The propagating source method has been extended to solve the Boltzmann equation with a quasi-linear diffusion scattering operator. A half-range polynomial expansion method is used to reduce the integral-diffusion form of the ‘collisional’ Boltzmann equation to an infinite set of linear hyperbolic partial differential equations in the harmonics of the polynomial expansion. The lowest-order truncation of the coupled set of equations yields an inhomogeneous form of the well-known telegrapher equation, which, unlike the homogeneous telegrapher equation, does not introduce physically unrealistic pulse solutions. Anisotropic quasi-linear scattering models for which the index $q$ of the power spectrum of magnetic fluctuations satisfies $1\,{<}\,q\,{<}\,2$ admit slow scattering through $90^{\circ}$ and no scattering through $90^{\circ}$ for $q \,{\ge}\,2$. Accordingly, four models that either allow or enhance scattering through $90^{\circ}$ are used to augment the standard quasi-linear model for pitch-angle scattering. These are mirroring, dynamical turbulence and two distinct wave-based models. In the case that mirroring is responsible for scattering particles through $90^{\circ}$, together with the standard QLT (quasi-linear theory) pitch-angle diffusion model for scattering within the forward and backward hemispheres, it is found that the QLT isotropic and anisotropic models are well approximated by relaxation time scattering models. As an application of the general study, the implications of the four models introduced to redress the difficulties faced by QLT in describing scattering through $90^{\circ}$ are briefly considered. An initial beam was found to relax more rapidly for either the dynamical turbulence or wave models with resonant scattering through $90^{\circ}$ than for mirroring models.

We develop a fully nonlinear theory of electrostatic stationary waves of the ion-cyclotron-acoustic type propagating in a magnetized plasma. The analysis is facilitated by the existence of two fundamental constants of the motion, namely conservation of momentum flux parallel to the ambient field, and conservation of energy in the direction of propagation of the wave. These lead to the structure of the waves being governed by a first-order differential equation for the longitudinal ion flow speed and, therefore, its properties are readily analysed. In the case of subsonic wave speeds, compressive soliton wave structures propagate in a cone of obliquity around the magnetic field. If the wave speed is supersonic, the waves are oscillatory in nature, and asymmetric about the compressive and rarefactive phases, essentially because, in the compressive phase, the flow is driven towards its sonic point, whereas in the rarefactive phase, the flow is driven away from its sonic point. As the initial ‘driver’ field approaches a critical value, the end point of the compression coincides with the sonic point, with the result that the waveform in the flow speed (and potential) forms a cusp. It is possible that this feature may provide an explanation for the spiky waveforms observed by FAST and other similar satellite observations.

In the context of ion-acoustic waves in a magnetized plasma comprising cold ions and non-isothermal electrons, the present authors have previously shown small amplitude, weakly nonlinear waves to be governed by a modified version of the Zakharov–Kuznetsov equation. In this paper, we consider a plane solitary travelling-wave solution to this equation that propagates at an angle $\alpha$ to the magnetic field, where $0\,{\le}\,\alpha\,{\le}\,\pi$. The multiple-scale perturbation method developed by Allen and Rowlands is used to calculate the growth rate of a small, transverse, long-wavelength perturbation. To first order there is instability for $0\,{\le}\,\sin\alpha\,{<}\,\sin\alpha_{\rm c}$, where the critical angle $\alpha_{\rm c}$ is identified. At second order, the singularity which apparently occurs in the growth rate at $\alpha\,{=}\,\alpha_{\rm c}$ is removed by using a method devised by Allen and Rowlands; then it is found that there is also instability for $\sin\alpha\,{\ge}\,\sin\alpha_{\rm c}$. A numerical determination for the growth rate is given for the instability range $0\,{<}\,k\,{<}\,3$, where $k$ is the wavenumber of the perturbation. For $k|{\rm sec}\,\alpha|\,{\ll}\,1$, there is excellent agreement between the analytical and numerical results. The results in this paper agree qualitatively with those of Allen and Rowlands for the Zakharov–Kuznetsov equation.

In this paper, we add a supplementary contribution and support to the path integral method by exploring the theory of radiation in plasma physics. This method, based on the Feynman path integral formalism, has the advantage of treating the electrons and ions on the same physical basis and both time-independent and time-dependent problems on the same footing. Since the main quantity in the problem of plasma radiation is the dipolar autocorrelation function of the radiator, we derive it using the path integral technique in its perturbative form. We show that the dipolar autocorrelation function could be written as a generalized expression taking into account the time-dependency effects.

