The Low Pressure Plane Symmetric Discharge

It is shown that the low pressure plane symmetric plasma equation, using the collision-free model of Tonks and Langmuir, can be solved analytically. Simple expressions are obtained for the mean velocity and the mean square velocity of the ions, and for the wall potential with respect to the plasma. The conditions for the formation of a stable plasma-sheath boundary are briefly examined and a general criterion is obtained without considering any specific mechanism of ion transport. No assumptions are made regarding the energy distribution of the ions, and the result is therefore a refinement on Bohm's original criterion which was derived by assuming a monoenergetic ion flux. With the aid of the criterion developed in the present treatment conclusions are then drawn in the case of the collision-free model regarding conditions applying at the plasma boundary. The experimental results are found to be consistent with these theoretical conditions.