
the anomalous transfer leads to decrease of the electron density in this zone.
By the predominating influence of the electron-atom collisions the electron distributing function is Maxwellian
distribution with the temperature [7]:

where χ is the coefficient of energy transfer.
The ionization frequency in this case is determined by the expression

where na is the concentration of neutral atoms, s0i is the cross section of ionization, Ei is the energy of ionization.
The relation of ionization frequencies at high voltage (v2) and low voltage (v1) boundaries

Therefore the ionization velocity at the high voltage boundary of the RF-layer is higher than it is at the low
voltage boundary. This leads to the change of the form of the ion distributing function among energies. Thus in the
RF-layer region we can observe a local lapse in the distributing function and a hump after the layer. The RF-field
parameters (amplitude, frequency and length of wave) define the localization and the energetic scale of the
anomalous electron transfer zone and the change of the ion distributing function among energies.
1. A. I. Morozov, Plasmas accelerators, edited by L. A. Artsimovich, . Moskow: Mashinostroeniye, 1973, pp. 5-15.
2. Y. E. Kreyndel, Plasmas source of electrons. Moscow: Atomizdat, 1977. p. 145.
3. N. A. Azarenkov, A. A. Bizyukov, I. A. Bizyukov, Vl. V. Bobkov, A. Y. Kashaba, K. N. Sereda, I. K. Tarasov, “Ion energy
distribution function control in Hall ion thrusters”, Proceedings of International symposium “Vacuum technologies and
equipment” (ISVTE-4), Ukraine, Kharkov, 2001. pp. 83-87.
4. N. A. Kervalishvili, A. V. Zharinov, J. Tekhn. Fiz., 35, issue 12, (1965).
5. V. E. Gollant, A. P. Gilinsky, I. E. Sakharov, Plasma physics principles, Moskow: Atomizdat, 1977.

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