  A careful study of plasma-material interactions is essential to understand
and improve the operation of devices where plasma contacts a wall. Key
contributions of this work include (i) novel continuum kinetic algorithms with
novel boundary conditions that directly discretize the Vlasov/Boltzmann
equation using the discontinuous Galerkin method, (ii) fundamental studies of a
plasma sheath physics with collisions, ionization, and physics-based wall
emission, and (iii) theoretical and numerical studies of the linear growth and
nonlinear saturation of the kinetic Weibel instability, including its role in
plasma sheaths. The continuum kinetic algorithm has been shown to compare well
with theoretical predictions of Landau damping of Langmuir waves and the
two-stream instability. Benchmarks are also performed using the electromagnetic
Weibel instability and excellent agreement is found between theory and
simulation. The role of the electric field is significant during nonlinear
saturation of the Weibel instability, which was not noted in previous studies.
A focus is put on understanding plasma sheath physics which is essential for
studying plasma-material interactions. Initial simulations are performed using
a collisionless model to match classical sheath theory and the Bohm criterion.
A collision operator and volumetric physics-based source terms are introduced
and effects of heat flux are briefly discussed. Novel physics-based boundary
conditions are developed and included in a general manner with the continuum
kinetic algorithm for bounded plasma simulations. These are the first continuum
kinetic simulations using self-consistent, wall emission boundary conditions
with broad applicability across a variety of regimes.
