Plasmas with moderate flow velocity and sound speed, but large Alfvén speed have been described by the semirelativistic magnetohydrodynamics (MHD) equations. While these are correct when restricted to their range of validity, they may have the undesirable effect of predicting unphysical accelerations, much faster than the ones of classical MHD. We present a family of planar models on which the Lorentz force acts more forcefully in the semirelativistic approach, yielding a flow velocity which rapidly exceeds the limits within which the equations are valid.

The ballooning magnetohydrodynamic (MHD) modes have been often suggested as a possible instability trigger of the substorm onset, and a mechanism of compressional waves in the outer magnetosphere and magnetotail. Commonly, these disturbances are characterized by the local dispersion equation that is widely applied for the description of ultra-low-frequency oscillatory disturbances and instabilities in the nightside magnetosphere. In realistic situations, especially in the inner magnetosphere, the magnetospheric plasma is composed of two components: background ‘cold’ plasma and ‘hot’ particles. The ballooning disturbances in a two-component plasma immersed into a curved magnetic field are described with the system of coupled equations for the Alfvén and slow magnetosonic (SMS) modes. We have reduced the basic system of MHD equations to the dispersion equation for the small-scale in transverse direction disturbances, and applied WKB approximation along a field line. As a result, we have derived a dispersion equation that can be used for geophysical applications. In particular, from this relationship the dispersion, instability threshold, and stop-bands of the Alfvén and SMS modes in two-component plasma have been examined.

Charging of dust grains and related phenomena are fundamental problems in the physics of complex plasmas. The relative motion of grains and plasma breaks the symmetry in dust charging and gives rise to the wake in plasma density and potential, which can significantly influence the dynamics of other grains. This paper gives an overview of dust charging in two- and multi-component plasma flows and related wake effects, and presents recent results from self-consistent particle-in-cell (PIC) simulations. The role of wakefields is considered in the context of charging of downstream grains.

The nonlinear Zakharov–Kuznetsov and the modified Zakharov–Kuznetsov equations are derived for dust-acoustic solitary waves (DASWs) in a magnetized four-component dusty plasma system comprising negatively charged cold dust, non-extensive electrons, and two-temperature thermal ions using standard reductive perturbation method. The combined effects of electron non-extensivity, strength of magnetic field, and its obliqueness on the DASWs profile are analyzed. Different ranges of non-extensive q-parameter are considered. Our results show that solitary waves, that their amplitude and width of which depend sensitively on the q-non-extensive parameter, can exist. Due to electron non-extensivity, our dusty plasma model can admit positive potential as well as negative potential solitons. The strength of magnetic field has no effect on the amplitude of solitary waves, whereas its obliqueness affects both amplitude and width of the solitary waves structure. Results show that the amplitude of soliton increases with increasing the velocity of soltion. For any magnitude of q there is an extremum for the direction of the magnetic field at which the width of soliton is maximum.

If a magnetized-orbit-charged grain encounters any abrupt inhomogeneity in plasma conditions during a gyro-orbit, such that the resulting in-situ equilibrium charge is significantly different between these regions (q1/q2 ~ 2, where q1 is the in-situ equilibrium charge on one side of the inhomogeneity, q2 is the in-situ equilibrium charge on the other side, and q1 < q2 < 0), then the capacitive effects of charging and discharging of the dust grain can result in a modification to the orbit-averaged grain trajectory, i.e. gyro-phase drift. The special case of q1/q2 is notioned for the purpose of illustrating the utility of the method. An analytical expression is derived for the grain velocity, assuming a capacitor approximation to the OML charging model. For cases in which a strong electric field suddenly appears in the wake or at the space-plasma-to-crater interface from solar wind and/or ultraviolet illumination and in which a magnetic field permeates an asteroid, comet, or moon, this model could contribute to the interpretation of the distribution of fields and particles.

In this paper, the effect of the magnetic field on one-dimensional plasma photonic crystal band gaps is studied. The one-dimensional fourfold plasma photonic crystal is applied that contains four periodic layers of different materials, namely plasma1–MgF2–plasma2–glass in one unit cell. Based on the principle of Kronig–Penney's model, dispersion relation for such a structure is obtained. The equations for effective dielectric functions of these two modes are theoretically deduced, and dispersion relations for transverse electric (TE) and transverse magnetic (TM) waves are calculated. At first, the main band gap width increases by applying the exterior magnetic field. Subsequently, the frequency region of this main band gap transfers completely toward higher frequencies. There is a particular upper limit for the magnitude of the magnetic field above which increasing the exterior magnetic field strength doesn't have any significant influence on the dispersion function behavior. (With an increase in incident angle up to θ1 = 66°, the width of photonic band gap (PBG) changes for both TM/TE polarization.) With an increase in incident angle up to θ1 = 66°, the width of PBG decreases for TM polarization and the width of PBG increases for TE polarization, but it increases with further increasing of the incident angle from θ1 = 66° to 89° for both TE- and TM-polarizations. Also, it has been observed that the width of the photonic band gaps changes rapidly by relative difference of the two-plasma frequency. Results show the existence of several photonic band gaps that their frequency and dispersion magnitude can be controlled by the exterior magnetic field, incident angle, and two plasma frequencies. The result of this research would provide theoretical instructions for designing filters, microcavities, fibers, etc.

