Calculation of incident ion distribution in a rectangular hollow cathode in magnetic field

Incident ion distribution inside a rectangular hollow cathode in a uniform magnetic field is studied analytically. The analysis shows that the ion distribution on one sidewall is not interfered by the other sidewall when the depth and width of the cathode are equal, and the ion distribution on the bottom surface related to the depth of the cathode and the number of ions on the bottom surface decrease monotonically from the centre to the sidewall.