AN ANALYSIS OF CYLINDRICAL BORIS SOLVER FOR TYPICAL PARAMETERS OF TWO-DIMENSIONAL PENNING ION SOURCE SIMULATION

Abstract

The cylindrical Boris solver is analyzed for typical two-dimensional Penning ion source simulation parameters. The analysis comprises the solver's accuracy and stability, especially for the latter simulation stages, typically after about 30 μs. The simulation is done for two cases; the first is a gyration simulation with a homogenous magnetic field, and the second uses the same setup as the Penning simulation. Several investigated quantities to determine the error are the radial position, axial position, and velocity magnitude (or kinetic energy). The error is calculated by comparing the result with the reference result from the exact solver with an incredibly small time step width, dt = 10-15 s. The result shows a discrepancy between cylindrical and cartesian Boris solvers. The velocity magnitude of the particle decays as time goes on for the cylindrical Boris solver, especially when the particle is close to the z-axis, an error not found on the cartesian solver. For typical Penning simulation parameters, the trajectory of individual particles is way off the reference trajectory. However, the mean position is relatively close to the reference compared to the dimension of the simulation domain. The kinetic energy is also relatively accurate, with a similar slow decay related to the deteriorating non-axial velocity components previously observed in the first case. Thus, for the simultaneous simulation of millions of particles, there should not be any significant observable difference in actual Penning simulation compared to Penning simulation with reference time step width.