A method for calculating near-optimum ion-extractor profiles

A process and program have been developed to interactively calculate the near-optimum electrode profiles for high-perveance ion-extraction systems. A Mathcadtrade program determines electrode profiles for high-current (high-perveance) high-quality beams. The program input starts with key parameters: plasma density, estimated mix of ions, extraction voltage, total current, plus desired output beam size and divergence. The computations simulate a spherically convergent extraction system that simultaneously minimizes the aberrations from the exit aperture while directly compensating for both the exit aperture de-focusing lens, and internal space charge in the beam. The program outputs cylindrical (r,z) coordinates of the emission and extractor electrodes, plus displays the beam perveance and output beam size and divergence. This technique was used successfully in multiple projects over the past 25 years. Electrode shapes used in past hardware tests are examined with the successive over relaxation (SOR) code PBGUNS in an accompanying paper.