This study investigates the impact of local thermal non-equilibrium on the stability analysis of partially ionized plasma within a porous medium. The plasma, heated from below, is enclosed by various combinations of bounding surfaces. Both nonlinear (via the energy method) and linear (utilizing the normal mode analysis method) analyses are performed. Eigenvalue problems for both analyses are formulated and solved using the Galerkin method. The study also explores the effects of compressibility, medium permeability and magnetic fields on system stability. The collisional frequency among plasma components and the thermal diffusivity ratio significantly influence energy decay. The results reveal that the Rayleigh–Darcy number is identical for both nonlinear and linear analyses, thus eliminating the possibility of a subcritical region and confirming global stability. The principle of exchange of stabilities is validated, indicating the absence of oscillatory convection modes. Medium permeability, heat-transfer coefficient and compressibility delay the onset of convection, demonstrating stabilizing effects. Conversely, the porosity-modified conductivity ratio hastens the convection process, indicating destabilizing effects. Rigid–rigid bounding surfaces are found to be thermally more stable for confining the partially ionized plasma. Additionally, the magnetic field exerts a stabilizing influence.

This paper presents a theoretical model of plasma equilibrium in the diamagnetic confinement mode in an axisymmetric mirror device with neutral beam injection. The hot ionic component is described within the framework of the kinetic theory, since the Larmor radius of the injected ions appears to be comparable to or even larger than the characteristic scale of the magnetic field inhomogeneity. The electron drag of the hot ions is taken into account, while the angular scattering of the hot ions due to Coulomb collisions is neglected. The background warm plasma, on the contrary, is considered to be in local thermal equilibrium, i.e. has a Maxwellian distribution function and is described in terms of magnetohydrodynamics. The density of the hot ions is assumed to be negligible compared with that of the warm plasma. Both the conventional gas-dynamic loss and the non-adiabatic loss specific to the diamagnetic confinement mode are taken into account. In this work, we do not consider the effects of the warm plasma rotation as well as the inhomogeneity of the electrostatic potential. A self-consistent theoretical model of the plasma equilibrium is constructed. In the case of the cylindrical bubble, this model is reduced to a simpler one. The numerical solutions in the limit of a thin transition layer of the diamagnetic bubble are found. Examples of the equilibria corresponding to the gas-dynamic multiple-mirror trap device are considered.

Kinetic theory of particles near resonances is a current topic of discussion in plasma physics and astrophysics. We extend this discussion to the kinetic theory of the interaction between alpha particles (energetic particles predicted to exist in large quantities in next-generation fusion experiments) and a neoclassical tearing mode (NTM), a resistively-driven perturbation which sometimes exists in a tokamak. We develop a quasilinear treatment of the interaction between alpha particles and an NTM, showing why an NTM can be a source of significant passing alpha particle transport in tokamaks. The limitations on quasilinear theory constrain our theory's applicability to small amplitude NTMs, highlighting the importance of nonlinear studies.

The decay of a turbulent magnetic field is slower with helicity than without. Furthermore, the magnetic correlation length grows faster for a helical than a non-helical field. Both helical and non-helical decay laws involve conserved quantities: the mean magnetic helicity density and the Hosking integral. Using direct numerical simulations in a triply periodic domain, we show quantitatively that in the fractionally helical case the mean magnetic energy density and correlation length are approximately given by the maximum of the values for the purely helical and purely non-helical cases. The time of switchover from one to the other decay law can be obtained on dimensional grounds and is approximately given by $I_{H}^{1/2}I_{M}^{-3/2}$, where $I_{H}$ is the Hosking integral and $I_{M}$ is the mean magnetic helicity density. An earlier approach based on the decay time is found to agree with our new result and suggests that the Hosking integral exceeds naive estimates by the square of the same resistivity-dependent factor by which also the turbulent decay time exceeds the Alfvén time. In the presence of an applied magnetic field, the mean magnetic helicity density is known to be not conserved, and we show that then also the Hosking integral is not conserved.

It is common wisdom that collisionless shocks become non-planar and non-stationary at sufficiently high Mach numbers. Whatever the shock structure, the upstream and downstream fluxes of the mass, momentum and energy should be equal. At low Mach numbers, these conservation laws are satisfied when the shock front is planar and stationary. When this becomes impossible, inhomogeneity and time dependence, presumably in the form of rippling, develop. In this study, we show that the shock structure changes as a kind of ‘phase transition’ when the Mach number is increased while other shock parameters are kept constant.

An ionized gas medium (plasma state) turns to a complex state of plasma or dusty plasma if micrometre- to submicrometre-sized solid dust particles are introduced in it. The dusty plasma medium exhibits fluid- as well as solid-like characteristics at different background plasma conditions. It supports various linear and nonlinear dynamical structures because of external perturbation and internal instabilities. The vortical or coherent structure in the dusty plasma medium is a kind of self-sustained dynamical structure that is formed either by instabilities or by external forcing. In this review article, the author discusses the past theoretical, experimental and computational investigations on vortical and coherent structures in unmagnetized and magnetized dusty plasmas. The possible mechanisms of the formation of vortices in a dust-grain medium are discussed in detail. The studies on the evolution of vortices and their correlation with turbulence are also reviewed.