Kinetic Alfvén solitons with hot electrons and finite electron inertia in a low-beta (β=8πn0 T/B2G, the ratio of the kinetic to the magnetic pressure) plasma is studied analytically, with the ion motion being considered dominant through the polarization drift. Both compressive and rarefactive kinetic Alfvén solitons are found to exist within a definite range of kz (the direction of propagation of the kinetic Alfvén solitary waves with respect to the direction of the magnetic field) for each pair of assigned values of β and M (Mach number). Unlike in previous theoretical investigations, β appears as an explicit parameter for the kinetic Alfvén solitons in this case. In addition, consideration of the electron pressure gradient is found to suppress the speed of both the Alfvén solitons considerably for A (=2QM2/βk2z, with Q the electron-to-ion mass ratio) less than unity.

The effect of a stochastic electron background on the stability of low-m tearing modes is studied. The coherent direct interaction approximation is applied to the drift-kinetic equation in order to include the effects of current density diffusion, electron density diffusion and magnetic field diffusion in the tearing mode equations. It is found that for the m=1 mode in the collisionless regime the magnetic field diffusion destabilizes the mode further, while in the collisional regime these diffusions may not significantly affect the mode; for the m[ges ]2 modes in the collisional and semicollisional regimes the electron density diffusion stabilizes the modes, while in the collisionless regime the effects of current density diffusion and electron density diffusion may balance each other without significantly affecting the modes.

The second-order approximation in a quasiparticle description of magnetized plasmas is studied. The second-order adiabatic invariant of quasiparticle motion is found. Global adiabatic invariants for a magnetized plasma are revealed, and their possible role in energy exchange between particles and fields, nonlinear mode cascades and global plasma stability is discussed.

A collision integral for three-wave interactions in a collisionless plasma is derived from the full plasma description by means of the Klimontovich–Dupree and Maxwell equations. This collision integral differs from its traditional counterpart (calculated within the framework of Vlasov theory) by an additional functional factor. This means that the changes in the wave spectral density, which are induced by three-wave interactions, occur with a rate other than that calculated in Vlasov theory.

The existence and properties of nonlinear lower-hybrid-like waves in a dusty plasma are discussed. It is found that both rarefactive and compressive types of solitons can exist in the presence of isothermal hot electrons and negatively charged dust grains. Only compressive solitons are found to occur when the dust grains are positively charged or the hot electrons are non-isothermal. The amplitude, velocity, width and nature of the nonlinear structure are greatly affected by the hot electron concentration as well as by the charge-to-mass ratio of the dust grains.

A study is made of the influence of nonlinearity upon the structure of a steady-state disturbance brought about by low-frequency (ω[Lt ]ωi) monochromatic magnetosound propagating in a transversally inhomogeneous low-pressure plasma (β[Lt ]me/mi), in the vicinity of the Alfvén resonance point for the case when the principal linear mechanism for forming the transverse structure is provided by magnetic field diffusion due to small plasma resistivity. It is shown that the nonlinear properties of the fundamental harmonic of a disturbance are determined by its self-action through a plasma density variation that it produces. The disturbance structure in the region of the Alfvén resonance is described.

The stability condition and growth rate of the ideal, internal m=n=1 kink mode in a toroidal plasma are calculated by means of a direct inverse-aspect-ratio expansion of the magnetohydrodynamic (MHD) equations, rather than by using the energy principle. The analysis is based on the use of computer-aided algebra. The general equation for incompressible MHD oscillations in a low-β circular tokamak is derived to lowest order in the inverse aspect ratio. This derivation generalizes the Pfirsch-Schlüter factor for the kinetic energy in toroidal geometry.

The non-oscillating part of the magnetic moment field (called the inverse Faraday effect (IFE) for this field from a circularly polarized wave in a medium) is calculated for the interaction of an elliptically polarized wave with a weakly ionized magnetized plasma in a kinetic theory model and with unmagnetized Vlasov plasmas. For a weakly ionized magnetized plasma, the induced field increases with both temperature and ambient magnetic field. For an unmagnetized plasma, it increases parabolically with temperature. The induced magnetic field is found to vary parabolically with temperature in the case of an unmagnetized Vlasov plasma.

In the analysis of the propagation of electromagnetic waves in the electron cyclotron frequency range, in both isotropic media and magnetoactive plasmas, the role of diffractive effects, which are not accounted for by geometrical optics, may no longer be neglected when highly collimated beams are to be employed. Moreover, when lenses, mirrors, refractive gradients and/or wave cut-offs are placed along the beam trajectory, the very concept of independent optical rays tends to introduce singularities, which do not always correspond to physical features. A quasi-optical approach has previously been shown to present the advantage of allowing a description (at the lowest order of approximation) of the diffractive widening of the beam. The specific aim of this paper is to test, when reflection, refraction or beam focusing indicates the need for particular attention, the solution method employed within such an approach. The results presented here concern the propagation and power deposition profiles, in a number of crucial physical situations, of narrow electron cyclotron beams launched, in Gaussian form, either into isotropic transparent media or through anisotropic toroidal plasmas of fusion interest.

The stochastic properties of a plasma are taken into account in the consideration of the modulational interactions of waves associated with lower-hybrid (LH) resonance. The limits of applicability of the theory of weak plasma turbulence in the description of the modulational processes are found. It is demonstrated that the development of the modulational instability of waves with frequencies at the LH resonance results in a rapid decrease in stochasticity. This effect is associated with the formation of coherent structures due to the modulational interactions. Eventually a state with local minima of entropy in places where the coherent structures are located is formed. The description of the interaction between waves and particles in the coherent structures is discussed.

