Numerical simulations for evaluation of EBW Heating development in LTX-$\beta$

The electrostatic Electron Bernstein wave (EBW) can propagate at frequencies near the electron cyclotron frequency throughout the over dense plasma of a Spherical Tokamak but not in vacuum or low-density extreme edges. A scheme to couple to the wave exploits physics that allows X-mode or O-mode wave to mode convert to an EBW at the plasma edge. The mode conversion efficiency is expected to sensitively depend on the electron density scale length (L$_{n}$) at the Upper Hybrid Resonance (UHR) layer with a theoretical maximum of 100\%. Full wave modelling of the O-X coupling in LTX-$\beta$ shows that at a moderate edge density, an O mode launched with finite k$_{||}$ gives optimized coupling efficiency greater than 65\%. At very steep edge density profiles, a normal X mode launch gives highest coupling. With a recently upgraded toroidal field capability to B$_{0}$ $\leq$ 3.4 kG in LTX-$\beta$, a 9.3 GHz launch frequency allows a range of narrow heat deposition across the entire minor radius. Genray ray tracing of EBW propagation launched at the UHR layer just inboard of the LCFS yields a span of the radial positions at which localised deposition occurs – core deposition at the fundamental cyclotron resonance for B = 3.0 kG and an edge deposition at radius r/a $>$ 0.7 for B = 2.05 kG.