The nonlinear dynamics of resonant slow MHD waves in weakly dissipative plasmas is investigated in cylindrical geometry with a twisted equilibrium magnetic field. Linear theory has shown that the wave motion is governed by conservation laws and jump conditions across the resonant surface considered as a singularity – first derived in linear ideal MHD theory by Sakurai, Goossens and Hollweg [Solar Phys.133, 227 (1991)]. By means of the simplified method of matched asymptotic expansions, we obtain the generalized connection formulae for the variables across the dissipative layer, and we derive a non-homogeneous nonlinear partial differential equation for the wave dynamics in the dissipative layer.

The regularization of magnetic islands is studied for the case when the electron temperature is larger than the ion temperature. The slab approximation is used. Drift effects are neglected, i.e., the case of superdrift magnetic islands, SDMIs, is analyzed. Then the regularization problem reduces to, first, a spreading of the step-functional velocity profile and the conventional delta-functional polarization current profile in the region near the island separatrix; second, finding the dispersion terms of the polarization current in this region; and, third, calculating the total polarization current contribution to the generalized Rutherford equation for the island width. It is shown that this problem can be solved if one allows for the effects of the electron pressure gradient in the parallel Ohm's law. The polarization current contribution in the case of islands regularized due to these effects proves to be the same as that in the case of nonregularized islands.

Stationary nonlinear one-dimensional electrostatic oscillations in a plasma containing dust grains with variable charge are considered through a cold-beam model. The new constraints brought by the presence of dusts on the BGK modes are clarified and the appearance of a soliton mode that was not present in the fixed-charge problem is investigated.

The generation of magnetic fields due to ponderomotive forces in astrophysical plasma consisting of electrons, ions and positrons is investigated theoretically. It is seen that collisional or non-collisional interactions (between electromagnetic waves and plasma particles) via ponderomotive forces in an inhomogeneous plasma can excite a magnetic field. The growth rate of the magnetic field is illustrated graphically for different values of the temperature and concentration of positrons in the plasma.

Starting from the one-dimensional energy integral and related stability theorems given by Newcomb [Ann. Phys (NY)10, 232 (1960)] for a linear pinch system, this paper analyses the stability of one-dimensional force-free magnetic fields in cylindrical coordinates (r, θ, z). It is found that the stability of the force-free field is closely related to the radial distribution of the pitch of the field lines: h(r) = 2πrBz/Bθ. The following three types of force-free fields are proved to be unstable: (i) force-free fields with a uniform pitch; (ii) force-free fields with a pitch that increases in magnitude with r in the neighbourhood of r = 0(d[mid ]h[mid ]/dr > 0); and (iii) force-free fields for which (dh/dr)r=0 = 0, Bθ α rm in the neighbourhood of r = 0, and (h d2h/dr2)r=0 > −128π2/(2m+4)2. On the other hand, the stability does not have a definite relation to the maximum of the force-free factor α defined by [dtri ]×B = αB. Examples will be given to illustrate that force-free fields with an infinite force-free factor at the boundary are stable, whereas those with a force-free factor that is finite and smaller than the lowest eigenvalue of linear force-free field solutions in the domain of interest are unstable. The latter disproves the sufficient criterion for stability of nonlinear force-free magnetic fields given by Krüger [J. Plasma Phys.15, 15 (1976)] that a nonlinear force-free field is stable if the maximum absolute value of the force-free factor is smaller than the lowest eigenvalue of linear force-free field solutions in the domain of interest.

A modified electron whistler dispersion law is derived in the cold-plasma approximation for analytical treatment and simplified numerical calculations of wave propagation in a wide range of ratios ωc/ωp of electron gyro- to plasma frequencies if the wave frequency is much less than ωp. The net contribution of ions to the wave dispersion law is expressed through the value of the lower-hybrid resonance frequency ωlhr only. This approximate dispersion law is valid in a wide frequency domain, that is, from the range of ωlhr until the domain where the contribution of ions can be neglected. A comparison of geometrical-optics ray trajectories calculated by the use of modified and total cold-plasma electron whistler dispersion laws is presented for the case of the Earth's plasma environment. Computer simulations of dynamical spectra of whistler waves excited by lightning discharges and registered in remote regions of the Earth's plasmasphere reveal good numerical stability of the developed ray-tracing code.

