Investigating Stationary Phase Violations in Kinetic RF Simulation of Real Plasmas

\renewcommand{\vec}[1]{\mathbf{#1}} The standard approach to linear, kinetic RF simulation in the ion-cyclotron and lower-hybrid frequency regimes in fusion plasmas utilizes the Fourier spectral method to capture the non-local plasma response [e.g., 1]. This response, i.e., the plasma current $\vec{j}_p$, is related to the wave electric field through a dielectric tensor $\bar{\sigma}$ for each Fourier mode $\vec{j}_p(\vec{k})=\bar{\sigma}(\vec{k})\cdot\vec{E}(\vec{k})$. $\bar{\sigma}$ is typically derived by solving the linearized Vlasov equation via the method of characteristics assuming stationary phase, constant amplitude electric field modes along those characteristics (i.e., a single $\vec{k}$ along unperturbed particle trajectories). This assumption is violated in real device magnetic field configurations. Here we examine the impact of variations in $\vec{k}$ along characteristics due to the poloidal magnetic field in Tokamak devices using the {\sc{Kinetic-j}} code [2]. We calculate $\vec{j}_p$ accounting for the variations in $\vec{k}$, compare with the analytic result, and discuss possible implications for present kinetic spectral RF codes. \\[4pt] [1] Jaeger E.F. et al., Phys. Rev. Lett. 90, 195001 (2003)\\[0pt] [2] Green D. L., http://meetings.aps.org/link/BAPS.2012.DPP.TP8.66