Three-Dimensional Mode Conversion Associated with Kinetic Alfv\'en Waves

We report the first three-dimensional (3-D) ion particle simulation of mode conversion from a fast mode compressional wave to kinetic Alfv\'en waves (KAWs) that occurs when a compressional mode propagates across a plasma boundary into a region of increasing Alfv\'en velocity. The magnetic field is oriented in the $\hat{z}$ direction perpendicular to the gradients in the background density and magnetic field ($\hat{x}$). Following a stage dominated by linear physics in which KAWs with large wave numbers $k_x \rho_i\sim 1$ (with $\rho_i$ being the ion Larmor radius) are generated near the Alfv\'en resonance surface, the growth of KAW modes with $k_y \rho_i \sim 1$ is observed in the nonlinear stage when the amplitude of KAWs generated by linear mode conversion becomes large enough to drive a nonlinear parametric decay process, accompanied by a simultaneous excitation of zonal flow modes with similar large $k_y$. The simulation provides a comprehensive picture of mode conversion and the fundamental importance of the 3-D nonlinear physics to transfer energy to large perpendicular $k_y$ modes, which can provide large transport across plasma boundaries in space and laboratory plasmas.