Effects of midplane density gradient in the propagation of High Harmonic Fast Waves considering high temperature anisotropy in the Scrape-Off Layer of NSTX-U

High-harmonic Fast Wave (HHFW) heating experiments in NSTX have shown that up to 60% of the injected power can be lost in the Scrape-Off Layer (SOL) when the density is above the fast wave cutoff density in front of the antenna, for which the fast wave is able to propagate into the plasma. This work models HHFW propagation in the SOL plasmas of NSTX-U using a 2D divertor SOL profile derived from the pressure assumption and the finite element temperature solution, which accounts for the high anisotropy of heat conduction in a 2D axisymmetric geometry. Previous HHFW modeling studies assume density is a function only of magnetic flux, decaying exponentially in the radial direction, which may be insufficient to accurately model the wavefield, especially in the divertor. In this work, the two-dimensional axisymmetric SOL temperature profile is first evaluated by solving the steady-state non-linear heat conduction equation, in which thermal conductivity depends on temperature, using a finite element approach in the Petra-M workbench. High-heat conduction anisotropy between the parallel and perpendicular direction to the background magnetic field is considered (κr = κ||/κ⊥ > 10^4). A 2D density profile is then obtained from a prescribed density profile at the outer midplane assuming pressure is uniform along a flux tube in the SOL from upstream to downstream. This approach results in density and temperature profiles in which the strong asymmetric nature of heat conduction between the parallel and perpendicular background magnetic field line is successfully captured. In particular, it is shown that for a parallel to perpendicular heat conduction anisotropy ratio of up to κr = κ||/κ⊥ = 10^8, the expected exponentially decaying temperature profile is obtained at the outer midplane, as well as the temperature-dependent thermal conduction profile along the flux tube, using a non-linear iterative solver with proper mesh refinement conditions. These numerical results demonstrate the capability of resolving 2D non-linear heat conduction equation in an arbitrary geometry and is particularly relevant for modeling heat conduction in the SOL of contemporary devices where the anisotropy ratio is in the range of κr = 106 to 108. Furthermore, this work focuses on investigating the effect of the SOL plasma density profile on parasitic HHFW propagation in the SOL. The simulation results show that the radial gradient of the density profile affects the wavefield propagation in the SOL. As the density profile broadens, the wavefield intensity and its poloidal extent are reduced in the SOL, and the core coupling is increased in the core. Similarly, as shown by collisional power deposition, which is used as a proxy for power absorption, the fraction of power deposited in the SOL decreases with a broadening profile. This result provides insights into the RF coupling physics, bridging our understanding between the low-harmonic fast wave and HHFW regimes.