Three-dimensional particle-in-cell simulations of ion diodes on PBFA II

The authors are now using the 3-D particle-in-cell code QUICKSILVER to simulate applied-B ion diode configurations on the PBFA II accelerator. These simulations are done in cylindrical coordinates, using realistic diode geometries, together with the externally applied magnetic field actually used for the given geometry. The external field itself is azimuthally symmetric, since it is computed with a 2-D magnetic diffusion solver, but the dynamic field solver and particle kinematics are fully three-dimensional. Qualitatively, the results of these new simulations are similar to those done previously in Cartesian coordinates with a uniform applied field. They show an instability with two distinct phases. Early in time, a diocotron instability grows rapidly, driven by the E x B drift of the electrons in the sheath. The frequency of the diocotron instability, f, is high compared to the ion transit time, τi, and the resulting beam divergence is low (10--15 mrad). However, as the diode continues to evolve towards higher current enhancement, a transition to a lower frequency (fτi < 1) phase with an unacceptably high beam divergence (> 30 mrad) occurs. Preliminary results of these new simulations indicate that the overall performance of the diode is sensitive to the magnetic field shape. Previous 2-D simulations have already shown that the axial profile of the ion beam current density depends strongly on the field shape. In the 3-D simulations, the instability is sensitive to the field shape, which affects not just the beam divergence, but the electron distribution in the diode. This in turn affects diode efficiency, impedance and current uniformity. They will present results of these simulations, and comparison with experimental data from PBFA II