Simple Way to Obtain the Velocity Distribution of the Electrons in Gas Discharge Plasmas from Probe Curves

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Abstract
Until now no simple technique of determining the velocity- or energy-distribution function of the electrons in gas discharge plasmas was known. Here a method of quickly finding this function from probe curves (preferably automatically plotted ones) is described. It is shown that for a given probe current-voltage curve J(U) the energy distribution function g(U) of the electrons is proportional to a simple function which may be graphically determined from J(U). This function is U−½ΔJ0/ΔU, where ΔJ0 is the distance between the intersections of the two tangents to the probe curve J(U) at the ends of the voltage interval ΔU with the current axis, and U is the (retarding) voltage in the middle of ΔU. It can be used for a determination of the energy distribution g(U) in a simple and straightforward one-step procedure which is faster and in practice more accurate than the two-step procedure previously used for finding g(U) by means of ∂2J/∂U2. A set of probe curves which stem from a Maxwellian distribution is evaluated in both the conventional and the new way. The electron temperatures obtained check excellently. A set of probe curves from strongly non-Maxwellian distributions in a Ne fireball discharge is evaluated. The presence of a fast and a slow group of electrons is revealed. The results are interpreted to some extent. Errors and dependability are discussed.

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