Simulations of electron/electron instabilities: Electromagnetic fluctuations

Electron/electron instabilities arise in collisionless plasmas when the electron velocity distribution consists of two distinct components with a sufficiently large relative drift speed between them. If the less dense beam component is not too tenuous and sufficiently fast, the electron/electron beam instability is excited over a relatively broad range of frequencies. This instability is often studied in the electrostatic limit, which is appropriate at ${\omega }_e{\mathrm{/|\Omega }}_e\text{|≫1,}$ where ${\omega }_e$ is the electron plasma frequency and ${\Omega }_e$ is the electron cyclotron frequency, but is not necessarily valid at ${\omega }_e{\mathrm{/|\Omega }}_e\text{|∼1.}$ Here linear Vlasov dispersion theory has been used and fully electromagnetic particle-in-cell simulations have been run in a spatially homogeneous, magnetized plasma model at ${\beta }_e\text{≪1}$ and 0.5 ${\mathrm{⩽\omega }}_e{\mathrm{/|\Omega }}_e\text{|⩽4.0.}$ Theory and simulations (run to times of order ${\text{100ω}}_e^{\text{−1}})$ of the electron/electron beam instability show the growth of appreciable magnetic fluctuations at ${\omega }_e{\mathrm{/|\Omega }}_e\text{|<2;}$ these waves bear right-hand elliptical magnetic polarization. The simulations reproduce the well-known slowing and heating of the beam; at ${\omega }_e{\mathrm{/|\Omega }}_e\text{|<1}$ this heating is predominantly parallel to the background magnetic field, but as ${\omega }_e{\mathrm{/|\Omega }}_e|$ becomes greater than unity the perpendicular heating of the beam increases. The simulations also demonstrate that, for ${\omega }_e{\mathrm{/|\Omega }}_e\text{|∼1,}$ electromagnetic fluctuations impart to the more dense electron core component significant heating perpendicular to the background magnetic field.