Numerical simulation of the instability of a nonuniform plasma flow: Nonlinear dynamics of slipping instability
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Numerical Simulation of the Instability of a Nonuniform Plasma Flow: Nonlinear Dynamics of Slipping Instability M. V. Kuzeleva and N. Sepehri Javanb a Moscow
State University, Leninskie gory, Moscow, 119992 Russia b Zanjan University, Zanjan, Iran Received November 14, 2006
Abstract—A kinetic model is proposed that describes the nonlinear dynamics of the instabilities of a transversely nonuniform plasma flow. It is shown that, in the linear approximation, the model yields the familiar boundary-value problem for the scalar potential in plasma. The slipping instability in a plane waveguide is considered as an example. The general dispersion relation for a flow with a stepwise uniform density profile and with a tangential discontinuity in its longitudinal velocity is analyzed qualitatively. The dynamics of the slipping instability is investigated numerically for a flow that is detached from the waveguide walls and whose longitudinal velocity obeys a linear, a sinusoidal, or a discontinuous distribution. In the nonlinear stage of the instability, the flow expands in such a way as to come into contact with the walls, the spread in the longitudinal velocities remains smaller than the initial velocity variation, and the longitudinal velocities of different transverse layers in the flow are not completely equalized. PACS numbers: 52.40.-w DOI: 10.1134/S1063780X07080089
1. In [1], a method was proposed for describing the nonlinear dynamics of spatially nonuniform particle fluxes by representing the particle distribution functions as integrals over the initial values for the equations of particle motions in self-consistent and external electromagnetic fields. Being kinetic, the method provides an efficient tool for investigating phenomena associated with the development of turbulence (in configuration space, this corresponds to the intersection of particle trajectories). It is known that turbulent phenomena occur characteristically in the nonlinear stages of numerous hydrodynamic beam instabilities [2, 3], when the field of particle velocities becomes non-single-valued and the hydrodynamic approach fails to hold [4]. In [1], the problem of steady injection of an annular electron beam into a cylindrical waveguide under conditions such that the beam becomes turbulent at a certain distance from the injection plane was studied by the method of integration over the initial values. However, even when the beam is not subject to the turbulence considered in [1], it is destroyed by various kinds of instabilities, such as slipping, diocotron, Buneman, current-convective instabilities, and so on [2, 5]. In the present paper, we apply the method of integration over the initial values to study the instability of an electron beam with a prescribed density profile P(x) (in an unperturbed state) and a nonuniform velocity profile u(x) in plane geometry. It is assumed that the beam propagates along the z axis in a plane waveguide (a region bounded by two metal planes at x = 0 and L)
against the background of infinitely heav
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