Benchmarking magnetized coupling coefficients: Comparing particle-in-cell simulations with analytic solutions of three-wave equations in backscattering geometry

In the presence of a strong oblique magnetic field, three-wave coupling coefficients noticeably differ from their unmagnetized values. Instead of the familiar Raman and Brillouin couplings, three-wave interactions are now mediated by magnetized plasma waves, and the general formula for magnetized coupling coefficients remains to be benchmarked against numerical simulations. This study focuses on backscattering, where pump and seed lasers are counter propagating at an oblique angle with the background magnetic field. To benchmark the formula, particle-in-cell (PIC) simulations are carried out in the linear regime, where pump depletion is negligible. To extract the coupling coefficients and wave damping rates from PIC simulations, the seed intensity is scanned, and numerical results are fitted to analytic solutions of the linearized three-wave equations. The general solution to the linearized problem is derived systematically using Laplace transform, to allow for arbitrary initial and boundary conditions in a semi-infinite plasma domain, which matches the setup of PIC simulations. The numerically extracted coefficients agree reasonably well with analytical results for a wide range of magnetic field strengths and propagation angles in regimes where the analytic formulae are valid.