Robert S. Spangler

Parallel inhomogeneous flows in a thermally anisotropic plasma: The electrostatic ion-acoustic branch

The linearized dispersion relation describing waves in a plasma having a uniform magnetic field, uniform density, and inhomogeneous parallel (to the magnetic field) flow is generalized to include thermal anisotropy (Ti⊥/Ti∥), a key feature existing in many space and laboratory plasmas. The growth rate and the real frequency at which the maximum growth rate occurs for the ion acoustic mode increases with increasing Ti⊥/Ti∥. The propagation angle, with respect to the background magnetic field, for ion acoustic waves is shown to depend on Ti⊥/Ti∥. Also presented is a generalized calculation of experimentally relevant perturbed distribution functions to include shear in the field-aligned flow.

Evidence for thermal anisotropy effects on shear modified ion acoustic instabilities

Inclusion of thermal anisotropy effects is shown to be required to describe recently reported experimental measurements as shear-modified, ion acoustic instabilities. For the reported experimental conditions, isotropic theory yields no instability growth that depends on the magnitude of the shear in the parallel flow.

Poiseuille advection of chemical reaction fronts: Eikonal approximation

An eikonal equation including fluid advection is derived from the cubic reaction-diffusion-advection equation, and is used to investigate the speeds and shapes of chemical reaction fronts subject to Poiseuille flow between parallel plates. Although the eikonal equation is usually regarded as valid when the front thickness is small compared to the radius of curvature of the front and to the size of the system, it is also found to be valid when the reaction front is thick with respect to the gap width. This new regime of applicability of the eikonal equation is consistent with its derivation, which requires only that the reaction front curvature and the fluid velocity vary negligibly across the front. The front distortion and the front speed increase with increasing η, defined as the ratio of the gap half-width to the reaction front thickness. Analytical limits of the front distortion and front velocity for small and large η are compared with general numerical results.