Coupled flows and oscillations in asymmetric rotating plasmas

Abstract

Nonlinear coupling among the radial, axial, and azimuthal flows in an asymmetric cold rotating plasma is considered nonperturbatively. Exact solutions describing an expanding or contracting plasma with oscillations are then obtained. It is shown that despite the flow asymmetry the energy in the radial and axial flow components can be transferred to the azimuthal component but not the vice versa, and that flow oscillations need not be accompanied by density oscillations.

Flow oscillations in radial expansion of an inhomogeneous plasma layer

“…It is shown that, despite the strong coupling among the different components, for the initial conditions considered oscillations appear mainly in the velocity component A 0e . This behavior is similar to that for a fully nonlinear homogeneous rotating plasma flow, where, depending on the initial conditions, natural oscillations tend to appear mainly in certain degrees of freedom and the energy tends to be transferred into that of rotation [20,21].…”

“…The time evolution of the system is then reduced to a set of ordinary differential equations. The approach is somewhat similar to that of separation of variables for solving linear partial differential equations [15], except that here the spatial dependence is predetermined by trial and error [16][17][18][19][20][21][22][23]. This implies that the number of problems that can be handled by this approach is somewhat restricted.…”

Energy coupling among the degrees of freedom in an electron–positron plasma

“…For example, the velocity fields of the electrons and positrons can be represented by [11] v j r = rA j (t), v j z = rB j (t) and v j φ = rC j (t). For a spatially uniform EP plasma the electric field can be written as…”

“…Besides useful for understanding quasi-steady dynamic states and fully nonlinear evolution of waves and instabilities, such exact solutions are also important for verifying new analytical and numerical methods for solving nonlinear partial differential equations, as well as in formulating more realistic problems [4,5]. Recently, an exact model for cold plasma motion is used to investigate the energy transfer among the different degrees of freedom in a rotating plasma [9][10][11]. The governing cold plasma equations are solved non-perturbatively by first constructing a basis solution for the inertial, or force free, motion of the electron and ion fluids.…”

Self-Similar Nonlinear Dynamical Solutions for One-Component Nonneutral Plasma in a Time-Dependent Linear Focusing Field

“…Collective dynamics of nonneutral plasmas are of considerable practical importance [2,[12][13][14][15][16][17][18][19][20]. Previous approaches for investigating collective dynamics of a nonneutral plasma typically first find an equilibrium solution, then analyze the evolution of linear perturbations relative to the equilibrium.…”