Parallel propagation effects on the type 1 electrojet instability

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 com- ponent 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 o (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. These also maximize with k  0 and have phase velocities closer tothan they have for purely perpen- dicular propagation. In all cases considered the phase velocity of the waves is a rapidly decreasing func- tion of angle as one moves away from pure perpendicular propagation. Observations of backscattered radar signals from the equatorial electrojet have provided the impetus for substantial theoretical research on the source of the density fluctuations that can provide the observed enhancements in the received signals. There is general agreement that the source of the den- sity fluctuations is an electron current across the magnetic field produced by E x B type particle drifts due to the disparity in the electron-neutral and ion-neutral collision frequencies (Farley, 1963a, b). Since the relative drifts produced are of the order of the ion sound speed vand since the electron and ion temperatures Te, are equal, the system would have been linearly stable to ion sound on collisionless time scales. However, for collisional time scales the system becomes un- stable to low-frequency long-wavelength modes (Bunernan, 1963). The nature of this instability is purely resistive. That is, the resistive medium extracts energy from the ion drift and transfers it to the negative energy wave (slow wave) associated with the drifting ions. This instability has been examined first by Farley (1963a, b) for a kinetic plasma and subsequently by Bunernan (1963) in the fluid approximation. In Farley's kinetic description, which neglected finite Debye length effects (kXo - 0), it was shown that the important modes were perpendicular,to the magnetic field. Lee et al. (1971) have extended Farley's results by in- cluding Debye length effects and found higher-frequency shorter-wavelength instabilities. Their calculation was restricted to modes propagating exactly perpendicular to the magnetic field (k = 0). Very recently, Lee and Kennel (1973) have considered a simple parallel propagation effect analysis on type 1 instabilities in the fluid limit, and they note that these modes may be more unstable than those that propagate across the magnetic field. Recent theoretical results (Krall and Liewer, 1971; McBride et al., 1972) have shown that even for a collisionless plasma with TeT, a current perpendicular to the magnetic field produces an instability with small but finite k (k/k  (rne/m)/'). This instability, usually called the modified two- stream instability, is a strong reactive type instability, and non- linear considerations show that one has to go to the strong- turbulence regime for saturation. We therefore feel that an examination of whether and when such modes (k,  0) be- come unstable in the electrojet is necessary before going to the