Characteristic behavior of the sheath formation in thermal plasma

Abstract

The plasma sheath equation, based on the quasipotential analysis, has been derived in a plasma taking finite ion temperature into account with a view to showing the characteristic behavior of the sheath formation in front of the electron absorbing wall. The derived Sagdeev potential equation, under small amplitude approximation, describes the Bohm sheath criterion, which enables one to find the required condition for the formation of sheath in plasmas. Later, the sheath equation is completely solved numerically by using the fourth-order Runge–Kutta method to yield the characteristic features of the potential variation in the sheath region. The main goal is to determine the sheath thickness and the potential variation in the sheath region and to compare the variation with those in cold ion plasma. Again, in the higher potential region, an improved Child’s law has been derived and the potential variation has been estimated numerically, which shows that the improved Child’s law improves the results as compared to that by Child’s law.