Theory and Simulation of the Beam Cyclotron Instability

Abstract

A detailed theory in conjunction with the results of computer simulation experiments is presented for the beam cyclotron instability. The main results are (1) After a period of exponential quasilinear development, turbulent wave‐particle interactions cause cross‐field diffusion of the electrons which smears out the electron gyroresonances. This occurs at a level of turbulence which scales as ${\Sigma }_{\kappa }{\mathrm{(|\hspace{0.17em}E}}_{\kappa }{\mathrm{\hspace{0.17em}|}}^2{\text{/4πN}}_0{T}_e{\mathrm{)\sim (\Omega }}_e{\mathrm{/\omega }}_e{)}^2{\mathrm{(\Omega }}_e{\mathrm{/kv}}_e)$ , where $\mathrm{\Omega e}$ and $\mathrm{\omega e}$ are the electron cyclotron and plasma frequencies, and results in a transition to ordinary ion sound modes that would occur in an unmagnetized plasma. The magnetic field serves to reduce the effects of electron trapping. (2) This level of turbulence appears to have virtually no effect on long wavelength fluid modes. (3) At this level the instability stabilizes if ordinary ion sound is stable due to ion Landau damping. For cold ions it continues to develop at the slower ion acoustic growth rate until the fields become strong enough to trap the ions. After the fields saturate, further plasma heating is much slower than exponential.