Axisymmetric Charge-Conservative Electromagnetic Particle Simulation Algorithm on Unstructured Grids: Application to Microwave Vacuum Electronic Devices

摘要

We present a 2.5-dimensional charge-conservative electromagneticparticle-in-cell (EM-PIC) algorithm optimized for the analysis of vacuumelectronic devices (VED) with cylindrical symmetry (axisymmetry). We explorethe axisymmetry present in the device geometry, fields, and sources to reducethe dimensionality of the problem from 3D to 2D. Further, we explore`transformation optics' principles to map the original problem in polarcoordinates to an equivalent problem on Cartesian coordinates with an effective(artificial) inhomogeneous medium introduced. The resulting problem in themeridian plane is discretized using an unstructured 2D mesh consideringTE-polarized fields and properly scaled charges. EM field and source variables(node-based charges and edge-based currents) are expressed as differentialforms of various degrees, and discretized using Whitney forms. Using leapfrogtime integration, we obtain a mixed finite-element time-domain scheme for thefull-discrete Maxwell's equations. We achieve a local and explicit time-updatefor the field equations by employing the sparse approximate inverse (SPAI)algorithm. Interpolating field values to particles' positions for solvingNewton-Lorentz equations of motion is also done via Whitney forms. Particlesare advanced using the Boris algorithm with a relativistic correction. In thescatter step, we apply a radial scaling factor on top of a charge-conservingscatter scheme tailored for 2-dimensional unstructured grids. As validationexamples, we demonstrate simulations that investigate the physical performanceof VEDs designed to harness particle bunching effects arising from the coherent(resonance) Cerenkov electron beam interactions within micromachined slow-wavestructures.