Tests of A 3D Self Magnetic Field Solver in the Finite Element Gun Code Michelle

We present some tests of a new prototype three-dimensional (3d) self magnetic field solver in the finite-element gun code MICHELLE. The first test is a fixed ray of current in a square drift tube. The magnetic field converges linearly or quadratically with element size when using a linear or quadratic basis, respectively. The second test is a relativistic axisymmetric laminar beam expanding freely in a round drift tube. The self-consistent solution for the particle trajectories is accurate. The third test transports a beam in a uniform external magnetic field. There is no indication of beam filamentation. The computational costs for the self magnetic field solver are higher than for the Poisson solver, but the costs are still acceptable in many applications.