Magnetic insulation of extraction Applied-B ion diodes

The difference in the operation of extraction geometry versus radial geometry Applied-B ion diodes is explained through the use of a general magnetic insulation condition for cylindrically symmetric ion diodes which is expressed in terms of the magnetic stream function. We find that Applied-B extraction geometries attempted so far have suffered from a magnetic field configuration defect which explains their rather poor performance. We present solutions to the extraction Applied-B ion diode problem, as well as 2D, electromagnetic particle-in-cell simulations of an example solution.