Laser ray tracing and power deposition on an unstructured three-dimensional grid

A scheme is presented for laser beam evolution and power deposition on three-dimensional unstructured grids composed of hexahedra, prisms, pyramids, and tetrahedra. The geometrical-optics approximation to the electromagnetic wave equation is used to follow propagation of a collection of discrete rays used to represent the beam(s). Ray trajectory equations are integrated using a method that is second order in time, exact for a constant electron-density gradient, and capable of dealing with density discontinuities that arise in certain hydrodynamics formulations. Power deposition by inverse-bremsstrahlung is modeled with a scheme based on Gaussian quadrature to accommodate a deposition rate whose spatial variation is highly nonuniform. Comparisons with analytic results are given for a density ramp in three dimensions, and a “quadratic-well” density trough in two dimensions.