Phenomenological Theory of the Kink Instability in a Slender Plasma Column

When one deals with a plasma column whose radius a is much smaller than its length L, one can think of it as of a thin filament whose kink instability can be adequately described simply by a 2D displacement vector, {xi}{sub x} = {xi}{sub s}(z,t); {xi}{sub y} = {xi}{sub y}(z,t). Details of the internal structure of the column such as the current, density, and axial flow velocity distribution would be lumped into some phenomenological parameters. This approach is particularly efficient in the problems with non-ideal (sheath) boundary conditions (BC) at the end electrodes, with the finite plasma resistivity, and with a substantial axial flow. With the sheath BC imposed at one of the end-plates, we find instability in the domain well below the classical Kruskal-Shafranov limit. The presence of an axial flow causes the onset of rotation of the kink and strong axial ''skewness'' of the eigenfunction, with the perturbation amplitude increasing in the flow direction. We consider the limitations of the phenomenological approach and find that they are related to the steepness with which the plasma resistivity increases at the plasma boundary with vacuum