Low-noise electromagnetic $δf$ particle-in-cell simulation of electron Bernstein waves

The conversion of the extraordinary $(X)$ mode to an electron Bernstein wave (EBW) is one way to get rf energy into an overdense plasma. Analysis of this is complex, as the EBW is a fully kinetic wave, and so its linear propagation is described by an intractable integro-differential equation. Nonlinear effects cannot be calculated within this rubric at all. Full particle-in-cell (PIC) simulations cannot be used for these analyses, as the noise levels for reasonable simulation parameters are much greater than the typical rf amplitudes. It is shown that the delta-f computations are effective for this analysis. In particular, the accuracy of those computations has been verified by comparison with full PIC, cold plasma theory, and small gyroradius theory. This computational method is then used to analyze mode conversion in different frequency regimes. In particular, reasonable agreement with the theoretical predictions of Ram and Schultz [Phys. Plasmas 7, 4084 (2000)] in the linear regime is found, where 100% $X−B$ mode conversion has been obtained when the driving frequency is less than twice the electron gyrofrequency. The results show that cold-plasma theory well predicts the mode conversion efficiency, as is consistent with the phase-space picture of mode conversion. From this it can be shown that nearly 100% $X−B$ mode conversion cannot be obtained when the frequency is higher than the electron second harmonic cyclotron frequency.