By solving the coupled equations of the electromagnetic field and electrostatic potential, we investigate solitary waves in an asymmetric electron–positron plasma and/or electron–positron–ion plasmas with delicate features. It is found that the solutions of the coupled equations can capture multipeak structures of solitary waves in the case of cold plasma, which are left out by using the long-wavelength approximation. By considering the effect of ion motion with respect to non-relativistic and ultra-relativistic temperature plasmas, we find that the ions’ mobility can lead to larger-amplitude solitary waves; especially, this becomes more obvious for a high-temperature plasma. The effects of asymmetric temperature between electrons and positrons and the ion fraction on the solitary waves are also studied and presented. It is shown that the amplitudes of solitary waves decrease with positron temperature in asymmetric temperature electron–positron plasmas and decrease also with ion concentration.

Dust acoustic solitary waves, blow-up solitary waves and periodic waves have been investigated in unmagnetized dusty plasmas with Maxwell-distributed electrons and ions, considering dust charge fluctuations using the bifurcation theory of planar dynamical systems. The basic equations are transformed to an ordinary differential equation involving the electrostatic potential. Applying the bifurcation theory of planar dynamical systems, we have established the existence of solitary, blow-up solitary and periodic waves. Four exact solutions of the solitary, blow-up solitary and periodic waves are derived depending on the physical parameters. Regarding the solitary, blow-up solitary and periodic waves, we have presented the combined effects of the density ratio of electrons and ions (${\it\alpha}$), the temperature ratio of electrons and ions $({\it\beta})$ and the speed of the travelling wave ($v$) on the characteristics of dust acoustic solitary, blow-up solitary and periodic waves.

The nonlinear properties of the ion acoustic waves (IAWs) in a three-component quantum plasma comprising electrons, and positive and negative ions are investigated analytically and numerically by employing the quantum hydrodynamic (QHD) model. The Sagdeev pseudopotential technique is applied to obtain the small-amplitude soliton solution. The effects of the quantum parameter $H$, positive to negative ion density ratio ${\it\beta}$ and Mach number on the nonlinear structures are investigated. It is found that these factors can significantly modify the properties of the IAWs. The existence of quasi-periodic and chaotic oscillations in the system is established. Switching from quasi-periodic to chaotic is possible with the variation of Mach number or quantum parameter $H$.

Based on large-signal theory, a one-dimensional theoretical model of a coaxial vircator is developed to give the microwave gain of the nonlinear beam–wave interaction, and the effect of injected current premodulation on the microwave gain is analysed theoretically. In addition, a coaxial vircator with improved dual-cavity modulation structure, which has the advantage of enhancing the effect of the modulation cavity on the injected electron beam by way of feedback microwaves, is presented. The simulation results are presented to test the validity of the proposed theory, and it can be seen that the system power efficiency can become further strengthened by adjusting the parameters of the microwave feedback channel until the feedback electric field is at the proper phase. Finally, through optimization, a structure capable of generating 7.05 GW average output power and 19.5 % power conversion efficiency at 2.95 GHz operating frequency is obtained.

We review the generation of zonal flow and magnetic field by coupled electromagnetic ultra-low-frequency waves in the Earth’s ionospheric E-layer. It is shown that, under typical ionospheric E-layer conditions, different planetary low-frequency waves can couple with each other. Propagation of coupled internal-gravity–Alfvén, coupled Rossby–Khantadze and coupled Rossby–Alfvén–Khantadze waves is revealed and studied. A set of appropriate equations describing the nonlinear interaction of such waves with sheared zonal flow is derived. The conclusion on the instability of short-wavelength turbulence of such coupled waves with respect to the excitation of low-frequency and large-scale perturbation of the sheared zonal flow and sheared magnetic field is deduced. The nonlinear mechanism of the instability is based on the parametric triple interaction of finite-amplitude coupled waves leading to the inverse energy cascade towards longer wavelength. The possibility of generation of an intense mean magnetic field is shown. Obtained growth rates are discussed for each case of the considered coupled waves.

Many naturally occurring and man-made plasmas are collisionless and turbulent. It is not yet well understood how the energy in fields and fluid motions is transferred into the thermal degrees of freedom of constituent particles in such systems. The debate at present primarily concerns proton heating. Multiple possible heating mechanisms have been proposed over the past few decades, including cyclotron damping, Landau damping, heating at intermittent structures and stochastic heating. Recently, a community-driven effort was proposed (Parashar & Salem, 2013, arXiv:1303.0204) to bring the community together and understand the relative contributions of these processes under given conditions. In this paper, we propose the first step of this challenge: a set of problems and diagnostics for benchmarking and comparing different types of 2.5D simulations. These comparisons will provide insights into the strengths and limitations of different types of numerical simulations and will help guide subsequent stages of the challenge.

