Diocotron instability for intense relativistic non-neutral electron flow in planar diode geometry

The extraordinary-mode eigenvalue equation is used to investigate detailed properties of the diocotron instability for sheared, relativistic electron flow in a planar diode. The theoretical model is based on the cold-fluid-Maxwell equations assuming low-frequency flute perturbations about a tenuous electron layer satisfying ω2/sub p//sub b/(x)<<ω2/sub c/ and chemical bondω-kV/sub y/(x)chemical bond2<<ω2/sub c/. The cathode is located at x = 0; the anode is located at x = d; the outer boundary of the electron layer is located at x = x+/sub b/<d; and the inner boundary of the layer is located at x = x-/sub b/<x+/sub b/. The extraordinary-mode