VOL. 80, NO. I JOURNAL OF GEOPHYSICAL RESEARCH JANUARY l, 1975 Parallel Propagation Effects on the Type 1 Electrojet Instability S. L. OSSAKOW, K. PAPADOPOULOS, J. ORENS, AND T. COFFEY Naval Research Laboratory, Washington, D.C. 2037.5 The Farley-Buneman instability has been extended to consider higher-frequency shorter-wavelength modes (thusincluding finite Debyelength effects), and these modes are allowed to propagate with a com- ponent parallel to themagnetic field (k• • 0). When thecurrent isdriven 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 growingmodes are in the regime of tens of centimeters, the phase velocities arecloser to theion thermal ¾elocity thanthose modes propagating at 90 ø (k• = 0). Maximum growth rates of off-angle p{opagation for different densities andcollision frequencies aresh6wn. Also, growth rates o'f unstable waves in the radar regime (1-10m) are shown fordrift velocities 1.5v, and 3v•. These also maximize with k• • 0 and have phase velocities closer to • than theyhave 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 haveprovided the impetus for substantial theoretical researchon 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- sityfluctuations is an electron current across themagnetic field produced by E x B type particledrifts due to the disparity in the electron-neutral and ion-neutral collision frequencies [Farley,1963a, b]. Since the relative driftsproduced are of the order of the ion soundspeed v• and since the electronand ion temperatures Te,• are equal, the systemwould have been linearly stable to ion sound on collisionless time scales. However, for collisional time scales the systembecomes un- stable to low-frequency long-wavelength modes [Bunernan, 1963]. The nature of thisinstability is purelyresistive. 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 hasbeen examined first by Farley [1963a, b] for a kineticplasma and subsequently by Bunernan [1963]in the fluid approximation. In Farley's kinetic description, which neglected finite Debye lengtheffects (kXo -• 0), it was shown that the important modes wereperpendicular,to the magnetic field. Lee et al. [1971] have extended Farley's resultsby in- cluding Debye length effects and found higher-frequency shorter-wavelength instabilities. Their calculation was restricted to modespropagating exactlyperpendicular to the magnetic field(k• = 0). Very recently, Lee andKennel [1973] have considered a simpleparallel propagationeffectanalysis on type 1instabilities in thefluid limit, andtheynotethat these modes may be more unstable than those that propagate across the magnetic field. Recenttheoreticalresults [Krall and Liewer, 1971;McBride et al., 1972] have shown that even for a collisionless plasma with Te • T•, a current perpendicular to the magneticfield produces an instability with smallbut finite k• (k•/k• • (rne/m•)•/•'). This instability,usuallycalled the modifiedtwo- stream instability, is a strong reactive typeinstability, and non- linear considerations show that one has to go to the strong- turbulence regime for saturation. We therefore feel that an examinationof whether and when such modes (k, • 0) be- come unstable in the electrojet isnecessary before going to the Copyright ¸ 1975by the American Geophysical Union. 141 nonlinear theory, which will correlate the observations with the equatorial microstructure. In the present note we consider the linear theory of the elec- trojet instability with finite Debye length effectsfor modes havinga smallcomponent parallelto the magnetic field (k• • 0). We focusour attention especially in the parameterregions where the nature of the instability changesfrom resistiveto reactive (for a large rangeof parameters applicable to the elec- trojet the instabilityis probablyresistive-inductive rather than purely resistive or purely reactive). We present numerical results relevantto the equatorial and the auroral electrojet and discuss their effect on the radar backscattered spectra.For the convenience of the readerwe give a simplephysical description of the nature of the electrojet type instability(resistive or reac- tive) in the appendix. THEORY The starting point of the calculationis the kinetic equation with the number-conserving Bhatnagar-Gross-Krook collision term [Bhatnagar et al., 1954] Ot mi.• c I '" ) n 1o,, -- -- I/ i ,e tl O where i ande referto ions and electrons; v• andt'e ai'e the ion- neutral and electron-neutral collisionfrequencies, respectively, and n -- d• (2) We also utilize Poisson's equation • . E = 4a'e f (]i and assume -- f') day (3) /0 e /)e3 3/• exp 7I' (4.)