The full second-order cold fluid theory of the diocotron and magnetron instabilities in the presence of crossed fields

The authors have recently solved the full second-order cold fluid equations, wherein one retains the second-order terms in the continuity equation. The authors recover the above result in the low-frequency limit, except that the diffusion coefficient from the full theory is twice that of the quasilinear theory. Also, they obtain the diffusion coefficient for the general case, and also at the magnetron instability. The response of the density to the magnetron instability is essentially the same as to the diocotron instability which has been previously described. Each of these unstable modes caused flattening of the density profile leading to stabilization via ''plateau-formation.''