Quasilinear theory of the diocotron instability for nonrelativistic non-neutral electron flow in planar geometry

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Abstract
A macroscopic cold‐fluid model is used to investigate the quasilinear stabilization of the diocotron instability for sheared, nonrelativistic electron flow. Planar diode geometry is assumed, with cathode and anode located at x=0 and x=d, respectively. The non‐neutral plasma is immersed in a strong applied magnetic field B0êz, and the electrons are treated as a massless (m→0) guiding‐center fluid with flow velocity Vb=−(c/B0)∇φ×êz, where ∂/∂z=0 is assumed, and the fields are electrostatic with E=−∇φ. All quantities are assumed to be periodic in the y direction with periodicity length L. The nonlinear continuity‐Poisson equations are used to obtain coupled quasilinear kinetic equations describing the self‐consistent evolution of the average density 〈nb〉(x,t) and spectral energy density Ek(x,t) associated with the y‐electric field perturbations. Here, the average flow velocity in the y direction is VE(x,t)=(c/B0)(∂/∂x)〈φ〉(x,t), where average quantities are defined by 〈ψ〉(x,t)=∫L0 (dy/L)ψ(x,y,t). Several general features of the quasilinear evolution of the system are discussed, including a derivation of exact conservation constraints. Typically, if the initial profile 〈nb〉(x, t=0) corresponds to instability with γk(0)>0, the perturbations amplify, and the density profile 〈nb〉(x,t) readjusts in such a way as to reduce the growth rate γk(t) and stabilize the instability. As a specific example, the quasilinear evolution of the <named-content...