Determination of axial steady-state potential distributions in collisionless single-ended Q-machines

A method is presented which permits one to reliably determine axial steady-state potential distributions in collisionless single-ended plasmas. The method requires standard measurements of plasma parameters at negative cold-plate biases, whence the (usually unstable) steady-state conditions at positive biases can be predicted by means of a simple theoretical extrapolation. In contrast to some models used in the literature, only two types of potential distributions are found to be possible at large positive cold-plate biases. A qualitative discussion of grid effects leads to the conclusion that a grid is equivalent to a massive cold plate only in the saturation regime of its current-voltage characteristics.