A single-particle theory is developed to investigate particle acceleration along and across a magnetic field and the generation of an electric field transverse to the magnetic field induced by electromagnetic waves in a magnetized plasma. The almost perpendicularly propagating waves accelerate particles via their Landau and cyclotron damping, and the ratio of parallel and perpendicular drift velocities vs∥/vd can be proved to be proportional to k∥/k⊥. Simultaneously, an intense cross-field electric field E0 = B0×vd/c is generated via the dynamo effect owing to perpendicular particle acceleration to satisfy the generalized Ohm’s law. This means that this cross-field particle drift in a collisionless plasma is identical to E×B drift. It is verified that the transport equations obtained are exactly equivalent to those derived from the θ-dependent quasilinear velocity-space diffusion equation obtained from the Vlasov–Maxwell equations.

The resonant transition radiation from an electron charge that moves along the concentration gradient of a cold isotropic plasma is calculated. The possibility of using this radio-emission for inhomogeneous plasma diagnostics is discussed. Measurements of this kind of radiation in a planar-stratified cold isotropic plasma give the possibility of finding out the profile function of the plasma concentration profile (parts of the plasma density profile where the density is increased over its previous maximum value along the direction of the plasma bunch velocity).

A wave coupling formalism for magnetohydrodynamic (MHD) waves in a non-uniform background flow is used to study parametric instabilities of the large-amplitude, circularly polarized, simple plane Alfvén wave in one Cartesian space dimension. The large-amplitude Alfvén wave (the pump wave) is regarded as the background flow, and the seven small-amplitude MHD waves (the backward and forward fast and slow magnetoacoustic waves, the backward and forward Alfvén waves, and the entropy wave) interact with the pump wave via wave coupling coefficients that depend on the gradients and time dependence of the background flow. The dispersion equation for the waves D(k,ω) = 0 obtained from the wave coupling equations reduces to that obtained by previous authors. The general solution of the initial value problem for the waves is obtained by Fourier and Laplace transforms. The dispersion function D(k,ω) is a fifth-order polynomial in both the wavenumber k and the frequency ω. The regions of instability and the neutral stability curves are determined. Instabilities that arise from solving the dispersion equation D(k,ω) = 0, both in the form ω = ω(k), where k is real, and in the form k = k(ω), where ω is real, are investigated. The instabilities depend parametrically on the pump wave amplitude and on the plasma beta. The wave interaction equations are also studied from the perspective of a single master wave equation, with multiple wave modes, and with a source term due to the entropy wave. The wave hierarchies for short- and long-wavelength waves of the master wave equation are used to discuss wave stability. Expanding the dispersion equation for the different long-wavelength eigenmodes about k = 0 yields either the linearized Korteweg–deVries equation or the Schrödinger equation as the generic wave equation at long-wavelengths. The corresponding short-wavelength wave equations are also obtained. Initial value problems for the wave interaction equations are investigated. An inspection of the double-root solutions of the dispersion equation for k, satisfying the equations D(k,ω) = 0 and ∂D(k,ω) = ∂k = 0 and pinch point analysis shows that the solutions of the wave interaction equations for hump or pulse-like initial data develop an absolute instability. Fourier solutions and asymptotic analysis are used to study the absolute instability.

The self-magnetisation of circumstellar disks is considered within an appropriate multifluid description. These disks are composed of ionised and neutral gas as well as of a charged dust component. The most important equation in this context is the general Ohm’s law that includes a magnetic field generation term due to relative dust–neutral fluid velocities. We show that circumstellar disks can carry their own significant magnetic fields. As long as the stellar gravitation sustains the accretion flow, the self-magnetisation of the disk does not saturate until the field strength reaches its local equipartition value. The magnetic field generation process is illustrated by idealised multifluid simulations that are not restricted to a kinematic description, but model the process in a self-consistent way.