Implementation of the logical sheath boundary condition in the COGENT code

Accurate modeling of the boundary sheath layer in plasma simulation necessitates addressing the fine-scale features of the sheath region. These scales are typically much smaller than the characteristic length scales of the plasma bulk, therefore including a sheath region in a numerical model would significantly increase the cost of simulations. To overcome these difficulties, the logical sheath boundary condition (BC) is used where the sheath is replaced by a boundary potential that reflects fast electrons and enforces the total electron and ion current through the boundary to be equal. Implementation of the logical sheath BC in the finite volume COGENT code requires assigning proper values of the probability distribution function (PDF) in the ghost cells, since the fluxes on the boundary cell faces are computed based on the values of the PDF in nearby cells. This procedure depends on the advection scheme used in the code and has been implemented and tested it for first and third order upwind schemes. When electrons are reflected by the sheath potential, it inevitably yields to formation of a sharp interface of the PDF in the velocity space. That in turn leads to Gibbs oscillations when high order advection schemes are used. Different approaches for smearing the interface and mitigating the oscillations are discussed.