Axial shear instability in a "tachion" region

Plasma axial-shear flow instability arises due to a variation in an equilib rium E x B rotation along the axial direction in which the magnetic field i s aligned. The two fluid MHD equations for incompressible perturbation (tak ing into account the FLR effects) being treated in WKB approximation in tra nsversal direction yield one scalar Klein-Gordon type equation with one-dim ensional effective potential U(s) and effective mass on(s). Only axisymmetr ic, paraxial geometry is analyzed in order to separate the desired effects from the effects related to a variation in cross-sectional shape of the mag netic flux tube. In this work the effective potential was considered for a semi-infinite bounded plasma, first in the form of a square well for analyt ical study and then in a linear nature to study in the so called "tachion" region. Growth rates as a function of the potential well depth and other pa rameters were calculated. The cases where effective mass is real and imagin ary "tachion" regime were considered. The results obtained are interesting for the stability problem of such open devices as GDT, GAMMA-10 AMBAL-M and the scrape-off layer in tokamak divertors.