The Boltzmann collision integral for binary encounters is restricted to rarefied gases and plasmas by the constraint that the mean free path be much larger than the range of interaction. For dense media the two lengths become comparable and a proper account of the mutual influence exerted by one particle on the other during a collision must be taken. There are also other situations involving charged–charged long-range interactions for which this condition is met even in rarefied plasmas. The matter is considered in this work with the solution of the BBGKY (Born, Bogoliubov, Kirkwood, (H. S.) Green, Yvon) equation to determine the joint distribution function for the encountering particles. It is shown, in particular, that for dense gases the results replace the traditional Enskog $\chi $ factor, whereas for plasmas oscillatory phenomena can be driven. The proposed theory constitutes an improvement over the revised Enskog theory (RET) to the extent that it is not restricted to the soft sphere encounters, but valid for any sort of field interaction between colliding particles. Moreover the correlation term replaces the unsuitable restitution coefficient of the RET approach, which is restricted to impact theory. The present material is important for studies in solar and terrestrial physics, which require the sole knowledge of the one particle distribution function, namely gas dynamics and Coulomb plasma research.

Dust charging in the sheath is investigated with the single dust model. The sheath profile and variation of dust charge are revealed under the effect of ion temperature. It is shown that the dust particles are rapidly positively charged in the pure ion sheath near the wall and that the ion motion effectively shifts the zero-point of the dust charge to the wall.

Magnetohydrodynamic processes in thin accretion disks involving magnetic viscosity are investigated. The relevant MHD equations for the thin disk approximation and the anomalous magnetic viscosity dependent on temperature $T$ and radius $r$ are included. These stationary structures, including distributions of the surface mass density, temperature, in-flow velocity and magnetic fields of a disk around a young stellar object, are numerically examined. It is shown that the consideration of anomalous viscosity is necessary for the validity of the distributions. For example, the surface density is a decreasing function of radius because of it and there is a strange increasing part in the distribution of the density if it is ignored. In particular the distribution of effective temperature is a smoothly decreasing function of radius with power index $q\,{=}\,{-}\frac{1}{2}$, corresponding to the observed radiation flux density, provided that the magnetic fields are suitably chosen.

The stability of the neutral current sheet is analyzed in the frame of Hall dynamics. The problem is treated analytically and results are verified by numerical processing. A new version of tearing instability is found and described. It scales more favorably with the Lundquist number and has smaller wavelengths. Combined Hall magnetohydrodynamic analysis shows that Hall effects dominate the diffusion layer and growth rate of the instability in a relatively large range of sheet widths. The effect of finite beta on instability is described.

Low-frequency instabilities excited by energetic oxygen ions are investigated. The model consists of Maxwellian distributions for electrons and protons and Dory–Guest–Harris loss-cone distribution for oxygen ions. The electrons and protons are treated as magnetized and oxygen ions as unmagnetized. The response of the electrons is fully electromagnetic and that of the protons and oxygen ions is electrostatic. A possible application of the investigation to space plasmas is pointed out.

Electron acceleration by the ponderomotive force of a laser pulse with duration less than the plasma wavelength in inhomogeneous underdense plasmas is studied by two-dimensional relativistic parallel particle-in-cell (PIC) code. Particular attention is paid to the mechanism of electron acceleration associated with the increasing group velocity of the laser pulse. In an underdense plasma layer with linearly descending density profile, the accelerated electrons move together with the laser pulse which propagates with increasing group velocity. In an inhomogeneous pre-plasma with linearly ramping density profile, as the incident laser propagates up the density gradient with decreasing group velocity, ponderomotive acceleration is reduced compared with the uniform pre-plasma. As the reflected laser propagates down the density gradient with increasing group velocity, the ponderomotive acceleration by the reflected laser is more effective due to increasing group velocity of the reflected light and the return currents induced by the incident laser light. Relativistic electrons with multi-tens-MeV energies are generated.

Starting from the full set of governing equations including the weak relativistic effect, three coupled nonlinear equations with higher order nonlinear and dispersive terms are derived, which describe the nonlinear evolution of a three-dimensional electromagnetic wave packet propagating in a plasma. Two particular cases are considered, where the space dependence of the dependent variables is either on the space coordinate along the direction of propagation of the wave or on that along an arbitrary fixed direction. In both cases the three coupled equations reduce to a single equation. This single equation is used to study the modulational instability of a uniform electromagnetic wave train. It is found that due to the inclusion of the weak relativistic effect there is always modulational instability, and a higher order nonlinear term in the evolution equation has a stabilizing influence.