An axially symmetric laser beam configuration irradiating a spherical capsule has been considered in the context of inertial confinement fusion (ICF). The laser beams are located at co-latitudes 49° and 131° and mimic the quad positions in the second cone of the Laser Mégajoule Facility. The capsule is directly irradiated by the laser beams whose energy deposition generates a nearly spherical shock wave. Two-dimensional hydrodynamic numerical simulations have been performed to analyse the non-uniformity of the shock wavefront launched inward throughout the target. Different laser intensity profiles, calculated by the illumination model, have been tested. The performance, in terms of shock non-uniformity, has been compared, and it is found that with an appropriate choice of the laser intensity profile it is possible to control the shock non-uniformity at early times.

A forced and damped Zakharov–Kuznetsov equation for a magnetized electron–positron–ion plasma affected by an external force is studied in this paper. Via the Hirota method, the soliton-like solutions are given. The soliton’s amplitude gets enhanced with the phase velocity ${\it\lambda}$ decreasing or ion-to-electron density ratio ${\it\beta}$ increasing. With the damped coefficient increasing, when the external force $g(t)$ is periodic, the two solitons are always parallel during the propagation and background of the two solitons drops on the $x{-}y$ plane, and amplitudes of the two solitons increase on the $x{-}t$ and $y{-}t$ planes, with $(x,y)$ as the coordinates of the propagation plane and $t$ as the time. When $g(t)$ is exponentially decreasing, the two solitons merge into a single one and the background rises on the $x{-}y$ plane, and amplitudes of the two solitons decrease on the $x{-}t$ and $y{-}t$ planes. Further, associated chaotic motions are obtained when $g(t)$ is periodic. Using the phase projections and Poincaré sections, we find that the chaotic motions can be weakened with ${\it\alpha}_{1}$, the amplitude of $g(t)$, decreasing. With ${\it\alpha}_{2}$, the frequency of $g(t)$, decreasing, a three-dimensional attractor with stretching-and-folding structure is found, indicating that the weak chaos is transformed into the developed chaos. Chaotic motions can also be weakened with ${\it\lambda}$, the phase velocity, decreasing, but strengthened with ${\it\beta}$, the ion-to-electron density ratio, and ${\it\alpha}_{2}$ decreasing.

The effect of a parallel viscous force induced damping and the magnetic precessional drift resonance induced damping on the stability of the resistive wall mode (RWM) is numerically investigated for one of the advanced steady-state scenarios in international thermonuclear experimental reactor (ITER). The key element of the investigation is to study how different plasma rotation profiles affect the stability prediction. The single-fluid, toroidal magnetohydrodynamic (MHD) code MARS-F (Liu et al., Phys. Plasmas, vol. 7, 2000, p. 3681) and the MHD–kinetic hybrid code MARS-K (Liu et al., Phys. Plasmas, vol. 15, 2008, 112503) are used for this purpose. Three extreme rotation profiles are considered: (a) a uniform profile with no shear, (b) a profile with negative flow shear at the $q=2$ rational surface ($q$ is the equilibrium safety factor), and (c) a profile with positive shear at $q=2$. The parallel viscous force is found to be effective for the mode stabilization at high plasma flow speed (about a few percent of the Alfven speed) for the no shear flow profile and the negative shear flow profile, but the stable domain does not appear with the positive shear flow profile. The predicted eigenmode structure is different with different rotation profiles. With a self-consistent inclusion of the magnetic precession drift resonance of thermal particles in MARS-K computations, a lower critical flow speed, i.e. the minimum speed needed for full suppression of the mode, is obtained. Likewise the eigenmode structure is also modified by different rotation profiles in the kinetic results.

The nonlinear propagation of positron-acoustic waves (PAWs) in an unmagnetized, collisionless, four component, dense plasma system (containing non-relativistic inertial cold positrons, relativistic degenerate electron and hot positron fluids as well as positively charged immobile ions) has been investigated theoretically. The Korteweg–de Vries (K–dV), modified K–dV (mK–dV) and further mK–dV (fmK–dV) equations have been derived by using reductive perturbation technique. Their solitary wave solutions have been numerically analysed in order to understand the localized electrostatic disturbances. It is observed that the relativistic effect plays a pivotal role on the propagation of positron-acoustic solitary waves (PASW). It is also observed that the effects of degenerate pressure and the number density of inertial cold positrons, hot positrons, electrons and positively charged static ions significantly modify the fundamental features of PASW. The basic features and the underlying physics of PASW, which are relevant to some astrophysical compact objects (such as white dwarfs, neutron stars etc.), are concisely discussed.

A nonlinear Zakharov–Kuznetsov (ZK) equation for ion acoustic solitary waves (IASWs) is derived using the reductive perturbation method (RPM) for magnetized plasmas in which the inertialess electrons and positrons are nonextensively $q$-distributed while ions are assumed to be warm and inertial. It is found that both compressive as well as rarefactive solitons coexist in the present model for different regions of non-extensive electron and positron parameters, $q_{e}$ and $q_{p}$. The magnetic field has no effect on the amplitude of the IASW, whereas the obliqueness angle of the wave propagation, the ion-to-electron temperature ratio ${\it\sigma}$ and positron-to-ion density concentration ratio $p$ affect both the amplitude and the width of the solitary wave structures. The transverse instability analysis illustrates that the one soliton solution has a constant growth rate, and it suffers from instability in the transverse direction. The relevance of the present study to astrophysical space plasmas is also discussed.