Charge Conserving Current Weights for PIC

Particle in cell (PIC) codes successfully model devices containing charged particles in electromagnetic fields. The motion of the particles generates currents which must be weighted to the cell edges in a charge conserving manner. The Villasenor-Buneman scheme accomplishes the current weighting for cubic cells. However, the use of cubic cells results in problematic staircase approximations to surfaces that are not aligned to one of the grid axes. PIC codes with alternate cell shapes are proposed to avoid the staircase approximation; thus, current weighting schemes are needed for arbitrary cell shapes. The Whitney 1-form basis functions used with the finite element method are used to derive charge conserving current weights on the alternate cell shapes. The presentation will describe the derivation of current weights and proof that the result is charge conserving. The derivation is applied to cubes, prisms, and tetrahedrons in 3-D, and to rectangles and triangles in 2-D. When applied to cubes, the derivation recovers the well-known Villasenor-Buneman current weights.