JOURNAL OF GEOPHYSICAL RESEARCH, VOL. 98, NO. A7, PAGES 11,587-11,599, JULY 1, 1993 A Turbulent TheoreticalFramework for the Study of Current-Driven E Region Irregularities at High Latitudes: BasicDerivation and Application to Gradient-Free Situations A.M. HAMZA AND J.-P. ST-MAURICE Department o! Ph•tsics, Universtrot of Western Ontario, London, Ontario, Ganada We have used a mode-coupling hypothesis to study the nonlinear evolution of E region irregu- !axities at high latitudes. Conservationof energy and the identification of two distinct time scales for the problem at hand has allowedus to obtain an expression in the fluid regime for the mean frequency and the spectral width of different types of echoesobserved by coherent radars. In this particular paper we have applied our results to a few simple cases, naxnely, to situations that are free of large-scalegradients and for which aspect anglesaxe closeto zero. Even though anomalous diffusion effects were also neglected, our theory nevertheless predicts that in the absence of den- sity gradients, strongly driven Farley-Buneman waves should normally saturate at a mean speed between 70% and 100% of the ion-acoustic speedof the medium. The theory also predicts that zero-frequencytype 2 wavesin strongly turbulent situations should have a frequency width, which when translated to a Doppler width, should be approximately equal to the ion acoustic speed of the medium. Those results are a direct consequence of assuming that mode coupling is responsible for the saturation of all linearly unstable wavesin the E-region plasma. A companion paper will consider the modificationsintroduced by large-scale density gradients. 1. INTRODUG'IION Linear theories have been successful in determiningthe cause of most E region irregularitiesseenby coherentscat- ter radars at low and high latitudes. Theories that havesur- vived the test of time include most prominently the Farley- Buneman mechanism [Farley, 1963; Buneman, 1963] andthe gradient-drift instability [Rogister and D'Angelo, 1970]. At high latitudes, it has alsobeenproposed that intense parallel currents carried by thermal electrons could lead to coherent echoes moving at the ion acoustic speed of the mediumeven though the local E x B drift couldbe markedlysmaller than that same ion acoustic speed [Chaturvedi et al., 1987;Villain et al., 1987, 1990]. While linear theories have been successful at providing ba- sicexplanations for the existence of large-amplitude plasma waves (for example, see the review by Fejer and Kelley [1980]),they are unableto predict many other important properties of the observed waves. For example, it is well known that linear theory cannot be used to compute wave axnplitudes (it produces a positive growth ratefor all times) orto compute spectral widths (the modes predicted bylinear theory are made of separate and independent eigenfrequen- Copyright 1993 by the AmericanGeophysical Union. Paper number 92JA02836. 0148-0227/93/92JA-02836505.00 cies).In addition, lineartheory cannot, in principle at least, evenproducethe right value for the mean frequency of the waves: once the waves have grown to large amplitudes and approach saturation, individual wave trains can no longer be simply described in terms of coherent fluctuations. Nonlinear theories must therefore be used in order to un- derstand some of the most basic properties of the turbulent plasma. A whole hierarchy of nonlinear ideas has been used in E region research and elsewhere. In order of complex- ity we will classify the theories of interest for the present study into the quasi-linear, resonance broadening,weakly turbulent, and fully turbulent groups. However,it should be rememberedthat other theories are possible, and that even within each one of the groupsconsidered here a num- ber of ingeniousideas have sometimes been proposed,mak- ing a classification into the basicgroups somewhat murky at times. It should nevertheless prove instructive to produce at least a broad view of the subject, since we will propose here yet another direction to tackle some of the challenges presented by the abundant da ta setsthat havenourished this field of study. 1.1. Zeroth-Order Effects To start with a more quantitative approach,we definethe unstable E region problem as the need to find a solution to an equation for the overall distribution function of the plasma. This includes finding self-consistent average and perturbed distributions for ions and electrons. The problem begins with an equation for the average velocity distribution 11.587