Abstract

VALDEBLANQUEZ, E. Legendre polynomial in space charge potentials for velocity analysers with spherical geometry. Rev. mex. fis. [online]. 2006, vol.52, suppl.3, pp.221-223. ISSN 0035-001X.

The analysis of space-charge effect in spherical geometries has been performed using kinetic theory. The current collected by central electrodes immersed in plasmas with a discriminant grid has been determined through the Poisson equation and truncated Maxwellian Distribution functions for the ions. We have assumed that the electrons are repelled by an entrance grid hold at a negative potential. This analysis leads to a strongly non linear dimensionless equation, where the lapalacian operator depends only of r and θ. The case of plane geometry was already published [8];, and a preliminary work in cylindrical geometry has been reported [4]. This equation has been solved approximately by expanding the above functions around the potential Φ_p, and the solution is given by the spherical Bessel functions and the Legendre polynomials.

Keywords : Space charge effects.

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