It is shown that the classical magnetohydrostatic equations of an infinitely conducting fluid reduce to the integrable potential Heisenberg spin equation subject to a Jacobian condition if the magnitude of the magnetic field is constant along individual magnetic field lines. Any solution of the constrained potential Heisenberg spin equation gives rise to a multiplicity of magnetohydrostatic equilibria which share the magnetic field line geometry. The multiplicity of equilibria is reflected by the local arbitrariness of the total pressure profile. A connection with the classical Da Rios equations is exploited to establish the existence of associated helically and rotationally symmetric equilibria. As an illustration, Palumbo's ‘unique’ toroidal isodynamic equilibrium is retrieved.

Probe theory is generally used to find the potential of dust particles immersed in plasma. The orbital motion limited theory (OML) is often used to find the potential at the probe surface, but the assumptions underlying this theory are usually not valid in the case of dust and the more general orbital motion (OM) theory is much harder to calculate. Solutions are given for the OM theory in a range of cases applicable to dust. It is shown that the surface potential the full theory gives reduces to the OML result for small probes. Commonly in dusty plasmas the OML surface potential is used, with the surrounding distribution given by Debye–Hückel, or Yukawa theory. This form, however, neglects ion depletion due to the absorption of particles on the probe surface. In this paper a new analytical solution to the system is given which is applicable to small probes and dust. This new expression is equivalent to Yukawa form, but takes ion absorption into account.

A new model of ball lightning is proposed. The main model assumption is that ball lightning has a core consisting of clouds of electrons and totally ionized ions which oscillate with respect to each other. According to the model, ball lightning emits high energy photons that are sometimes dangerous for human beings, and in a number of situations it can kill humans by electric pulses; the ball lightning energy can be of the order of 106 J and even greater. The electric charges that need to be injected into the atmosphere to create ball lightning and the currents, providing the injection of such charges, are estimated. These estimates predict that ball lightning can be created in the experiments with ordinary lightning or powerful electrical installations.

The initial processes excited directly by high-frequency (HF) heating waves include parametric decay instabilities, which decay the HF heating wave to a frequency-downshifted Langmuir/upper hybrid sideband together with an ion acoustic/lower hybrid wave as the decay mode, and oscillating two stream instabilities, which decay the HF heating wave to two oppositely propagating Langmuir/upper hybrid sidebands and purely growing mode/field-aligned density irregularities. These instabilities provide effective channels to convert heating waves to electrostatic plasma waves in the F region of the ionosphere. The following-up parametric instabilities include the cascades of Langmuir pump waves into Langmuir sidebands and ion acoustic waves/lower hybrid waves, and the decay of upper hybrid waves to Langmuir sidebands and ion decay modes, as well as the filamentation of those HF electrostatic waves to generate field-aligned density irregularities. The instability thresholds, growth rates, angular distribution and regions of excitation are determined.

The evolution of a magnetic field line in two dimensions near a neutral sheet is analysed. It is found that the general features of this evolution are rather independent of any particular model, provided that the magnetic field is small and the current density does not vanish. The time of arrival of a field line to the neutral sheet as well as its breaking and reconnection are proved to be finite and to satisfy a simple formula whose main parameter is the resistivity, which may be a spatial function. The shape of the evolving field lines satisfies a differential equation whose solution in some simple cases is shown to agree with certain classical reconnection configurations. Hyperresistivity is found to be more often a hindrance than a positive contribution to the reconnection process.

The motivation of this paper is to study the formation of a sheath in plasma contaminated with additional negative ions. Sheath formation has been analysed through the solution of the Sagdeev potential equation derived in a plasma by using the pseudopotential method. Because of the negative ions, it has been shown that the sheath formation, in contrast to that in a simple plasma, faces difficulties. A potential barrier from which modes are reflected is introduced and the potential variation beyond it is complex which, in turn, shows new findings. It is also revealed that the potential variation should be estimated in the plasma sheath in the presence of low as well as high negative-ion concentrations. The levitation of a dust grain into the sheath and its characteristic behaviour have also been investigated. Furthermore, the dust size in the ideal plasma sheath along with the causes of formation of the dust atmosphere have been studied.