Geodesic
Some problems on the two-fluid MHD with a~transverse magnetic field
Matematičeskoe modelirovanie, Tome 8 (1996) no. 2, pp. 75-90.

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The two-fluid model of the dense plasma dynamics distinguishes the ion and electron velocities, takes into account the Hall effect and electrode polarity. The two-fluid MHD equations are in general of second order, quasilinear, but they degenerate into a first order nonlinear system in the case of two-dimensional problems with transverse magnetic field. For this system we obtained conditions of its being hyperbolic (evolutionary) and found characteristic velocities, when the exchange parameter is small. In investigations of axisymmetric plasma flow in coaxial channels of plasma accelerators we state more precisely the boundary conditions at the electrodes in regimes when the electric current is transferred by electrons or by ions. To simulate the Hall boundary layers near electrodes the equations must include a high finite plasma conductivity. 
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     author = {K. V. Brushlinskii and T. A. Ratnikova},
     title = {Some problems on the two-fluid {MHD} with a~transverse magnetic field},
     journal = {Matemati\v{c}eskoe modelirovanie},
     pages = {75--90},
     publisher = {mathdoc},
     volume = {8},
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     year = {1996},
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K. V. Brushlinskii; T. A. Ratnikova. Some problems on the two-fluid MHD with a~transverse magnetic field. Matematičeskoe modelirovanie, Tome 8 (1996) no. 2, pp. 75-90. http://geodesic.mathdoc.fr/item/MM_1996_8_2_a7/