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 Σκ(| Eκ |2/4πN0Te)∼(Ωe/ωe)2(Ωe/kve), where Ωe and ωe 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.
The Farley-Buneman instability has been extended to consider higher-frequency shorter-wavelength modes (thus including finite Debye length effects), and these modes are allowed to propagate with a component parallel to the magnetic field (k• • 0). When the current is driven sufficiently hard (drift speeds in the range 2-3 times the ion thermal velocity o•), the growth rates of these modes maximize slightly away from the perpendicular to the magnetic field, and thus the importance of k• • 0 is shown. Although the wavelengths of these maximum growing modes are in the regime of tens of centimeters, the phase velocities are closer to the ion thermal ¾elocity than those modes propagating at 90 ø (k• = 0). Maximum growth rates of off-angle p{opagation for different densities and collision frequencies are sh6wn. Also, growth rates o'f unstable waves in the radar regime (1-10 m) are shown for drift velocities 1.5v, and 3v•. In the present note we consider the linear theory of the electrojet instability with finite Debye length effects for modes having a small component parallel to the magnetic field (k• • 0). We focus our attention especially in the parameter regions where the nature of the instability changes from resistive to reactive (for a large range of parameters applicable to the electrojet the instability is probably resistive-inductive rather than purely resistive or purely reactive). We present numerical results relevant to the equatorial and the auroral electrojet and discuss their effect on the radar backscattered spectra. For the convenience of the reader we give a simple physical description of the nature of the electrojet type instability (resistive or reactive) in the appendix.
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