Phase Space Analysis of Hybrid Kinetic-MHD Simulations

We present new phase space analysis of energetic particle simulations using the hybrid kinetic-MHD option\footnote{C.~C.~Kim, \textit{PoP}, \textbf{15} 072507 (2008)} in the NIMROD code.\footnote{C.~R.~Sovinec et al., \textit{JCP}, \textbf{195} 355 (2004)} The intent of these new $\delta\!f$ PIC\footnote{S.~E.~Parker and W.~W.~Lee, \textit{PFB}, \textbf{5} 77 (1993)} phase space diagnostics is to help elucidate the physics of energetic particle interactions with MHD modes. In particular we will examine the evolution of $\delta\!f$ in $(v_\parallel,v_\perp)$ space and convolution of the terms in the $\delta\!f$ evolution equation. The contributions from passing and trapped subpopulations are also examined and both are shown to contribute significantly to energetic particle-MHD mode evolution. This phase space analysis reveals that the region near the trapped/passing boundary is a key region of activity. The analysis is in its developmental stage and primarily phenomenological, but continued development and refinement will mature these tools to quantitative and potentially predictive measurements.