Continuum electrostatic probe theory with magnetic field

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Abstract
A continuum electrostatic probe theory is developed for a slightly ionized, collision-dominated plasma in the presence of a uniform magnetic field. The governing equations are nonlinear and coupled. A quasilinearization technique is applied to solve the equations numerically using finite difference approximations, in the case of spherical probes larger than a Debye length, the magnetic field being weak. When the probe size is not very large or the probe potential is small, the detailed analysis of the sheath is not necessary. But when the probe potential is large, the sheath needs a separate treatment. The sheath equations are essentially one-dimensional and the magnetic field parameters do not appear explicitly. In the absence of an analytic solution for either the sheath or the main region, both solutions are matched numerically in an overlap region. The effect of magnetic field on the nature of the distribution of the charged particles and the potential in space and on the probe surface is investigated in detail. The phenomenon of “potential overshoot” in the case of a probe biased near plasma potential is clearly revealed. A few representative current-voltage characteristics at various magnetic fields are drawn. A systematic procedure for the interpretation of the probe characteristics is developed.