Fully-relativistic electron Bernstein wave current drive simulations in the STEP spherical tokamak

Abstract

Electron Bernstein waves (EBWs) are theorised to efficiently drive current in spherical tokamak power plants, e.g. Spherical Tokamak for Energy Production (STEP). At high temperatures ($T_e \gtrsim 4\,$keV), relativistic effects can significantly impact wave propagation. This work presents relativistic calculations of EBW wave propagation, damping, and current drive (CD) in a conceptual STEP plasma. Kramers-Kronig relations are exploited to efficiently evaluate the fully-relativistic dispersion relation for arbitrary wave-vectors, leading to a $> \! 50$x speed-up compared to previous efforts. Current drive efficiency is calculated using both linear and quasilinear codes. Thus, for the first time, large parametric scans of fully-relativistic EBW CD simulations are performed through ray-tracing. In STEP, three main classes of rays are identified. The first class propagate deep into the core ($\rho < 0.5$), but exist only if relativistic effects are accounted for. They damp strongly at the fundamental harmonic on nearly-thermal electrons and thus drive little current. A second class of rays propagate to intermediate depths ($\rho \approx 0.3 - 0.7$) before damping at the 2nd harmonic. Their CD efficiencies are significantly altered due to relativistic changes to trajectory and polarisation. The third class of rays damp strongly far off-axis ($\rho > 0.7$), predominantly at the second harmonic. These ray trajectories are sufficiently short and ``cold'' that relativistic effects are unimportant. In linear CD simulations, the optimal launch point corresponds to this third class of rays, suggesting that non-relativistic simulations are adequate. However, quasilinear calculations indicate that, at reactor relevant powers, current drive is maximised at $\rho \approx 0.6$. This quasilinear optimal point corresponds to the second class of rays, for which relativistic propagation does matter.