Abstract
The influence of a transverse magnetic field on the characteristics of the positive column of a planar low-pressure discharge is studied theoretically. The motion of magnetized electrons is described in the framework of a continuous-medium 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 secondorder 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 calculated, 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 maximum 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 counter-directed ion flux.
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References
V. L. Granovskii, Electrical Current in Gas: Steady-State Current (Nauka, Moscow, 1971) [in Russian].
W. H. Schottky, Z. Phys. 25, 342 (1924).
K. N. Ul’yanov, Teplofiz. Vys. Temp. 38, 367 (2000) [High Temp. 38, 344 (2000)].
L. Tonks and I. Langmuir, Phys. Rev. 34, 876 (1929).
L. Elsgolts, Differential Equations and the Calculus of Variations (Nauka, Moscow, 1965; Mir, Moscow, 1970).
M. L. Krasnov, A. I. Kiselev, and G. I. Makarenko, Integral Equations (Nauka, Moscow, 1968) [in Russian].
O. B. Firsov, Zh. Tekh. Fiz. 24, 445 (1956).
A. V. Zharinov and V. P. Shumilin, Zh. Eksp. Teor. Fiz. 130, 371 (2006) [JETP 103, 324 (2006)].
E. Kamke, Gewöhnliche Differentialgleichungen (Acad. Verlag, Leipzig, 1959; Nauka, Moscow, 1976).
V. F. Tarasenko and S. I. Yakovlenko, Tr. IOFAN 63, 7 (2007).
K. N. Ul’yanov, Fiz. Plazmy 34, 367 (2008) [Plasma Phys. Rep. 34, 331 (2008)].
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Original Russian Text © Ya.I. Londer, K.N. Ul’yanov, 2011, published in Fizika Plazmy, 2011, Vol. 37, No. 10, pp. 909–918.
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Londer, Y.I., Ul’yanov, K.N. Kinetic theory of the positive column of a low-pressure discharge in a transverse magnetic field. Plasma Phys. Rep. 37, 848–857 (2011). https://doi.org/10.1134/S1063780X1109011X
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DOI: https://doi.org/10.1134/S1063780X1109011X