3D simulations of an electrostatic quadrupole injector

Analysis of the dynamics of a space charge dominated beam in a lattice of electrostatic focusing structures requires a full three‐dimensional code that includes self‐consistent space charge fields and the fields from the complex conductor shapes. The existing WARP3d code, a particle simulation code which has been developed for HIF applications, contains machinery for handling particles in three‐dimensional fields. A successive overrelaxation field solver with subgrid‐scale placement of boundaries for rounded surfaces and four‐fold symmetry has been added to the code. The electrostatic quadrupole (ESQ) injector for the ILSE accelerator facility being planned at Lawrence Berkeley Laboratory is shown as an application. The issue of concern is possible emittance degradation because the focusing voltages are a significant fraction of the particles’ energy and because there are significant nonlinear fields arising from the shapes of the quadrupole structures.