The method of matched asymptotic approximations is used to examine an ordering of the physical quantities in a collisional plasma–collisional sheath model that has not been previously explored, namely in the constant ion mean free path model with high electric field. The asymptotic theory for a collision- dominated space-charge sheath at a negative surface is developed for the case when the ions interact with neutral particles as rigid spheres while the electric field is high both in the sheath and in the quasineutral plasma. The ion mobility is inversely proportional to the square root of the electric field in such a case. The ratio λD/L of the Debye length at the center of the quasineutral plasma to a characteristic dimension of the plasma is considered as a small asymptotic parameter. The general structure of the asymptotic solution obtained is similar to that in the case of low electric field (or in the framework of the model of constant collision frequency), considered by previous workers; however, the scalings are different. In particular, the thickness of the sheath is found to have the order λ4/5DL1/5, while the respective order in the case of low electric field is λ2/3DL1/3.

Inelastic Compton scattering of photons by hydrogenic ions in a classical nonideal plasma is investigated. An effective pseudopotential model taking into account plasma screening and collective effects is applied to describe the interaction potential in a nonideal plasma. The screened atomic wave functions and energy eigenvalues for the ground and excited states of the hydrogenic ion in a classical nonideal plasma obtained by the Ritz variational and perturbational methods. The expression for the lowest-order transition matrix element is obtained by a two-photon process associated with terms quadratic in the vector potential A. The inelastic Compton scattering cross-section horn the 1s ground state to the 2p excited state is obtained as a function of the incident photon energy, Debye length, and the non-ideality plasma parameter. It is found that the collective effect reduces the cross-section. The collective effect on the cross-section is decreased with increasing Debye length.

Orientation phenomena for direct 1s → 2p±1 excitations in electron–hydrogenic-ion collisions are investigated in a classical nonideal plasma. An effective pseudopotential model taking into account plasma-screening and collective effects is applied to describe the interaction potential in a nonideal plasma. The orientation parameter for direct 1s → 2p±1 excitations in a nonideal plasma is obtained as a function of the impact parameter, the nonideal-plasma parameter, the Debye length, and the projectile energy. The result shows that the nonideal effect reduces the propensity of the 1s → 2p−1 transition. It is also found that the nonideal effect on the orientation parameter increases with increasing projectile energy.

The classical electron–ion Coulomb bremsstrahlung process is investigated in a nonideal plasma. An effective pseudopotential model taking into account plasma-screening and collective effects is applied to describe the electron-ion interaction potential in a nonideal plasma. The screened hyperbolic-orbit trajectory method is applied to the motion of the projectile electron in order to investigate the bremsstrahlung radiation cross-section as a function of the scaled impact parameter, eccentricity, nonideal-plasma parameter, Debye length, projectile energy, and photon energy. It is found that the collective effect reduces the bremsstrahlung radiation cross-section on both the soft- and hard-photon cases. For small impact parameters, the nonideal-plasma effect on the bremsstrahlung radiation cross-section is found to be quite small. It is also found that the maximum position of the bremsstrahlung radiation cross-section gets closer to the target ion with increasing nonideal-plasma effect.

An exact Sagdeev equation for arbitrary-amplitude solitary kinetic Alfvén waves in a non-thermal plasma is derived. For small β′, the proportion of fast electrons, an analytical expression for the exact pseudopotential V (φ) is obtained. For several values of β′, the Sagdeev potential V (φ) has been calculated by integrating the Sagdeev equation. It is found that, depending on the values of β′, both hump and dip solitons exist.

Numerical calculations are performed based on a set of equations that describe the non-steady, nonlinear interactions between a moving body in space and plasma. The results show that density cavitons and potential solitons are formed owing to modulational instability if the envelope of the high-frequency modulational field is sufficiently intense.

This paper considers single-particle trajectories in a planar sheared force-free magnetic field. A specific feature of this magnetic configuration is the absence of both gradient and curvature magnetic drifts, as well as a diamagnetic force along field lines. Therefore, in the framework of the drift approximation, the motion of the particle guiding centre does not feel the magnetic field's non-uniformity. Here we discuss how the latter affects actual particle trajectories, making them quite different from simple circular gyromotion even when the Larmor radius is small. It is also shown how magnetic confinement ceases to work when the Larmor radius becomes comparable to the spatial scale of the field variation.