Multiscale Modeling of a Short Relativistic Electron Bunch Interacting With Long Resistive Structures at Cryogenic Temperatures

This paper presents multiscale modeling of electromagnetic interaction between a short relativistic electron bunch and long resistive structures at cryogenic temperatures. The considered physical problems include multiple spatial scales such as structure, bunch size, and skin depth. In order to simulate such multiscale problems, a directionally implicit finite-difference time-domain (FDTD) scheme based on Maxwell's equations in the presence of a relativistic bunch current is developed by using a magnetically mixed Newmark-leapfrog formulation. With the so-called magic time step, the resultant FDTD scheme has no accumulation of numerical dispersion errors for all frequencies in the direction of the motion. In order to model the anomalous skin effect (ASE) of metals in time domain, the developed scheme is combined with a rational function approximation of the first-order Leontovich surface impedance boundary condition. The scheme is verified in comparison with analytical approaches. ASE resistive wall effects are assessed for beam pipes and a step collimator.