Kinetic theory of the positive column of a low-pressure discharge in a transverse magnetic field
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KINETICS
Kinetic Theory of the Positive Column of a LowPressure Discharge in a Transverse Magnetic Field Ya. I. Londer and K. N. Ul’yanov Lenin AllRussia Electrotechnical Institute, Krasnokazarmennaya ul. 12, Moscow, 111250 Russia Received December 28, 2010; in final form, February 4, 2011
Abstract—The influence of a transverse magnetic field on the characteristics of the positive column of a pla nar lowpressure discharge is studied theoretically. The motion of magnetized electrons is described in the framework of a continuousmedium model, while the ion motion in the ambipolar electric field is described by means of a kinetic equation. Using mathematical transformations, the problem is reduced to a second order ordinary differential equation, from which the spatial distribution of the potential is found in an analytic form. The spatial distributions of the plasma density, mean plasma velocity, and electric potential are calcu lated, the ion velocity distribution function at the plasma boundary is found, and the electron energy as a function of the magnetic field is determined. It is shown that, as the magnetic field rises, the electron energy increases, the distributions of the plasma density and mean plasma velocity become asymmetric, the maxi mum of the plasma density is displaced in the direction of the Ampère force, and the ion flux in this direction becomes substantially larger than the counterdirected ion flux. DOI: 10.1134/S1063780X1109011X
1. INTRODUCTION Lowpressure discharges are electric discharges operating at pressures of p < 1 Torr and current densi ties in the range 10–3–1 A/cm2, when stepwise pro cesses, bulk recombination, and gas heating are of minor importance [1]. Under these conditions, the electron temperature Te and the density of neutral gas atoms N are nearly constant across the positive col umn (PC), the plasma in the PC is partially ionized, and Te is much higher than the neutral gas temperature Ta. The electron and ion fluxes at each point of the PC cross section are equal to one another, i.e., the mean ion and electron velocities are the same. Depending on the gas atom density and PC transverse dimensions, the PC operates in a collisional or collisionless mode. In the collisional mode, when the electron and ion mean free paths are shorter than the PC transverse dimensions, the PC can be described in the framework of a continuousmedium model. Based on this model, Schottky [2] developed the wellknown diffusion the ory of the PC, in which the density distribution of the quasineutral plasma ( N e = N i ) is found from the ambipolar diffusion equation. According to the diffu sion theory, the relative distribution of the plasma den sity in a cylindrical PC is described by the universal formula N i (r ) N i (0) = J 0(2.4r / R), where J0 is the zero order Bessel function, while the electron temperature is determined from the boundary condition N i (R) = 0 and decreases with increasing product NR. It should be noted that the diffusion equation in [2] was derived under the fo
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