A set of nonlinear governing equations for interactions of transverse plasmons with pair plasmas is derived from Vlasov–Maxwell equations. It is shown the ponderomotive force induced by high-frequency transverse plasmons will expel the pair particles away, resulting in the formation of density cavity in which transverse plasmons are trapped. Numerical results show the envelope of wave fields will collapse and break into a filamentary structure due to the spatially inhomogeneous growth rate. The results obtained would be useful for understanding the nonlinear propagation behavior of intense electromagnetic waves in pair plasmas.

It is shown that nonlinear interaction between large amplitude circularly polarized EM wave and dusty plasma leads to a non-stationary ponderomotive force, which in turn produces a vortex ring and magnetic field. Then the ensuing vortex ring in the direction of propagation of the pump wave can accelerate the micron-size dust particles, which are initially at rest and eventually form a non-relativistic dust jet. This effect is purely non-stationary and unlike linear vortices, dust particles do not rotate here. Specifically, it is pointed out that the vortex ring or closed filament can become potential candidate for the acceleration of dust in tokamak plasmas.

Intense non-thermal radiation spikes were observed prior to energy quench in HT-7 tokamak. The dynamic properties of non-thermal electrons have been analyzed. Observation manifests that some non-thermal electrons are confined in the vicinity of q = 1 magnetic surface which results in hot spot phenomenon just before disruption.

On a characteristic surface Ω of a hyperbolic system of first-order equations in multi-dimensions (x, t), there exits a compatibility condition which is in the form of a transport equation along a bicharacteristic on Ω. This result can be interpreted also as a transport equation along rays of the wavefront Ωt in x-space associated with Ω. For a system of quasi-linear equations, the ray equations (which has two distinct parts) and the transport equation form a coupled system of underdetermined equations. As an example of this bicharacteristic formulation, we consider two-dimensional unsteady flow of an ideal magnetohydrodynamics gas with a plane aligned magnetic field. For any mode of propagation in this two-dimensional flow, there are three ray equations: two for the spatial coordinates x and y and one for the ray diffraction. In spite of little longer calculations, the final four equations (three ray equations and one transport equation) for the fast magneto-acoustic wave are simple and elegant and cannot be derived in these simple forms by use of a computer program like REDUCE.

Plasma filamentation is often encountered in collisionless shocks and inertial confinement fusion. We develop a general analytical description of the two-dimensional relativistic filamentary equilibrium and derive the conditions for existence of potential-free equilibria. A pseudopotential equation for the vector-potential is constructed for cold and relativistic Maxwellian distributions. The role of counter-streaming is explained. We present single current sheet and periodic current sheet solutions, and analyze the equilibria with electric potential. These solutions can be used to study linear and nonlinear evolution of the relativistic filamentation instability.

We investigate under which parameter regimes the magnetohydrodynamic (MHD) Rankine–Hugoniot conditions, which describe discontinuous solutions to the MHD equations, allow for slow, intermediate and fast shocks. We derive limiting values for the upstream and downstream shock parameters for which shocks of a given shock-type can occur. We revisit this classical topic in nonlinear MHD dynamics, augmenting the recent time reversal duality finding by in the usual shock frame parametrization.

We theoretically investigate conditions for the refraction of long-wavelength dust acoustic waves by arrays of periodic cylinders in a dusty plasma. This is based on a recent analysis of the refraction of shallow water waves by periodic cylinder arrays (Hu and Chan, Phys. Rev. Lett.95 (2005), 154501). In the dusty plasma case, however, the boundary conditions involve the formation of voids around the cylinders. Possible experimental conditions are discussed.

This paper presents a simple description of three-wave decay interactions involving a pump dispersive Alfvén wave (DAW), decay DAW and decay slow wave (SW) in a uniform magnetized plasma. When the ponderomotive nonlinearities are incorporated in DAW dynamics, the model equations governing the nonlinear excitation of the SWs by DAW in the low-β plasmas (β ≪ me/mi as applicable to solar corona) are given. The expressions for the coupling coefficients of the three-wave interaction have been derived. The growth rate of the instability is also calculated and found that the value of the decay growth time comes out to be of the order of milliseconds at the pump DAW amplitude B0y/B0 = 10−3.

Nonlinear equations which govern the dynamics of low-frequency (ω ⪡ ωci, where ω is the perturbation frequency of the wave and ωci is the ion gyro-frequency), ion-temperature-gradient-driven modes in the presence of equilibrium density, temperature and magnetic field gradients are derived. New set of nonlinear equations are derived. In the nonlinear case, new types of solutions in the form of dipolar vortices and vortex streets are found to exist in dense quantum plasma. These structures are found to be formed on very short spatial scales.

We investigate the relativistic electron motions in a two-frequency wiggler magnetic field with self-generated fields. The equations of motion are derived from the Hamiltonian which include the self-generated field, and we find the steady-state orbit from the equations of motion. The stability of electron motion in a two-frequency wiggler is examined by the numerical simulation. We analyze the a dynamical systems using the fast Fourier transformation and the Poincarè surface of section to find the critical value which have the periodical electron motion and to optimize the two-frequency wiggler.

This brief communication discusses theoretically a resistive ion-dust streaming instability in a collisional dusty plasma, where the ions and electrons are magnetized, and the dust is unmagnetized. The instability is driven by ions streaming along the magnetic field. The emphasis is on the case where the dust has large thermal speed, and where the ion drift speed is ≲ the ion thermal speed. Application to possible laboratory experimental parameters is considered.

It is shown that the direction of the drag force imposed on non-spherical grain by plasma flow is not necessarily aligned with the flow velocity. The implications of this fact for a grain dynamics are discussed.

A particle-in-cell numerical simulation of the electron Weibel instability is applied in a frame of Darwin (radiationless) approximation of the self-consistent fields of sparse plasma. As a result, we were able to supplement the classical picture of the instability and, in particular, to obtain the dependency of the basic characteristics (the time of development and the maximum field energy) of the thermal anisotropy parameter, to trace the dynamic restructuring of current filaments accompanying the non-linear stage of the instability and to trace in detail the evolution of the initial anisotropy of the electron component of plasma.