A second-order approximation is formulated and studied within the context of the quasi-particle description of magnetized plasmas. The general case of relativistic particles in non-uniform but stationary magnetic fields, and in additional force fields that are strongly non-uniform but slowly evolving in time compared with particle gyrations with the cyclotron frequency, is considered. In order to reveal the physical significance of the second-order approximation, the mean (reduced) particle velocity is calculated up to second order, when polarization particle drift as well as the renormalization of the lower-order result become equally significant. A general expression for the velocity of particle polarization drift is obtained in terms of quasi-particle properties, and with account taken of finite-Larmor-radius effects and non-uniformity of magnetic fields. A guiding-centre transformation is found that makes it possible to achieve equal mean velocities of particle, guiding centre and quasi-particle up to second order. Then polarization drifts enter the particle, guiding-centre and quasi-particle equations of motion.

Solitary waves in an ion-beam-plasma system are investigated theoretically using the pseudo-potential method, including finite temperatures of plasma ions and beam ions. The beam velocity is high enough to avoid ion-ion instability. Three kinds of solitary waves are possible, corresponding to ion- acoustic waves and to fast and slow space-charge waves in the beam. To observe the formation of solitary waves from an initial positive pulse, numerical simulations are performed. For the slow beam mode, a smaller solitary wave appears at the leading part of the pulse, which is a result of negative nonlinearity and anomalous dispersion of the slow mode, and is the opposite behaviour to the cases of the ion-acoustic wave and to the fast beam mode. Overtaking collisions of a solitary wave with a fast-mode solitary wave or with a slow-mode solitary wave are simulated.

A peculiarity of the quasi-optical propagation of a Gaussian beam of electromagnetic waves is that it requires a treatment taking account, step by step, of all of its rays together. The dispersion relation from which such a ray- tracing may be deduced is in fact characterized not only by the medium where the beam is launched but also by the intrinsic beam structure. The behaviour of three-dimensional Gaussian beams in the electron-cyclotron frequency range is considered, with particular attention paid to their propagation in toroidal plasmas of fusion interest (with ITER-like parameters and various magnetic equilibrium configurations), to the generality of their launching conditions and to their power deposition profiles around resonant layers.

Large-amplitude magnetic field fluctuations often accompanied by density variations are frequently observed in front of the earth's bow shock and in the vicinity of comets by extraterrestrial in situ measurements. They are identified as a manifestation of magnetohydrodynainic (MHD) waves in space plasmas. Because of their large amplitudes (i.e. because the magnetic field amplitude is of the order of the ambient magnetic field, for instance), these fluctuations cannot be satisfactorily described by linear wave theory. In this paper the properties of one-dimensional MHD waves of arbitrary amplitude, i.e. so-called simple MHD waves, are investigated, and a relationship is derived between the enhancement of the magnetic field and the density as well as the propagation velocity. Fast large-amplitude magnetosonic waves exhibit wave steepening. Here the dependence of the steepening time on the wave amplitude is derived and illustrated numerically.

The contribution of higher-order nonlinearity to nonlinear ion-acoustic waves in a weakly relativistic plasma consisting of a warm ion fluid and hot non- isothermal electrons is studied using reductive perturbation theory. At the lowest order of the perturbation theory a modified Korteweg–de Vries equation is obtained. At the next order a linear inhomogeneous equation is obtained. The stationary solution of the coupled equations is obtained using the renormalization method introduced by Kodama and Taniuti for reductive perturbation theory.

An application of the self-consistent multiple-scattering theory of electromagnetic waves to drift turbulent vortices is presented. Using the known single-vortex solution, the integral equation describing the scattering from a finite density of drift turbulent vortices is obtained. Rather than solving this equation and then averaging, the averaging operation is taken first to obtain statistical moment equations, from which the coherent and incoherent scattering follow. These results are expressed in a Fourier basis, and the cross-section is evaluated. Limiting forms of the theory and straightforward generalizations are discussed.

We study an ideal MHD plasma with the non-vanishing invariants energy, crosshelicity and magnetic helicity, confined in a cylinder with infinitely conducting walls and an externally applied magnetic field B0. The magnetic and velocity fields are expanded in base vector fields, satisfying Δ × Bλ = Bλ. Boundary conditions are imposed to make the curl a self-adjoint operator. The three invariants depend on the time-dependent coefficients of the base vector fields, and are used to construct the partition function to gather statistical information about the equlibrium thermodynamic state to which the plasma relaxes after a turbulent transition. For zero external magnetic field but large magnetic helicity, the energy resides preferentially in magnetic field fluctuations. A sizeable fraction of the kinetic energy initially present is transformed into magnetic energy. The energy condenses via an inverse cascade predominantly to the lowest energy eigenstate, in agreement with results obtained by Taylor. However, since we consider the whole spectrum of eigenstates, the energy does not exclusively occupy the lowest eigenstate. If the eigenvalues are densely spaced (as in a thin torus), the higher eigenmodes also contain appreciable amounts of energy, resulting in a finite pressure of the plasma. For constant and finite external magnetic field, the average induced magnetic field exactly cancels the external field. This indicates that, on a statistical average, the plasma is diamagnetic or superconducting. Superimposed on the average statistical state are fluctuations that may become large if the magnetic helicity is large.