Monte-Carlo formulation of both time dependent and stationary ray-tracing methods including cross-beam energy transfer, Raman and Brillouin scatterings

A complete theoretical understanding of inertial confinement fusion experiments requires a quantitative description of all laser/plasma phenomena at stake such as Brillouin and Raman scattering, cross-beam energy transfer (CBET), and including the laser-smoothing techniques. This level of description is alas too expensive in regards of the simulation size.
To reduce the problem, a popular method consists in approximating the Maxwell equations with the WKB envelop solution, that provides the eikonal and transport equations. The latter are then solved using the “ray-tracing approach”. However, this Monte-Carlo (MC) method, as implemented in many hydrodynamic codes, is not clearly formulated and may appear as “intuitive”. As a result, it is often difficult to self-consistently include other effects than the laser energy deposition.
We have formulated two MC methods in order to solve the time dependent and the stationary eikonal and transport equations. The energy exchange between lasers, as well as Raman and Brillouin scatterings in the convective regime, are described as “collisions” or more exactly as ray creation/destruction. The method is fast and the solutions have been validated with particle-in-cell simulations and with known analytical solutions in homogeneous plasma.