Perpendicularly Propagating Plasma Cyclotron Instabilities Simulated with a One-Dimensional Computer Model

Abstract

Perpendicular propagating $\text{(k‖\hspace{0.17em}=\hspace{0.17em}0)}$ cyclotron instabilities of velocity distributions ${\mathrm{f(\upsilon }}_{\perp }{\mathrm{)\hspace{0.17em}=\hspace{0.17em}\delta (\upsilon }}_{\perp }{\mathrm{\hspace{0.17em}-\hspace{0.17em}\upsilon }}_0{\text{)/2πυ}}_{\perp }$ and similar loss cone distributions with velocity spreads are simulated with a one‐dimensional computer model. Essentially noise‐free starting conditions are created by loading phase space in a uniform way. Growth starting from machine roundoff levels can be observed at precisely the linear Vlasov theory predictions, up to the saturated level, many orders of magnitude above the starting point. When the growth is dominated by a single wavenumber, the post‐saturation time behavior of the electric field is dominated by recurring peaks separated by the cyclotron period. This causes the major frequency components of the nonlinear signal to be at or near harmonics of the cyclotron frequency rather than the linear real frequency, which is nonharmonic. The amplitude of succeeding bursts decays slowly, suggesting the existence of quasistable nonlinear states. A nonlinear instability has also been observed. Furthermore, we have examined another $k_{\Vert }\text{\hspace{0.17em}=\hspace{0.17em}0}$ instability, a double hump mode arising from the combination of a stable loss cone plus a small amount of cold ions.