Kinetic Solvers with Adaptive Mesh in Phase Space

An Adaptive Mesh in Phase Space (AMPS) methodology has been developed for solving multi-dimensional kinetic equations by the discrete velocity method. A Cartesian mesh for both configuration (r) and velocity (v) spaces is produced using a tree of trees data structure. The mesh in r-space is automatically generated around embedded boundaries and dynamically adapted to local solution properties. The mesh in v-space is created on-the-fly for each cell in r-space. Mappings between neighboring v-space trees implemented for the advection operator in configuration space. We have developed new algorithms for solving the full Boltzmann and linear Boltzmann equations with AMPS. Several recent innovations were used to calculate the discrete Boltzmann collision integral with dynamically adaptive mesh in velocity space: importance sampling, multi-point projection method, and the variance reduction method. We have developed an efficient algorithm for calculating the linear Boltzmann collision integral for elastic and inelastic collisions in a Lorentz gas. New AMPS technique has been demonstrated for simulations of hypersonic rarefied gas flows, ion and electron kinetics in weakly ionized plasma, radiation and light particle transport through thin films, and electron streaming in semiconductors. We have shown that AMPS allows minimizing the number of cells in phase space to reduce computational cost and memory usage for solving challenging kinetic problems

Ionization waves (striations) in low-current DC discharges in noble gases obtained with a hybrid kinetic-fluid model

A hybrid kinetic-fluid model is used to study ionization waves (striations) in a low-current plasma column of DC discharges in noble gases. Coupled solutions of a kinetic equation for electrons, a drift-diffusion equation of ions, and a Poisson equation for the electric field are obtained to clarify the nature of plasma stratification in the positive column and near-electrode effects. A simplified two-level excitation-ionization model is used for the conditions when the nonlinear effects due to stepwise ionization, gas heating, and Coulomb interactions among electrons are negligible. It is confirmed that the nonlocal effects are responsible for the formation of moving striations in DC discharges at low plasma densities. The calculated properties of self-excited waves of S, P, and R types in Neon and S type in Argon agree with available experimental data. The reason for Helium plasma stability to stratification is clarified. It is shown that sustaining stratified plasma is more efficient than striation-free plasma when the ionization rate is a nonlinear function of the electric field. However, the nonlinear dependence of the ionization rate on the electric field is not required for plasma stratification. Striations of S, P, and R types in Neon exist with minimal or no ionization enhancement. Effects of the column length on the wave properties have been demonstrated in our simulations

Profiling and modeling of dc nitrogen microplasmas

This article explores electric current and field distributions in dc microplasmas, which have distinctive characteristics that are not evident at larger dimensions. These microplasmas, which are powered by coplanar thin-film metal electrodes with 400-μm minimum separations on a glass substrate, are potentially useful for microsystems in both sensing and microfabrication contexts. Experiments in N2N2 ambient show that electron current favors electrode separations of 4 mm at 1.2 Torr, reducing to 0.4 mm at 10 Torr. The glow region is confined directly above the cathode, and within 200–500 μm of its lateral edge. Voltage gradients of 100 kV/m exist in this glow region at 1.2 Torr, increasing to 500 kV/m at 6 Torr, far in excess of those observed in larger plasmas. Numerical simulations indicate that the microplasmas are highly nonquasineutral, with a large ion density proximate to the cathode, responsible for a dense space-charge region, and the strong electric fields in the glow region. It is responsible for the bulk of the ionization and has a bimodal electron energy distribution function, with a local peak at 420 eV. © 2003 American Institute of Physics.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/69877/2/JAPIAU-94-5-2845-1.pd