Non-Linear Instabilities in an Inhomogeneous Plasma

The low-frequency drift modes of a low-pressure isothermal inhomogeneous plasma can be stabilized if the shear of the magnetic field lines exceeds a critical value given by the expression r/Ls = (1/2 √2) (a/r), where Ls is the shear length, r the characteristic length of density variation, and a the ion Larmor radius. The authors first show that, even if r/Ls <(1/2 √2) (a/r), it is possible to achieve a substantial reduction in the rate of growth of the modes and thereby satisfy the conditions for applying the theory of weak turbulence. If a/r « 1 , the normal modes are very easily stabilized, but convective perturbations are known to persist and these can become amplified by propagating in the direction of the density gradient. These perturbations can be excited only by thermal fluctuations, which are explicitly calculated. The maximum amplitude of the relative density fluctuations are then deduced. If the plasma is fairly dense, weak shear is sufficient to maintain these fluctuations at a level at which the resulting diffusion is negligible. In both these cases of weak turbulence, however, non-linear instability may arise and cause diffusion that is far more substantial than the linear theories predict. On the one hand, the authors note that the energy of the drift waves is negative if their phase velocity parallel to the magnetic field is greater than the thermal velocity of the electrons, and discuss the development of the non-linear instability which results as a function of shear. On the other hand, they show that non-linear reflection of the convective perturbations may occur before they reach the region where they would be absorbed by the ion Landau effect. They estimate the threshold which the amplitude of the initial perturbations must pass for a non-linear instability to develop. (author)