A multi-symplectic formulation of ideal magnetohydrodynamics (MHD) is developed based on the Clebsch variable variational principle in which the Lagrangian consists of the kinetic minus the potential energy of the MHD fluid modified by constraints using Lagrange multipliers that ensure mass conservation, entropy advection with the flow, the Lin constraint, and Faraday's equation (i.e. the magnetic flux is Lie dragged with the flow). The analysis is also carried out using the magnetic vector potential à where α=Ã⋅dx is Lie dragged with the flow, and B=∇×Ã. The multi-symplectic conservation laws give rise to the Eulerian momentum and energy conservation laws. The symplecticity or structural conservation laws for the multi-symplectic system corresponds to the conservation of phase space. It corresponds to taking derivatives of the momentum and energy conservation laws and combining them to produce n(n−1)/2 extra conservation laws, where n is the number of independent variables. Noether's theorem for the multi-symplectic MHD system is derived, including the case of non-Cartesian space coordinates, where the metric plays a role in the equations.

The method of nonlinear complex geometrical optics (NCGO) is proposed in this paper for description of the evolution of a spatially narrow Gaussian beam (GB) in an inhomogeneous nonlinear plasma. NCGO method deals with first-order ordinary differential equations for the complex curvature of the wave front and for GB amplitude and for second-order ordinary differential equation for GB width. Thus, NCGO simplifies the description of GB diffraction and self-focusing effects as compared to the known methods of plasma physics and this way it can be assumed to be attractive and comprehensive approach in problems of plasma heating by electromagnetic waves. Moreover, we demonstrate in this paper some regularity for nonlinear inhomogeneous plasma in the framework of which central ray of a GB is not subjected to nonlinear refraction within NCGO method boundary applicability. On the contrary, the beam width, wave front curvature, and GB amplitude are modified by diffraction and self-focusing processes. General properties of the beam propagation are illustrated with results of numerical modeling for two particular cases: GB diffraction and self-focusing along curvilinear trajectory with torsion in axially symmetric plasma column and GB reflection from nonlinear inhomogeneous plasma layer. We prove in this paper that NCGO is new effective method of plasma physics, which can be applied for improvement of ray tracing techniques and plasma diagnostics.

The Magnetized Dusty Plasma Experiment (MDPX) device is a newly constructed research instrument for the study of dusty (complex) plasmas. The MDPX device is envisioned as an experimental platform in which the dynamical behavior of all three charged plasma components, the electrons, ions, and charged microparticles (i.e., the ‘dust’) will be significantly influenced by the magnetic force. This brief paper will provide a short overview of the design, magnetic performance, and initial plasma measurements in the MDPX device.

The relaxation of an electron-depleted electronegative dusty plasma with two-negative ions is investigated. When the ratio of canonical vorticities to corresponding flows of all the plasma species is the same and all inertial and non-inertial forces are present, the relaxed state appears as a double Beltrami magnetic field which is the superposition of two force-free relaxed states. The numerical results show that highly diamagnetic relaxed magnetic fields can be obtained by controlling the flow and vorticities through a single Beltrami parameter. The study is useful to investigate the creation of diamagnetic plasma configurations which are considered to be very important in the context of nuclear fusion.

The dust acoustic wave (DAW), associated with longitudinal dust oscillations in dusty plasmas, can be self-excited from the free energy of ion streaming. It is not only a fundamental plasma wave but also a paradigm to understand the generic dynamical behaviors of self-excited nonlinear longitudinal density waves through optically monitoring particle motion and dust density evolutions over a large area. In this paper, the dynamical behaviors of the wave-particle interaction and wave breaking in ordered self-excited DAW with straight wave fronts, and the defect-mediated wave turbulence with fluctuating defects and chaotic low amplitude hole filaments along defect trajectories in the 2+1D space-time space, are briefly reviewed. The first experimental observation of acoustic vortices with helical waveforms in self-excited acoustic-type defect-mediated wave turbulence, and the dynamics of spontaneous pair generation, propagation, and pair annihilation of acoustic vortices, is demonstrated and discussed.

