Description
Electron plasma waves (EPW) or ion Bernstein waves (IBW) have been identified as a possible source of radiofrequency emissions detected at FTU during runaway electrons (RE) plasma discharges [C. Castaldo et al., Nucl. Fusion 64 (2024) 086003]. The relevant spectrograms exhibit a set of line emissions with frequencies roughly given by integer multiples of the ion cyclotron frequency of the main ion species, and almost constant frequency gaps. The observed emission frequencies, corresponding to the ones of IBW and EPW near their confluence region, are driven unstable via Cherenkov resonance, as indicated by numerical stability analysis performed with the REDHPW code. The free energy source is provided by the anisotropy or the presence of a local maximum of the RE distribution function in the momentum space. The latter can be modeled by a skew normal distribution, consistently with experimental results at FTU and with numerical solutions of the Fokker-Planck equation for RE obtained in other scenarios. In tokamak plasmas, the amplification of IBW or EPW is favorited by the low group velocity perpendicular to the static magnetic field, compared to the parallel group velocity, occurring in the proximity of their confluence region. Therefore, wave packets can propagate along magnetic surfaces, keeping almost constant drive by RE, until the non-uniformity of the magnetic field deviates their trajectory. Saturation of the wave amplitude also occurs due the quasilinear flattening of the distribution function in the momentum space region producing the wave-particle interaction. The numerical code FAREDW (Finite Amplitude Runaway Electron Driven Waves) has been implemented to evaluate the finite amplification of RE-driven waves from their thermal noise level, based on a ray-tracing code coupled with REDHPW and considering the time evolution of the distribution function. The latter is provided by numerical solutions of a Fokker-Planck equation under the hypothesis of quasilinear diffusion. Comparison of calculated power spectra of line emissions with the frequency spectra detected is proposed.