Dispersion relations for elliptically polarized extraordinary as well as linearly polarized ordinary electromagnetic waves propagating across an external magnetic field in a dense magnetoplasma are derived, taking into account the combined effects of the quantum electrodynamical (QED) field, as well as the quantum forces associated with the Bohm potential and the magnetization energy of the electrons due to the electron-1/2 spin effect. The QED (vacuum polarization) effects, which contribute to the nonlinear electron current density, modify the refractive index. Our results concern the propagation characteristics of perpendicularly propagating high-frequency electromagnetic waves in dense astrophysical objects (e.g. neutron stars and magnetars), as well as the next-generation intense laser–solid density plasma interaction experiments and quantum free-electron laser schemes.

The existence of Bernstein–Greene–Kruskal (BGK)-like trapped ion modes in dusty plasmas is investigated by means of the pseudo-potential method applied to the Vlasov–Poisson system. The nonlinear dispersion relation, determining the phase velocity, and the pseudo-potential, representing the wave form and hence its spectral decomposition, are derived and analysed with respect to the effect of dust. Dust is found to diminish the region in ω, k-space, where periodic wave solutions of fast and slow mode character exist. Localized wave solutions in the form of solitary ion holes, owing their existence to the presence of dust, coexist as well, but turn into slow ion acoustic double layers in the limit of vanishing dust.

Low-frequency fluctuations are observed in a plasma confined by a strong dipole magnet and containing an energetic high-pressure population of trapped electrons. The quasi-coherent fluctuations have frequencies characteristic of drift frequencies of the lower temperature background plasma and have large toroidal and radial extent. They are excited throughout a wide range of plasma conditions determined by the level of neutral gas pressure. However, for a sufficiently high rate of neutral gas fueling, the plasma density profile flattens and the fluctuations disappear.

In this paper we numerically investigate the effects of various geometrical parameters of a backward wave oscillator (BWO), filled with a magnetized plasma of uniform density and driven by a mild relativistic solid electron beam, on the instability growth rate (Γ) of a free electron laser (FEL). The FEL instability is numerically calculated and the result is compared with the instability growth rate of an annular electron beam for the same set of parameters. The instability growth for a solid electron beam scales inversely to the seventh power of relativistic gamma factor γ0 and directly proportional to the corrugation amplitude.

Reconnection is believed to be responsible for plasma acceleration in a large number of space and astrophysical objects. Onset of reconnection is usually related to instabilities of current sheet equilibria. Analytical self-consistent models of an equilibrium current sheet (Harris equilibrium) are known for non-relativistic plasmas and some special cases of relativistic plasmas. We develop a description of generalized Harris equilibria in collisionless non-relativistic and relativistic plasmas. Possible shapes of the magnetic field are analyzed.

The Korteweg–de Vries–Zakharov–Kuznetsov (KdV-ZK) equation describes the nonlinear behaviour of long-wavelength weakly nonlinear ion-acoustic waves propagating obliquely to an external uniform (space independent) static (time independent) magnetic field in a plasma consisting of warm adiabatic ions and a superposition of two distinct population of electrons, one due to Cairns et al. (1995 Geophys. Res. Lett.22, 2709), which generates the fast energetic electrons, and the other the well-known Maxwell–Boltzman distributed electrons. It is found that the compressive or rarefactive nature of the ion-acoustic solitary wave solution of the KdV-ZK equation does not depend on the ion temperature if σc<0 or σc>1, where σc is a function of β1, nsc and σsc. This β1 is the non-thermal parameter associated with the non-thermal velocity distribution function of electrons (Cairns et al.), nsc is the ratio of the unperturbed number density of the isothermal electrons to that of the non-thermal electrons and σsc is the ratio of the average temperature of the non-thermal electrons to that of the isothermal electrons. The KdV-ZK equation describes compressive or rarefactive ion-acoustic solitary wave according to whether σc<0 or σc>1. When 0 ≤ σc ≤ 1, the KdV-ZK equation describes compressive or rarefactive ion-acoustic solitary wave according to whether σ>σc or σ<σc, where σ is the ratio of the average temperature of ions to the effective temperature of electrons. If σ takes the value σc with 0 ≤ σc ≤ 1, the coefficient of the nonlinear term of the KdV-ZK equation vanishes and for this case the nonlinear evolution equation of the ion-acoustic wave is a modified KdV-ZK (MKdV-ZK) equation. It is found that the four-dimensional parameter space, originated from the physically admissible values of the four-parameters β1, σ, σsc and nsc of the present extended plasma system, can be decomposed into five mutually disjoint subsets with respect to the critical values of the different parameters, and the nonlinear behaviour of the same ion acoustic wave in those subsets can be described by different modified KdV-ZK equations. A general method of perturbation of the dependent variables has been developed to obtain the different evolution equations. The applicability of the different evolution equations and their solitary wave solutions (along with the conditions for their existence) have been investigated analytically and graphically.

The dispersion relation for superluminal waves in degenerated and isotropic electron–positron plasmas is investigated. The dispersion equation of linear waves is derived from the relativistically correct form of the dielectric function and the Fermi distribution function. Analytical dispersion laws for the real part of the wave frequency are derived by applying the long-wavelength approximation and the short-wavelength approximation. Using the numerical simulation method, we obtain the full dispersion curve which cannot be given by an analytic method.

Assuming a non-relativistic three species electron–positron–ion plasma, the counterstreaming instability is investigated for waves propagating parallel and perpendicular to a homogeneous background magnetic field. To support previous analytical investigations (Tautz and Sakai 2007), the instability is investigated by means of self-consistent particle-in-cell simulations. It is shown that the presence of a third particle species is responsible for a variety of new features that cannot be seen either from an electron–ion plasma or for an electron–positron plasma.

The Kelvin–Helmholtz instability on the interface of two magnetized compressible fluids with tangential discontinuity is studied in two situations. For a sharp interface, the stability conditions of the surface with tangential discontinuity is investigated. It is shown that in this case magnetohydrodynamic modes such as Alfvén and the magnetosonic waves can propagate. When a transition layer exists between two fluids and the density and magnetic field change across this layer, numerical solutions show that the increase of the Mach number and compressibility has a destabilizing effect while the magnetic field and density increase has a stabilizing effect.

The pinch process of plasma columns generated by capillary discharge is studied theoretically with a snow-plow model. The multiple pinch evolution of plasma is obtained from the theoretical results. The effects of pressure and current amplitude on multiple pinches are calculated, and the results show that the pinch time decreases nonlinearly with decreasing pressure or increasing current. In the experiment, the laser spike of Ne-like Ar at 46.9 nm is obtained with an X-ray diode (XRD). The pressure filling in the capillary is changed to observe the variation of lasing onset time. According to real current waveforms, the pinch process is simulated. The results show that the laser spike occurs around the third pinching time. In addition, the experimental results indicate that there is an optimum pressure for the laser output.

The importance of thermal radiation on the Jeans instability is discussed for a magnetized dusty plasma with gravitational effects. The one-fluid MHD equations are developed by assuming that the entropy of each subsystem of plasma is conserved, when the temperature of the plasma species is non-relativistic. The dispersion relation in this case shows that thermal radiation helps to stabilize the Jeans instability. It is shown that the plasma is stable in a certain range of wavelengths. The magnetic field stabilizes the Jeans instability when the wave propagates across the magnetic field. However, for oblique propagation it is seen that the magnetic field does not stabilize the Jeans instability.