A. R. Karimov

Coupled flows and oscillations in asymmetric rotating plasmas

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.

Coupled azimuthal and radial flows and oscillations in a rotating plasma

Nonlinear coupling between the radial, axial, and azimuthal flows in a cold rotating plasma is considered nonperturbatively by first constructing a basis solution for a rotating flow. Simple but exact solutions that describe an expanding plasma with oscillatory flow fields are then obtained. These solutions show that the energy in the radial and axial flow components can be transferred to the azimuthal component but not the vice versa. Nonlinear electron velocity oscillations in the absence of electron density oscillations at the same frequency are shown to exist.

Large quasineutral electron velocity oscillations in radial expansion of an ionizing plasma

Radial expansion of an ionizing gas or plasma cylinder into vacuum is investigated. An exact model for the evolution of the density and velocity fields of the electrons, ions, and neutrals, including the effect of photo and electron-impact ionization on the flow characteristics is developed and solutions obtained. A quasineutral nonlinear electrostatic mode involving rapid oscillations in the electron velocity but not in the density can occur in the expanding plasma. The mode turns out to be almost unaffected by weak ionization.

Nonlinear solutions of a Maxwellian type for the Vlasov–Poisson equations

The nonlinear dynamics of collisionless unmagnetized plasma is considered. Time-dependent one-particle distribution functions of a Maxwellian type that can be expressed as a series in positive powers of the electrostatic potential are obtained. The influence of conditions on the formation and existence of Maxwellian equilibria is discussed.

Nonlinear Langmuir oscillations under nonequilibrium conditions

The influence of external ionization sources on the characteristics of Langmuir oscillations in a partially ionized plasma is considered. It is demonstrated that in the case of continuous sources of ionization the nonlinear Langmuir oscillations are nonharmonic and are determined by the Airy equation.

Amplification of initial perturbations in simple hydrodynamic systems

Abstract The nonlinear dynamics of nondissipative systems of simple hydrodynamic type that are subjected to small, albeit finite, perturbations in the initial conditions is considered. Only the nonlinearity of the system and influence of the initial conditions are taken into account. Initial conditions admitting the formation of steady wavelet-structures in the density profile are found.

Expansion of a cold non-neutral plasma slab

Expansion of the ion and electron fronts of a cold non-neutral plasma slab with a quasi-neutral core bounded by layers containing only ions is investigated analytically and exact solutions are obtained. It is found that on average, the plasma expansion time scales linearly with the initial inverse ion plasma frequency as well as the degree of charge imbalance, and no expansion occurs if the cold plasma slab is stationary and overall neutral. However, in both cases, there can exist prominent oscillations on the electron front.

Nonlinear solutions of the Vlasov–Poisson equations

Based on the kinetic description, properties of collisionless unmagnetized plasma are studied. Time-dependent solutions of the nonlinear Vlasov–Poisson equations are found. Several dynamical structures of a Maxwellian type are presented.

Evolution of a Cold Non-neutral Electron–Positron Plasma Slab*

Evolution of a non-neutral cold electron–positron plasma slab is investigated. Initially the slab consists of a quasineutral plasma core bounded on both sides by layers containing only positrons (or electrons). Results from a nonperturbative, or mathematically exact, analysis of the governing fluid conservation equations and the Poisson equation show that despite their equal mass and charge magnitude, the electron and positron fronts can expand separately as well as a single fluid, and that nonlinear surface oscillations can be excited on the expansion fronts.

Influence of chemical reactions on the nonlinear dynamics of dissipative flows

The nonlinear dynamics of resistive flow with a chemical reaction is studied. Proceeding from the Lagrangian description, the influence of a chemical reaction on the development of fluid singularities is considered.