The perveance function [particle accelerators]

A method of analyzing the divergence characteristics of particle beams that utilize a Pierce geometry accelerator is described. The technique combines measurements of gradient grid current and arc current to develop an analytic expression, (perveance function), that could prove beneficial to beam operations. Unlike thermocouple or Doppler measurements of beam divergence, which only indicate the magnitude of the beam angle, the perveance function exhibits bipolar linearity with arc current changes. Additionally, the value of the arc current at which the perveance function equals zero is the operating point for minimum beam divergence. As a result, a single measurement with the perveance function can indicate whether the beam is overfocused or underfocused, and also determine the change in the magnitude and direction of the operating point to achieve optimum focus. This method is superior to present procedures, which tune the source by hunting for the minimum divergence. The perveance function is a relatively simple relationship that can be easily realized in hardware electronics or computer software