The optical emission characterization of the plasma-assisted pulsed laser ablation of the magnesium sulfate target is discussed in this study. The emission spectrum produced by the magnesium sulfate plasma in the wavelength range 200–700 nm has been carefully investigated for different experimental conditions. The spectra analysis was performed by assuming the local thermodynamic equilibrium (LTE) approximation and calculating the plasma temperature with the Boltzmann plot method using neutral Mg spectral lines. The plasma temperature was obtained for different positions along the expansion axis, which allowed obtaining the electron population distribution as a function of the distance from the target. The plasma temperature along the expansion axis allowed evaluating the evolution of the excited states population when the plume expands. Moreover, the Stark broadening method has been employed for electron number density measurements. In this study, the Stark width of the Mg (I) spectral line at 285.21 nm was used. Besides, we have studied the variation of electron temperature (Te) and electron number density (Ne) as a function of laser irradiance.

The plasma sheath dynamics adjacent to the cathode in the presence of electrons, ions, and doubly ionized ions have been simulated in this work. The aim of the present investigation is, therefore, to study the effect of the doubly ionized ions on the characteristics of the plasma sheath dynamics such as potential distribution, sheath length, and ions dose and velocity near the surface (cathode). It was shown that the presence of the doubly ionized ions can increase the normalized potential of all positions in sheath region, sheath length, and ion/doubly ionized ions density ratio on the target. Obtained results may be helpful for analyzing the practical results of the surface operations such as ion implantation and plasma polymerization, etc.

Analytical models for weakly nonlinear electron plasma waves are considered in order to obtain dynamic equations for the space-time evolution of their local power spectra. The model contains the wave kinetic equation as a limiting case for slow, long wavelength modulations. It is demonstrated that a finite spectral width in wavenumbers has a stabilizing effect on the modulational instability. The results invite a simple heuristic relation between the spectral width and the root-mean-square amplitude of stable stationary turbulent Langmuir wave spectra. A non-local average dispersion relation is derived as a limiting form by using the formalism developed for the spectral dynamics.

A theoretical investigation is carried out to study the basic properties of dust-acoustic (DA) shock waves propagating in a magnetized non-thermal dusty plasma (containing cold viscous dust fluid, non-thermal ions, and non-thermal electrons). The reductive perturbation method is used to derive the Korteweg–de Vries–Burgers equation. It is found that the basic properties of DA shock waves are significantly modified by the combined effects of dust fluid viscosity, external magnetic field, and obliqueness (angle between external magnetic field and DA wave propagation direction). It is shown that the dust fluid viscosity acts as a source of dissipation, and is responsible for the formation of DA shock structures in the dusty plasma system under consideration. The implications of our results in some space and laboratory plasma situations are briefly discussed.

Nonlinear interaction of Langmuir and ion-acoustic waves in two-electron temperature plasma is investigated. New integrable wave interaction regime was discovered, this regime corresponds to the Langmuir soliton with three-hump amplitude, propagating with a speed close to the ion–sound speed in the conditions of strong non-isothermality of electronic components. It was discovered that besides the known analytical solution in the form of one- and two-hump waves, there exists a range of solutions in the form of solitary waves, which in the form of envelope has multi-peak structure and differs from the standard profiles described by hyperbolic functions. In case of fixed plasma parameters, different group velocities correspond to the waves with different number of peaks. It is found that the Langmuir wave package contains both even and uneven numbers of oscillations. Low-frequency potential here has uneven number of peaks. Interrelation of obtained and known earlier results are also discussed.

The filamentation instability due to the interaction of two relativistic electron and ion beams with magnetized plasma in a waveguide is studied within the framework of a macroscopic cold fluid description. It is assumed that the background plasma provides charge and current neutralization of the injected beams. The dispersion relation is obtained by solving wave eigenvalue equation. The resulting dispersion equation is analyzed numerically over a wide range of system parameters. It is found that the velocity difference factor can strongly affect the filamentation instability.

Dispersion relations of dust-lattice waves in three-dimensional body-centered cubic (bcc) and face-centered cubic (fcc) dusty plasma crystals are derived taking into account particle–wake interactions. Results show that resonance coupling between the longitudinal and out-of-plane transverse wave modes set in if the vertical confinement is below a certain critical value. The imaginary part of the wave frequency shows that the hybrid mode cannot propagate in the crystal.

In this paper, a collisionless unmagnetized plasma sheath consisting of electrons following non-extensive q-distribution, and cold mobile inertial ions is studied in the stationary state. In this type of plasma with non-Maxwellian electron distribution (Tsallis statistical mechanics), the effective electron temperature (Te, eff) and electron screening temperature (Te,*) are evaluated. The other plasma sheath phenomena such as the Bohm sheath criterion, Debye shielding, floating potential, and sheath length are investigated in the presence of q-non-extensive velocity-distributed electrons. It is observed that above-mentioned phenomena depend significantly on the non-extensive parameter q.