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A second-order linear differential reduced from the largest possible theoretical equation is derived for determining the linear value [V81k and Haerendel, 1971; Hudson and eigenmodes of striation instabilities along the Kennel, 1975b; Glassman and Sperling, 1983]. ion polarization currents can drive inductive Perkins et al., 1973; Goldman et al., 1976; tions suggest that the current patterns associated Sperling, 1983; Glassman and Sperling, 1983]. The with the instabilities cannot extend to the higher neutral density is an example of one parameter altitudes in the magnetosphere where ion Pedersen which obviously depends on altitude and position currents are negligible. A corollary remark is along the geomagnetic field.Artificial that in the earlier calculations the geomagnetic explosions in the ionosphere, such as barium field lines at higher altitudes are equipotenreleases or nuclear explosions, produce plasmas rials. The calculations presented in this paper which are nonuniform along the geomagnetic field. demonstrate that the current patterns associated Because plasma parameters are functions of the with the striation instabilities can extend into coordinate along the geomagnetic field, the ac the magnetosphere [Sperling, 1984]. conductivity is also a function of the coordinate.In the work by Goldman et al. [1976] it is Flutelike instabilities are nonuniform along the assumed that the modal potential is constant along geomagnetic field, and so their growth rates are the geomagnetic field within the unstable plasma cloud. Our calculations do not make this simplification, but rather self-consistently calculate

A linear dispersion relation is It has been previously demonstrated that derived for the collisional gradient drift insta-parallel eigenmodes of the collisional gradient bility under the assumption that partial short-drift instability become increasingly localized circuiting of perpendicular arebipolar electric along the geomagnetic field as perpendicular wave fields, ion inertia, and ion viscosity are the numbers increase [Goldman et al., 1976• Sperling significant factors in the "freezing" of stri-and Glassman, 1985; Sperling, 1984aj. This ations with perpendicular scale sizes of several localization is a direct consequence of the finite hundred meters. Quantitative evaluation of this parallel conductivity of real ionospheric dispersion relation indicates that eigenmodes plasmas. Indeed, for the perpendicular scale tend to be localized to low-density portions of sizes appropriate to "frozen" $triations, very the plasma when short-circuiting is active. good estimates for the eigenfrequencies can be HOwever, the eigenmodes can extend in relatively obtained from a local algebraic dispersion uniform fashion across the density gradient when relation which ignores the contribution from short-circuiting is very small. This situation parallel electron currents [Sperling and would appear to be conducive to the formation of Glassman, 1984]. This is consistent with the fact striations. Hence the calculations suggest that that, as eigenmodes become more localized along short-circuiting of perpendicular arebipolar the geomagnetic field, the eigenmodes sample electric fields is weak at the sharp perpendicular increasingly more uniform plasma. Moreover, the density gradients where striations begin to calculations of eigenfrequencies and parallel evolve. The observation of perpendicular density eigenmodes show that the collisional gradient gradients which are persistent and sharp supports drift instability acquires a substantial real the idea that short-circuiting is weak. With the frequency for perpendicular scale sizes approassumption that short-circuiting is zero, a priate to "frozen" striations and when there is no dispersion relation is derived with full ion perpendicular arebipolar electric field in the viscous contributions. Evaluation of this dis-basic plasma model upon which the striations persion relation suggests that the finite ion develpp [Sperling and Glassman, 1985; Sperling, gyroradius contributions are the dominant factor 1984b]. The acquisition of a real frequency is in $triation "freezing." Accordingly, an important, since it indicates a difference between expression is derived for estimating the outer eigenmodes for smaller and larger values of the scale wave number appropriate to "frozen" stri-perpendicular wave number and also suggests a ations, and an appropriate application is made to possible reason for the observed perpendicular the "U-shaped curve" formulation of striation scale sizes of "frozen" striations. Indeed, the dynamics. instability becomes more like a drift mode, causing small nonlinear den...

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