Analysis of Pulse Probe

概要

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A cuurent response of a Langmuir probe is analyzed theoretically when a step-wise voltage of a small amplitude is applied to the probe. The analysis is based on the linearized Bolt zman-Vlasov equations for electrons and ions, including collision terms, and Poissons equation, to which Fourie-Laplace transformations are applied with an initial condition that the energy distribution is Maxwellian befor the step voltage δVo is applied. The external electric field due to the presence of the finite probe potential is assumed to have a form as Eext (x, t) =- (δV/L) ·D (x), where δV is zero for t<0 and δVo for t≥0, L is a constant representing an effective penetration depth of the external field and D (x) is a function of x. The collision frequencies are assumed to be independent of the energies of the charged particles. The effect of Landau damping is taken into considerations. It is shown that, for an electron plasma, the current flowing into the probe is given approximately by δj (O, t) = δjo.e-νt sinωpt, where δjo is a constant proportional to δVo/L and the electron density, v and ωp are the collision frequency and the plasma frequency respectively. A discussion is also made on the current response for an electron-ion plasma.
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