Simulating Magnetized Laser-Plasma Interaction by Numerical Solutions of Three-Wave Interaction and Advection

Magnetized laser-plasma interactions (MagLPIs) have a broad set of applications in photonics and optics, and even more importantly for the rapidly growing field of nuclear fusion. Lasers are often used to compress and heat fusion fuel in inertial confinement, and recent breakthroughs using magnetic fields to enhance inertial confinement devices need better models for understanding MagLPIs with strong fields and dense plasmas. Recent theoretical advances have allowed us to model these interactions using three-wave-equations in the slowly varying amplitude limit. My research is focused on developing a numerical solver for these equations using several algorithms. To benchmark the algorithms, I have compared numerical results to analytical ones in special circumstances where analytical solutions can be found. For the nonlinear interaction terms, we use a Hamiltonian splitting algorithm, which has good conservation properties. For the advection terms, first and second order upstream finite difference methods produced good approximate results. Better results can be obtained using the Monotonic Upstream-centered Scheme for Conservation Laws (MUSCL), particularly in cases of sharp changes to the wave envelope.