Density Distributions in Cylindrical and Rectangular Plasma Sources

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Abstract
The plasma density distributions in plasma sources with cylindrical and rectangular configurations are obtained by solving the diffusion equation based on a plasma model. In this model, the initial density distribution is given at the upper stream of each source, and the side walls of the plasma chambers are surrounded by magnetic multipole fields in order to obtain a uniform high-density plasma on the target wall. The results give the density distributions in the sources and the plasma particle fluxes flowing into the target walls. The forms of the initial density distribution in the upper stream of each source are also discussed. Calculated examples are shown for cylindrically unsymmetric and rectangular configurations. The equations derived in this paper are useful for the design of plasma sources capable of generating a uniform high-density plasma over a wide area.