Analytical Solutions of Space Charge Problems for Different Geometries Including Collisions

Space charge effects are very important in vacuum electronics and plasma boundary interactions and desing of plasma systems. Here, a new solution technique is presented for finding analytic solutions to the nonlinear Poisson equation with a single charge species. Using this technique, currents, current density, sheath lengths, Debye lengths are obtained for collisional and collisionless charge transport in one dimensional Cartesian , cylindrical and spherical system. The method is also applicable to other nonlinear differential equations having power-like solutions.