Propagator Computational Method for Drift-Diffusion Equations to Describe Plasma-Wall Interaction

Plasmas evolve under sharp conditions such as localized currents, charge separation and absorption or emission of particles. The plasma-wall interaction is one of these singularities. Numerical methods based upon differences usually fail under these abrupt boundary conditions leading to new spurious noise and singularities of numerical nature. Here, we extend the path-sum integral numerical method to account for abrupt boundary conditions in plasma drift-diffusion equations. The boundary-path-integral solution also shows the advantages of the smoothing affects of the diffusive short-time propagators for unbounded domains. The proposed scheme is free of artificial numerical smoothing functions to mask sharp behaviours. This stable, robust and grid-free algorithm is applied to test cases of plasma-wall interaction with an advancing scheme that simultaneously copes with disparate electron and ion time scales.