Cascade mechanism of nonlinear interactions between modes in a turbulent plasma

A hydrodynamical model of plasma turbulence is developed. A cascade concept is utilized to solve the problem of closure, which is characteristic of any nonlinear system. The spectra of kinetic and electrostatic energies are investigated for both the collisional and collisionless cases. In the former case, the spectrum of potential energy from the electrostatic potential fluctuations, as a function of the wave number
k
, and denoted by
G(k)
, follows the laws
G \sim k^{-3/2}
and
k^{-9/2}
in the inertial and dissipative subranges, respectively. In the latter case, the dissipative law
G \sim k^{-5}
is derived. The solutions of the kinetic energy spectrum are also found. The anomalous diffusion, called the Bohm diffusion, is derived in the present theory, and is found to play the role of a sink of energy flux across a potential spectrum.