This paper complements an earlier one in which we considered the diffusion and drift across a magnetic field induced by a turbulent spectrum of fluctuations. We examine here the effects of these on the propagation of an unstable spectrum of modes. In the first paper a nonlinear dispersion relation is derived in a general closed form. This is then examined in the limint of short wavelengths (i.e.wavelengths much less than the gyroradii) and results of other authors are retrieved. In particular it is found that modes supported by the magnetic field are quashed whenever a particle may diffuse a wavelength per gyroperiod. For instance, in the context of current-driven instabilities (current across the magnetic field), electron cyclotron instabilities are quashed but not the ion-acoustic. The dispersion characteristics of the latter are unchanged except in that the drift which sustains the instability is altered by the presence of a turbulent (E × B) type drift. Depending on the level of fluctuations and magnetic field strength, this may amount simply to a rotation of the cone of unstable modes or may form a countercurrent which in turn suppresses the original current driving the instability.

In the second half of the paper the problem of calculating the fluctuation spectrum of the electric field is addressed since this is essential for a self-consistent computation of the diffusion tensor and turbulent drift appearing in the nonlinear dispersion relation.