Repeated-Cascade Theory of Turbulence in an Inhomogeneous Plasma

Turbulent-plasma phenomena in laboratories and in the ionosphere are often associated with plasma inhomogeneities. As a plasma inhomogeneity, we consider a partially ionized gas with a mean density gradient in a nonuniform mean electric field and a strong magnetic field. Because of drift instabilities, the plasma becomes turbulent in the plane transverse to the magnetic field. We propose a method of a repeated cascade, and derive the spectral distributions for the turbulent density and field fluctuations in the production, inertia, and dissipation subranges of the universal spectrum. The results predict $k^{-3\mathrm{}}$, $k^{-1\mathrm{}}$, and $k^{-5\mathrm{}}$ laws in the respective subranges for the density spectrum, and a single $k^{-3\mathrm{}}$ law for the field spectrum. As the plasma inhomogeneity may be embedded in an atmospheric turbulence, we also study the effect of the atmospheric turbulence which drives the plasma inhomogeneity. The theoretical predictions are found to agree with data from laboratory plasma experiments.