Ion-Temperature-Sensitive Effect in Transient Langmuir Probe Response

A theory is presented for a method, recently proposed by Hester and Sonin, of determining the ion temperature in a plasma by measuring the transient current to a cylindrical Langmuir probe after applying a potential Vp(−eVp≫κTe) under conditions where collection is collision free and the ratio of probe radius to Debye length is small. The ion component of the current does not approach its final steady-state value monotonically, but exhibits a strong, ion-temperature-dependent overshoot in the first few ion-plasma periods following the biasing of the probe. Analytical formulas are derived for the case of a Maxwellian plasma, and convenient graphical results are presented. The possible masking of the overshoot by a transient displacement current is discussed; it is shown how to avoid such displacement effects. For the overshoot to be sensitive to the ion temperature Ti, the probe must be near plasma (zero) potential before applying Vp(eVp−<0.1κTe, Vp− being that initial potential); this is not a drawback of the method, but, on the contrary, it can be used to accurately determine plasma potential along with Ti.