Precise Approximate Solution for the Bohm Sheath Potential

The Poisson equation for the plasma sheath potential near a wall, leads to a nonlinear differential equation, whose analytic solution is not known. The usual approximation taking only the first non-null term does not give good accuracy. Other approximations taken two additional terms are better, but they fail to give good accuracy in the intermediate region. Here a new analytic approximated solution is presented with much higher accuracy, and more precise results, not only near and far away of the wall, but also in the transition region. Two figures showing these new analytic solutions as a function of the relevant parameters are presented. The advantages of the present solution compared with those of pervious works are shown.