Causes and cures for errors in the simulation of ion extraction from plasmas

For many years, computer programs have been available to simulate the extraction of positive ions from plasmas. The results of such simulations may not always agree with measurements. There are different reasons for this: the mathematical formulation must match with the simulated physics, the number of meshes must be high enough to correctly take into account the nonlinear space charge in the sheath, and ray tracing must be done in sufficiently small steps, using numerically correct field components and partial derivatives. In addition to these hidden problems the user may create errors by a wrong choice of parameters, which are not matching the assumptions of the mathematical formulation. Examples are the use of a positive ion extraction program for the extraction of negative ones, the choice of a wrong angle between the plasma electrode and the beam boundary in the vicinity of the meniscus, and the use of too few trajectories. The design of extraction electrodes generally has the aim to optimize the optical properties and the current of the ion beam. However, it is also important to take into account the surface fields in order to avoid dark currents and sparking.