Electromagnetic Electron-Ion Streaming Instability

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Abstract
Instabilities produced by a current across a magnetic field and propagating obliquely to the field are studied in connection with the description of hydromagnetic shock waves. It is shown that there exist unstable waves of mixed polarization which can be described as coupled ion beam and whistler modes with frequencies given by ω≈k·u where u is the streaming velocity of the ions relative to the electrons. These waves are investigated in the small electron Larmor radius approximation and in the frequency range Ωi ≪ ω ≪ Ωe where Ωi and Ωe are the cyclotron frequencies of the ions and electrons, respectively. The maximum growth rate is limited by γ < 123 (meu/2miυ¯e)1/3Ωe where υ¯e is the electron thermal velocity. The effect of collisions is considered, and the possibility of observing the instability in oblique shock wave experiments is discussed.