An intense short-pulse laser propagating through a plasma undergoes self-pulse distortion due to the combined effects of nonlinearity-induced self-focusing and dispersion. The nonlinearity arises as a result of relativistic mass variation. The low-intensity front of the pulse converges mildly, while the high-intensity later portions self-focus strongly. However, at the intensity maxima, the self-focusing effect is masked by the saturation effect of the nonlinear refractive index. The group velocity is also a function of intensity; as a result, the front of the pulse becomes sharpened, while the tail tends to be broadened.

The higher-order growth rate of instability for obliquely propagating kinetic Alfvén and ion-acoustic solitons in a magnetized non-thermal plasma have been obtained by the multiple-scale perturbation expansion method developed by Allen and Rowlands (1993). The growth rate of instability is obtained correct to order k2, where k is the wave number of a long-wavelength plane-wave perturbation. The corresponding lowest-order stability analysis has been considered recently by Bandyopadhyay and Das (2000b). It has been found that the kinetic Alfvén solitary waves are stable at the order of k but are unstable at the order of k2. It has also been found that the growth rate of instability at the order of k for ion-acoustic solitary waves is free from the parameters of the non-thermal plasma but at the order of k2 depends on the parameters of the non-thermal plasma.

Energy gain by an electron during its motion in the fields of the fundamental TE10 mode excited by microwave radiation in a rectangular waveguide is analysed. Expressions have been obtained for the fields of the mode, the angle of deflection and the acceleration gradient of the electron when it is injected along the direction of mode propagation. An electron of energy 25 keV gains 120.44 keV when a microwave of intensity 1010 Wm−2 at frequency 6 GHz is employed to excite the mode in a waveguide of width 0.03 m and height 0.02 m. The effects of the microwave frequency and the width of the waveguide are to decrease the electron energy gain for fixed microwave intensity. However, higher acceleration gradients are obtained when the electron is injected with greater initial energy.

A specific type of plasma-wave instability in a hot magnetoactive collisional plasma due to a weak external electric field and weak spatial inhomogeneity is considered for the cases of kinetic Alfvén-like waves. These low-frequency waves with ω [Lt ] Ωi (where Ωi is the ion gyrofrequency) are solutions of the corresponding dispersion relation. The model integral of Bhatnagar, Gross, and Krook is used for the description of collisions. The quasistatic time variation of the electric field amplitude makes it possible to use the ‘direct initiation’ mechanism to describe instability development. An expression for the growth rate is obtained in the framework of linear theory. The instability in question occurs for a certain equation of state of the plasma. For this equation of state, a numerical analysis of the obtained instabilities is performed.

The dynamics of a Hall thruster is investigated numerically in the presence of a plasma–wall interaction. The plasma–wall interaction is a function of the wall potential, which in turn is determined by the secondary electron emission and sputtering yield. In the present work, the effect of secondary electron emission and sputter yield have been considered simultaneously. Owing to disparate temporal scales, ions and neutrals have been described by a set of time-dependent equations while electrons are considered in a steady state. Based on the experimental observations, a third-order polynomial in electron temperature is used to calculate the ionization rate. The changes in the plasma density, potential and azimuthal electron velocity due to the sputter yield are significant in the acceleration region. The change in ion and electron velocity and temperature is small. The neutral velocity, which decreases initially, starts increasing towards the exit consistent with the computed neutral density profile. The results are qualitatively compared with the experiments.

Reconnective annihilation of magnetic field leads to the formation of magnetic flux cells with small scales, followed by enhanced transverse plasmons occurring in a thin current sheet with a very small vertical extent. The analysis here focuses on the nonlinear interaction between the flux and plasmons. The transverse plasmon field is modulationally unstable in the Lyapunov sense. When the initial pumping wave amplitude attains the threshold of instability, this instability occurs with a high growth rate. Nonlinear development of modulational instability eventually results in self-similar collapse, due to nonlinear equilibrium, giving rise to a spatially intermittent, collapsing magnetic flux, very similar to a turbulent pattern. The Maxwell stress tensor from the turbulence flux determines the anomalous magnetic viscosity, i.e. the parameter α. It is shown that the instability is responsible for the alternation of outburst or quiescent states in astrophysical accretion disks. When the instability occurs, the parameter α is large. In the quiescent state, the instability is suppressed, leading to a smaller, collapse-quenching value of α.

A technique is developed for analysing the linear collapse properties of spatially linear two-dimensional null points with open boundary conditions. A treatment is given of the collapse of nulls which have current and flow so that they are initially in a steady-state balance between a magnetic force, a pressure force and a centrifugal force. This extends the previous results for initially current-free X-type nulls with no flow. It is found that all X-points, regardless of the current and flow tend to collapse. Also, O-points collapse in the absence of a plasma flow, but O-points with a large current and possessing a highly super-Alfvénic plasma flow can be stable against linear collapse.