The stopping power S=S1+SB for charged particles in non-ideal degenerate quantum plasmas is calculated with the help of the dielectric formalism in an approximation corresponding to taking account of the Barkas effect (the term SB; the term S1 corresponds to the Bethe formula). It is found that for a high projectile velocity vp>vF (where vF is the Fermi velocity) in non-ideal plasmas, SB∝e3pv−3p (where ep is the charge of the projectile), the well-known law for the Barkas effect, SB∝e3pv−5p being valid only for ideal plasmas. This relation explains a number of experiments on stopping of different charged particles (protons, muons and heavy ions) in metals without the introduction of fitted parameters. The possibility of extending of this theory to gaseous non-ideal plasmas arising in inertial-confinement fusion (ICF) experiments is also briefly discussed.

The theory of electron-beam interaction with Bernstein plasma modes is developed for conditions of active space plasma experiments as well as experiments in large vacuum chambers. Translational movement of the beam along a magnetic field and Larmor rotation of the beam are considered as sources of free energy for wave build-up. Part of the energy of translational movement is lost to the excitation of Langmuir plasma oscillations. Bernstein modes then slowly grow owing to a ‘fan’-type instability. In this case the emission spectrum consists of lines near the half-harmonics of the electron gyrofrequency, ≈(n+½)ωc. Larmor gyration of the beam is not destroyed by the excitation of Langmuir turbulence, and thus there is strong hydrodynamic interaction of the rotated beam with the Bernstein modes. Integer harmonics of gyrofrequency nωc are generated in this case, with the spectral maximum near the upper-hybrid plasma frequency.

A novel Lagrangian integral formalism is applied to pure electron diodes. Analytical expressions are obtained in terms of the injected current and of the potential drop for two DC states. These two states are either completely transmitted flows or flows with partial reflection at a virtual cathode. Splitting rates and other quantities are presented for arbitrary potentials.

Six ansatzes are investigated for their potential to allow three-dimensional (3D) ideal magnetohydrodynamic (MHD) equilibria. The ansatzes are based on a Clebsch representation for the magnetic field, B=∇H × ∇k, and a ‘generalized Clebsch representation’, B=∇×(∇K × ∇k), with ∇k being one of the coordinate directions of a cylindrical coordinate system. Three classes of equilibria, all with a straight magnetic axis, are obtained. Equilibria of the first class have a purely poloidal magnetic field of the Clebsch type with k=z and include the 3D equilibria already known. Equilibria of the other two classes have a purely toroidal (i.e. here longitudinal) magnetic field and pressure surfaces that can be chosen such that poloidal sections are closed. The second class is based on a Clebsch representation with k=θ. Solutions contain a free function of θ that determines the poloidal sections of the pressure surfaces at, say, z=0. The behaviour in the toroidal direction is then fixed but not periodic. For the third class, the generalized Clebsch representation with k=z is used. The equilibria are similar to those of the second class, with two important differences. They contain no free function and field lines are not planar. Finally, 3D vacuum fields, which exhibit 3D magnetic surfaces, are presented. They have the same geometry as the equilibria of the third class, and in fact can be obtained as a certain limit from these equilibria. Possible applications of the equilibria found are mentioned.

The magnetic configuration in the confinement zone of a tokamak admits a magnetic flux-bifurcation for critical values of the edge parameters and given injected power when the initial L-state is so defined as to be associated with a stationary magnetic entropy. Assuming the ITER89-P scaling of the energy confinement time in the L state, it is shown that the power is changing along the bifurcation threshold, for fixed values of the edge parameters, according to the law P=Cn0.77B0.97 (where n is the average density and B is the toroidal magnetic field), where the numerical value of the constant C follows from ITER89-P and is consistent with observations of the L–H transition. It is also shown that the observed independence of the threshold with respect to the current is a consequence of the fact that, at the threshold point, the ratio between the auxiliary power and the Ohmic power PΩ in the confinement region is constant when the current is changing and that the value of PΩ at the threshold is a very slow function of the current.

Bohm sheath criteria and double layers are investigated in general multispecies plasmas containing a number of lighter, thermal species, described by Boltzmann distributions, in the presence of a number of heavier species described by cold fluid theory. A nonlinear description for one-dimensional stationary self-similar electrostatic modes is given using the Sagdeev potential. We generalize the classic Bohm sheath criteria by giving appropriate multispecies definitions of drift and ion-acoustic velocities, leading to a global supersonic condition. We also discuss plasmas with only one Boltzmann species, to show that double layers cannot be supported at all, no matter how many cold fluid species are present, and do so by analytical rather than numerical means, based on the full Sagdeev potential. Series expansions for weak double layers occurring in the literature can only claim to find double layers, erroneously as we indicate, by not confirming whether the necessary consistency relations are obeyed, and also by not checking that ‘neglected’ terms in the expansion overwhelm those retained.

A covariant version of Vlasov theory is used to derive the linear response 4-tensor for a relativistic magnetized thermal plasma, generalizing Trubnikov's 3-tensor form. The charge-continuity and gauge-invariance conditions imply a set of integral identities, and use of these identities allows one to derive a manifestly gauge invariant form for the response 4-tensor. This form implies an alternative version of Trubnikov's 3-tensor. The different versions lead to different expressions in the weakly relativistic small-gyroradius limit. Arguments are given as to how this inconsistency should be resolved.