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

Abstract

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. (© 2014 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

Three species one-dimensional kinetic model for weakly ionized plasmas

“…The collision operators are constructed to satisfy the standards of conservative properties accounting for elastic collisions. Inelastic collision terms, as ionization or recombination process could be included in a straightforward manner as non-homogeneous source-sink terms 15,16 .…”

Propagator integral method for plasma physics kinetic equations with practical applications

“…The procedure to solve convective-diffusion equations is reviewed and studied in deep, extending the application presented in previous works, as [23,26,27]. Additionally, the method is extended for the first time to deal with new differential problems as pure convective or ordinary equations.…”

“…In that work, the semi-analytical Propagator Integral Method (PIM) [22][23][24][25][26][27] was used to solve a two species one-dimensional plasma (electrons and ions) close to a wall described by a drift-diffusion fluid model and accounting for the self-consistent electric field through the Poisson's equation. The main goal of this thesis is to apply the PIM to solve equations that commonly appear in the study of plasmas from a Kinetic Theory perspective, including convection-diffusion, purely convective problems or the Poisson's equation.…”

“…where L * (q ′ , t ′ ) is the same operator as in (2.1) but evaluated at source variables [22,23,45,49,52] and P τ = P τ (q; q ′ ) ≃ Π(q, t; q ′ , t − τ ) is the short-time approximation of the real unknown transition probability. The resolution of this problem is usually simple since parameters involved in it are formally constant.…”

“…In this chapter, some general procedure to include boundary effects is presented, but the general problem is far from being solved. Nevertheless, any method to include non-homogeneous boundary conditions should add an additional term to the advancing scheme, that includes the effect of the boundary to the advancing scheme as 6) where f (q, t + τ ) denotes the approximation to the real solution obtained by means of the short time approximation, τ ′ represents an intermediate time between t and t + τ , P τ −τ ′ accounts for the possible dependency of the propagator in short times and f B is the boundary term [23,52]. This term depends on the propagator and the method chosen to incorporate boundary conditions.…”