Nonlinear quantum Hall-MHD equations for a warm dense magnetoplasma with an anisotropic electron pressure are derived. The nonlinear equations include the quantum force associated with electron tunneling effects. The newly found equations can be used to investigate the dense plasma stability, as well as different types of waves, instabilities, and nonlinear structures in a warm dense magnetoplasma.

The existence of localized ion waves in a dense quantum plasma is established. Specifically, ion solitary waves are stationary solutions of the equations composed of the nonlinear ion continuity and ion momentum equations, together with the Poisson equation and the inertialess electron momentum equation in which the electric force is balanced by the quantum force associated with the Bohm potential that causes electron tunneling at nanoscales. The solitary ion waves are characterized by a large-amplitude electrostatic potential and ion density maxima and smaller amplitude minima on the flanks of the solitary waves. We identify the speed interval for the existence of the ion solitary waves around a quantum Mach number that is of the order of unity.

A non-local theory is used to study the effects of the corrugation parameter ε of a plasma-filled slow wave structure, the cyclotron frequency of a pumped magnetic field Ω and the relativistic gamma factor γ0 on the instability growth Γ of a free electron laser in the presence of an external finite axial magnetic field. The dispersion relation is derived and the growth rate is formulated in the Raman regime. The growth rate is approximately proportional to ε. There is a considerable decrease in the instability growth when the cyclotron frequency is close to ω0. The growth rate approximately scales inversely as the 19/2 power of the relativistic gamma factor.

We evaluate the correlated stopping power of a swift chain of N charges aligned with its (non-relativistic) velocity. We find that the distance required between two charges for the chain to act as a separated set of isolated charges is much larger than the dynamical screening length because the wake effect is very important when the chain elements are situated close to each other.

The existence of magnetosonic solitons in dusty plasmas is investigated. The nonlinear magnetohydrodynamic equations for a warm dusty magnetoplasma are thus derived. A solution of the nonlinear equations is presented. It is shown that, owing to the presence of dust, static structures are allowed. This is in sharp contrast to the formation of the so-called shocklets in usual magnetoplasmas. A comparatively small number of dust particles can thus drastically alter the behavior of the nonlinear structures in magnetized plasmas.

Low-frequency magnetic field fluctuations are observed in space plasmas, e.g. as upstream waves at the Earth's bow shock. Such upstream waves can steepen into very large amplitude wave phenomena, e.g. short large-amplitude magnetic structures (or SLAMS for short), shocklets or discrete wave packets. Such observations motivated us to study the nonlinear behavior of low-frequency and large-amplitude plasma waves in terms of the full nonlinear Hall–MHD framework. In the case of stationary (nonlinear) waves, the Hall–MHD equations can be rewritten in the so-called Sakai–Sonnerup system of equations that describe this plasma state and provide oscillatory and solitary types of solutions. An overall parameter study on the polarization characteristics, together with the magnetic field components and density variations of the different ranges of solutions, is presented here. These results can be further on applied to the theoretical treatment of particle interaction with such waves, e.g. at shocks in space plasmas, possibly leading to particle acceleration.

Monte Carlo simulation is conducted for a strongly coupled one-dimensional confined-particles system. We deal with an infinite chain of positively charged dust particles. The particles interact through the Yukawa screened potential. It is found that a critical value exists for the number of closest neighbors that are involved in the interaction. The inter-particle distance at equilibrium is found. Using these results, we study the dust-acoustic as well as the dust-lattice modes for two situations. In the first we neglect the friction force while in the second situation the presence of an ambient gas in plasma is considered.

In this paper we study the propagation of nonlinear ion-acoustic waves in plasmas with negative ions. The Gardner equation governing these waves in plasmas with the negative ion concentration close to critical is derived. The weakly nonlinear theory of modulational instability based on the use of the nonlinear Schrödinger equation is discussed. The investigation of the nonlinear dynamics of modulationally unstable quasi-harmonic wavepackets is carried out by the numerical solution of the Gardner equation. The results are compared with the predictions of the weakly nonlinear theory.

The random displacement of magnetic field lines in the presence of magnetic turbulence in plasmas is investigated from first principles. A two-component (slab/two-dimensional composite) model for the turbulence spectrum is employed. An analytical investigation of the asymptotic behavior of the field-line mean square displacement (FL-MSD) is carried out. It is shown that the magnetic field lines behave superdiffusively for very large values of the position variable z, since the FL-MSD σ varies as σ ~ z4/3. An intermediate diffusive regime may also possibly exist for finite values of z under conditions which are explicitly determined in terms of the intrinsic turbulent plasma parameters. The superdiffusive asymptotic result is confirmed numerically via an iterative algorithm. The relevance to previous results is discussed.

In this paper we review some theoretical aspects of the dynamics of the mesoscale filaments extending along the magnetic field lines in the edge plasma, which are often called ‘blobs’. We start with a brief historical survey of experimental data and the main ideas on edge and SOL plasma transport, which finally evolved into the modern paradigm of convective very-intermittent cross-field edge plasma transport. We show that both extensive analytic treatments and numerical simulations demonstrate that plasma blobs with enhanced pressure can be convected coherently towards the wall. The mechanism of convection is related to an effective gravity force (e.g. owing to magnetic curvature effects), which causes plasma polarization and a corresponding E× B convection. The impacts of different effects (e.g. X-point magnetic geometry, plasma collisionality, plasma beta, etc.) on blob dynamics are considered. Theory and simulation predict, both for current tokamaks and for ITER, blob propagation speeds and cross-field sizes to be of the order of a few hundred meters per second and a centimeter, respectively, which are in reasonable agreement with available experimental data. Moreover, the concept of blobs as a fundamental entity of convective transport in the scrape-off layer provides explanations for observed outwards convective transport, intermittency and non-Gaussian statistics in edge plasmas, and enhanced wall recycling in both toroidal and linear machines.