Grid effects on velocity analyzers of variable geometry

Abstract

A complete theory of a planar electrostatic velocity analyzer is developed for the case of a discriminating grid composed of parallel cylindrical wires. Exact solutions for the potential distribution inside the analyzer and for the depletion of the discriminating potential in the grid plane are calculated by means of a Schwarz–Christoffel transformation. It is shown that the dependence of the collector current on the discriminating voltage deviates from the simple exponential law. The analysis shows the following effects: a stretching and displacement of the V axis of the characteristics and a decrease of the collector saturation current. A new expression to calculate the plasma temperature from the characteristic curve is given.