3D Self Magnetic Field Calculation in the Finite-Element Gun Code Michelle

Abstract

Summary form only given. Self-consistent three-dimensional (3D) self magnetic fields are desired for devices with relativistic beams or a 3D geometry, the latter including multiple beam guns and sheet beam guns. We have recently implemented a prototype 3D self magnetic field solver in the 2D/3D finite-element gun code MICHELLE. The implementation follows the proposal presented last year. We are still testing and developing the solver, but so far on a variety of tests it has met or exceeded our expectations, save one. The positive experience to date encourages us to continue developing the 3D solver and also to formulate and implement a 2D version of the solver. The solver employs the curl-curl formulation for the magnetic vector potential A using edge basis functions. The new current accumulation algorithm combined with MlCHELLE's unique particle tracker for unstructured grids is efficient and accurate. The conjugate gradient (CG) matrix solver works well because the source vector is compatible with the singular finite-element matrix. Boundary conditions are important for compatibility. Our solver requires the tangential component of A to be zero on the boundary, a condition equivalent to perfectly conducting walls. This is appropriate for short pulsed beams inside conducting drift tubes. The model must also be well posed: the boundary must be connected to provide a return path for current. Otherwise, the source vector may be incompatible. Numerical integration errors can also make the source vector incompatible, but compatibility is guaranteed with a modest number of integration points, as indicated by a theory that also applies to charge-conserving current accumulation in electromagnetic particle-in-cell codes