Estimate of Electron Cyclotron Harmonic Wave Amplitude during Marginal Stability

We conduct a comprehensive study of wave growth and quasi-linear diffusion to estimate the amplitude of electron cyclotron harmonic (ECH) waves during marginal stability. We model the evolution of electron pitch angle distributions due to interaction with ECH waves using a 2-D bounce-averaged Fokker-Planck equation to obtain the electron distribution in a marginally-stable state. After fitting the resultant electron distributions using multi-component subtracted bi-Maxwellians we estimate the maximum path-integrated gain using the HOTRAY ray tracing code. By varying the diffusion coefficients based on the assumed amplitude of the wave electric field, we determine the expected amplification of ECH waves. We find that the ECH wave amplitude consistent with marginal stability is significant (~1mV/m) at active times, when freshly injected electrons are present, but can drop to very low values (~0.01mV/m) at quiet times. Our results provide information regarding the generation ECH waves under a variety of activity levels, ambient plasma parameters and current sheet thicknesses.