Linear instabilities in the quasistatic guiding-center plasmas

A numerical scheme is developed to study the stability of the linearized three-dimensional guiding-center equations of a plasma of cold ions and hot electrons. The linear growth rates of the Kelvin-Helmholtz instabilities resulting from a velocity shear introduced by a non-uniform E*B drift are calculated numerically. In particular, the theory of neutrally stable waves in two dimensions is verified for a velocity profile of the form of a sine function, and the instability growth rates of the oscillations in the neighborhood of the neutrally stable waves are calculated numerically and are shown to be in very good agreement with theory. The effect of large wavelength oscillations along the magnetic field on these instabilities is studied. The numerical scheme is also used to study the linear instabilities of the density drift waves in an inhomogeneous plasma.