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Riggin & Kadish 1989
Riggin, D. and Kadish, A. (1989). Nonlocal theory of long-wavelength plasma waves associated with sporadic E layers. Journal of Geophysical Research 94: doi: 10.1029/88JA04096. issn: 0148-0227.

In this paper we calculate the nonlocal growth rate of gradient drift plasma waves under conditions where the electron density gradient scale length changes with altitude. The results are compared with the local growth rate and discussed in the context of the kilometer-scale waves which have been observed in the vicinity of mid-latitude sporadic E layers. These large-scale waves drastically violate the local approximation, kLm≫1, where k is the irregularity wave number and Lm is the minimum gradient scale length on the edge of a layer. The first step in the analysis is to derive a general eigenmode equation, starting with the same assumptions usually used in the derivation of the local dispersion relation for long wavelength waves. Modeling a sporadic E layer as a slab, the nonlocal growth rate spectrum is found by solving the eigenmode equation for this profile. The solution is an algebraic dispersion relation with a growth rate spectrum which is roughly proportional to k, rather than the k2 dependence predicted by conventional local theory at long wavelengths. At short wavelengths the nonlocal growth rate determined with the slab is unbounded, in disagreement with local theory. The slab is an inadequate model for short wavelength waves and a bound on the growth rate is instead derived from a theory which can be applied to any realistic profile with nonzero Lm. At short wavelengths this bound is identical to the local growth rate expression, while at long wavelengths the bound remains proportional to k and thus is consistent with the dispersion relation for a slab. Nonlocal effects alone do not explain the dominance of kilometer scales, but they do tend to favor the excitation of long wavelengths. ¿ American Geophysical Union 1989

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Abstract

Keywords
Ionosphere, Ionospheric irregularities, Ionosphere, Midlatitude ionosphere, Ionosphere, Plasma waves and instabilities
Journal
Journal of Geophysical Research
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American Geophysical Union
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