Patching collisionless plasma and sheath solutions to approximate the plasma-wall problem

This paper is concerned with patching the plasma and the sheath solutions for collisionless ions, in order to approximate the full solution of the plasma-wall problem from the center to the wall. A method to find an adequate patching point is developed, and analytic expressions for the plasma characteristics at the patching point are given. The patched solution gives a good approximation of the full solution and can replace the full solution for all practical purposes. The method presented in this paper does not depend on any parameter and can, therefore, be used even when the solution of the plasma-wall problem cannot be computed numerically.