Directed Electron Velocity Distributions in Rare Gas Discharges Using Guard Ring Probes

Abstract

An experimental technique for determining detailed properties of anisotropic electron velocity distributions is described. For a planar Langmuir probe it is shown that g(v_z) = -[(m^(∂)J_(p))/(e^(2∂)V_(p))] where v_z = √[2(e/m)V_p] and g(v_z) gives the density of electrons with velocities normal to the probe in the range v_z to v_z + dv_z. This expression is valid for any distribution function making it possible to study anisotropies merely by changing the orientation of the probe. If the distribution function is isotropic the above expression is valid for cylindrical and small spherical probes as well. This technique is applied to the measurement of the directional properties of electron velocity distributions in the positive column of neon and helium hot cathode discharges. The necessary planar probe consists of a 0.01 inch diameter circular probe surrounded by a 0.090 inch square guard-ring. The measured distributions were Druyvesteyn in form except that all electrons were shifted in energy (in the direction of the external field) by an amount proportional to Eλ(v_z). Here E is the magnitude of the external electric field and λ(v_z) the electron mean free path as a function of v_z. The experimental conditions are shown to be identical with those necessary in the derivation of the Druyvesteyn distribution.

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