The ionization length in plasmas with finite temperature ion sources
Jelić, Nikola ...
The ionization length is an important quantity which up to now has been precisely determined only in plasmas which assume that the ions are born at rest, i.e., in discharges known as cold ion-source ...plasmas. Presented here are the results of our calculations of the ionization lengths in plasmas with an arbitrary ion source temperature. Harrison and Thompson (H&T) [Proc. Phys. Soc. 74, 145 (1959)] found the values of this quantity for the cases of several ion strength potential profiles in the well-known Tonks-Langmuir [Phys. Rev. 34, 876 (1929)] discharge, which is characterized by cold ion temperature. This scenario is also known as the singular ion-source discharge. The H&T analytic result covers cases of ion sources proportional to exp() with the normalized plasma potential and =0,1,2 values, which correspond to particular physical scenarios. Many years following H&T's work, Bissell and Johnson (B&J) [Phys. Fluids 30, 779 (1987)] developed a model with the so-called warm ion-source temperature, i.e., regular ion source, under B&J's particular assumption that the ionization strength is proportional to the local electron density. However, it appears that B&J were not interested in determining the ionization length at all. The importance of this quantity to theoretical modeling was recognized by Riemann, who recently answered all the questions of the most advanced up-to-date plasma-sheath boundary theory with cold ions [K.-U. Riemann, Phys. Plasmas 13, 063508 (2006)] but still without the stiff warm ion-source case solution, which is highly resistant to solution via anz available analytic method. The present article is an extension of H&T's results obtained for a single point only withion source temperature Tn=0 to arbitrary finite ion source temperatures. The approach applied in this work is based on the method recently developed by Kos et al.
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