Density gradient effect on oscillating two-stream instability in an inhomogeneous plasma

The equilibrium number density gradient effect on the oscillating two-stream instability is considered in an inhomogeneous plasma. The coupled mode equations which take into account the density gradient terms are formulated in terms of two second order differential equations for the purely growing mode. From the standard WKB solutions of the equations, it is found that the threshold should be higher than the value obtained by neglecting the density gradient terms. The equilibrium density gradient terms plys a more significant role in raising the threshold as the ratio of inhomogeneity scale length to Debye length decreases, in which case, the WKB solution is likely to become less accurate. (Author)