In this paper, a point of view is assumed where the tokamak is treated as a thermodynamic system open to external interactions. Those stationary states of the plasma are considered that are associated with a stationary entropy, i.e. with equilibrium between the entropy produced by the plasma and the entropy injected into it through the auxiliary heating. By means of the concept of magnetic entropy (a quantity that measures, in the framework of information theory and under suitable constraints, the probability of coarse-grained current density configurations), the responses can be analysed of the equilibrium magnetic configuration and of the related pressure profile to the intensity and to the deposition profile of the auxiliary heating when a condition of stationary entropy is attained. These factors are found to have considerable bearings on the magnetic equilibrium – in particular on the generation of states with negative magnetic shear. Moreover, the existence of a thermodynamic relation between entropy production and thermal conductivity involves a connection between magnetic structure and transport properties, and implies a strong reduction of the heat flow in the region of low or negative shear. Examples of practical interest are discussed both in the case of a homogeneous and that of a sharply localized power deposition.

We provide a revised, and substantially enriched, version of an old study of ours, dealing with the theory of the slow evolution of a strictly dissipative, cylindrical plasma column in vacuum [J. Plasma Phys.43, 217–237 (1990)]. After correcting a technical mistake made in our previous formulation of the model of the physical system under consideration, we develop a fully amended version of the associated theory, paying special attention to the problem's well-posedness. A number of comments, generalizations and further details have also been added.

The nonlinear theory of driven magnetohydrodynamic (MHD) waves in resonant slow-wave layers developed by Ruderman et al. [Phys. Plasmas4, 75 (1997)] is used to study the interaction of sound waves with a one-dimensional planar magnetic plasma configuration. The physical problem studied here is the same as that considered by Ruderman et al. [Phys. Plasmas4, 91 (1997)]. The difference is in the description of the wave motion in the resonant layer. Ruderman et al. assumed that dissipation dominates non-linearity in the resonant layer and considered the nonlinear term in the governing equation for the wave motion in the resonant layer as a perturbation. In contrast, it is assumed in the present paper that nonlinearity dominates dissipation in the resonant layer. The solution to the governing equation for the wave motion in the resonant layer is obtained in the approximation of strong nonlinearity, and it is shown that the amplitude of the wave motion saturates when the Reynolds number tends to infinity. This solution is then used to derive the nonlinear connection formula that determines the jump across the resonant layer in the velocity component in the direction of inhomogeneity. The nonlinear connection formula is, in turn, used to obtain a nonlinear one- dimensional integral equation describing the outgoing sound wave, which appears owing to partial reflection of the incoming sound wave from the inhomogeneous plasma. The solution to this integral equation is obtained in the form of a sinusoidal wave under the assumption that an incoming sound wave contains the fundamental harmonic only. The coefficient of wave-energy absorption is calculated analytically in the long-wavelength approximation and numerically for arbitrary wavelengths.

Plasma screening effects on elastic electron–ion collision processes in a Lorentzian (kappa)-distribution plasma are investigated using the eikonal method. The electron–ion interaction potential is obtained by introducing a plasma dielectric function εκ. The semiclassical straight-line trajectory method is applied to the path of a projectile electron in order to investigate the variation of the eikonal phase as a function of impact parameter and spectral index κ. In the first-order eikonal approximation, the dynamic plasma screening effect on the eikonal phase is found to be a static screening effect, and depends only on the Debye length and spectral index. The position of the maximum of the differential elastic eikonal cross-section recedes from the ion core with increasing spectral index. The plasma screening effect on the eikonal cross-section increases with decreasing spectral index.

Relaxation phenomena in two-dimensional (2D) plasma crystals have been investigated, including both the self-consistent electric charge of dust particles and the electron and ion velocity distribution functions, by means of a modified 2D particle-in-cell (PIC) method. The results obtained show that the mutual interaction of dust particles in such crystals leads to special properties of the background electrons and ions due to their selective collection by dust particles during the relaxation. These electrons and ions can behave as non-ideal components of dusty plasmas in plasma crystals even in cases where their numbers in the Debye cube are large. This effect is caused by their intensive charge exchange with dust particles, which provides dusty plasmas with the status of open statistical systems. The selective collection of electrons and ions by dust particles also causes their deviation from the initial equilibrium as well as the non-equilibrium evolution of the self-consistent electric charge of the dust particles. Relaxation phenomena in plasma crystals have to be taken into account in all cases of strong changes of plasma parameters, for example due to strong oscillations and waves in these crystals.