We show that large-amplitude, non-planar, Alfvén-wave (AW) packets are exact nonlinear solutions of the relativistic magnetohydrodynamic equations when the total magnetic-field strength in the local fluid rest frame (b$b$) is a constant. We derive analytic expressions relating the components of the fluctuating velocity and magnetic field. We also show that these constant-b$b$ AWs propagate without distortion at the relativistic Alfvén velocity and never steepen into shocks. These findings and the observed abundance of large-amplitude, constant-b$b$ AWs in the solar wind suggest that such waves may be present in relativistic outflows around compact astrophysical objects.

An equilibrium statistical mechanics theory for the Hasegawa–Mima equations of toroidal plasmas, with canonical constraint on energy and microcanonical constraint on potential enstrophy, is solved exactly as a spherical model. The use of a canonical energy constraint instead of a fixed-energy microcanonical approach is justified by the preference for viewing real plasmas as an open system. A significant consequence of the results obtained from the partition function, free energy and critical temperature, is the condensation into a ground state exhibiting a blob-hole-like structure observed in real plasmas.

Lane formation dynamics of driven two-dimensional pair-ion plasmas is investigated in under-damped cases where the effect of particle inertia cannot be neglected. Extensive Langevin dynamics simulations using an OpenMP parallel program are carried out to analyse the effect of obstacle and geometric aspect ratio on lane formation dynamics previously reported in Sarma et al. (Phys. Plasmas, vol. 27, 2020, 012106) and Baruah et al. (J. Plasma Phys., vol. 87, 2021, 905870202). Lanes are found to form when like particles move along or opposite to the applied field direction. Lane order parameter, cumulative order parameter and distribution of the order parameter have been implemented to detect phase transition. The effect of geometric aspect ratio on the stability of lanes is systematically determined in both the presence and absence of an obstacle. Here, a specular reflective boundary condition is implemented to mimic an obstacle. We demonstrate that an obstacle promotes the merging of lanes, and the system gradually transitions to a partially mixed phase with higher value of aspect ratio. The occurrence of lane mixing phenomena at the separation boundary of two oppositely flowing lanes at higher value of aspect ratio is observed. In the presence of an oscillatory electric field, the lane merging tendency is reduced to a large extent as compared to the system where a constant electric field is applied. Furthermore, in the presence of both space- and time-varying electric fields, an appearance of a void is observed on either side of the obstacle. The study finds that the presence of an external magnetic field promotes acceleration of the phase transition process towards the lane mixing phase; it also reveals the existence of electric field drift in the system. Our findings may prove to be useful in understanding the nature of lane dynamics in naturally occurring pair-ion plasma systems as well as their relevance to technological applications that exploit or mitigate self-organization.

In this work, simulations of multipetawatt lasers at irradiances {\sim }10^{23} \ \mathrm {W}\ \mathrm {cm}^{-2}${\sim }10^{23} \ \mathrm {W}\ \mathrm {cm}^{-2}$, striking solid targets and implementing two-dimensional particle-in-cell code was used to study particle acceleration. Preformed plasma at the front surface of a solid target increases both the efficiency of particle acceleration and the reached maximum energy by the accelerated charged particles via nonlinear plasma processes. Here, we have investigated the preformed plasma scale length effects on particle acceleration in the presence and absence of nonlinear quantum electrodynamic (QED) effects, including quantum radiation reaction and multiphoton Breit–Wheeler pair production, which become important at irradiances {\sim } 10^{23}\ \mathrm {W}\ \mathrm {cm}^{-2}${\sim } 10^{23}\ \mathrm {W}\ \mathrm {cm}^{-2}$. Our results show that QED effects help particles gain higher energies with the presence of preformed plasma. In the results for all cases, preplasma leads to more efficient laser absorption and produces more energetic charged particles, as expected. In the case where QED is included, however, physical mechanisms changed and generated secondary particles (\gamma$\gamma$-rays and positrons) reversing this trend. That is, the hot electrons cool down due to QED effects, while ions gain more energy due to different acceleration methods. It is found that more energetic \gamma$\gamma$-rays and positrons are created with increasing scale length due to high laser conversion efficiency ({\sim }${\sim }$24 % for \gamma$\gamma$-rays and \sim$\sim$4 % for positrons at L = 7\ \mathrm {\mu }\textrm {m}$L = 7\ \mathrm {\mu }\textrm {m}$ scale length), which affects the ion and electron acceleration mechanisms. It is also observed that the QED effect reduces the collimation of angular distribution of accelerated ions because the dominant ion acceleration mechanism is changing when QED is involved in the process.

Steady plasma flows have been studied almost exclusively in systems with continuous symmetry or in open domains. In the absence of continuous symmetry, the lack of a conserved quantity makes the study of flows intrinsically challenging. In a toroidal domain, the requirement of double periodicity for physical quantities adds to the complications. In particular, the magnetohydrodynamics (MHD) model of plasma steady state with the flow in a non-symmetric toroidal domain allows the development of singularities when the rotational transform of the magnetic field is rational, much like the equilibrium MHD model. In this work, we show that steady flows can still be maintained provided the rotational transform is close to rational and the magnetic shear is weak. We extend the techniques developed in carrying out perturbation methods to all orders for static MHD equilibrium by Weitzner (Phys. Plasmas, vol. 21, 2014, p. 022515) to MHD equilibrium with flows. We construct perturbative MHD equilibrium in a doubly periodic domain with nearly parallel flows by systematically eliminating magnetic resonances order by order. We then utilize an additional symmetry of the flow problem, first discussed by Hameiri (J. Math. Phys., vol. 22, 1981, pp. 2080–2088, § III), to obtain a generalized Grad–Shafranov equation for a class of non-symmetric three-dimensional MHD equilibrium with flows both parallel and perpendicular to the magnetic field. For this class of flows, we can obtain non-symmetric generalizations of integrals of motion, such as Bernoulli's function and angular momentum. Finally, we obtain the generalized Hamada conditions, which are necessary to suppress singular currents in such a system when the magnetic field lines are closed. We do not attempt to address the question of neoclassical damping of flows.

The GENE-3D code, the global stellarator version of the established GENE framework, has been extended to an electromagnetic gyrokinetic code. This paper outlines the basic structure of the algorithm, highlighting the treatment of the electromagnetic terms. The numerical implementation is verified against the radially global GENE code in linear and nonlinear tokamak simulations, recovering excellent agreement between both codes. As a first application to stellarator plasmas, linear and nonlinear global simulations with kinetic electrons of ion temperature gradient (ITG) turbulence in Wendelstein 7-X were performed, showing a decrease of ITG activity through the introduction of electromagnetic effects via a finite plasma-\beta$\beta$. The upgrade makes it possible to study a large variety of new physical scenarios, including kinetic electron and electromagnetic effects, reducing the gap between gyrokinetic models and physically realistic systems.

A general procedure for understanding plasma behaviour when resonant wave–particle interactions are the sole destabilizing and transport mechanism or only heating and/or current drive source is highlighted without recourse to involved numerical or analytical treatments. These phenomena are characterized by transport that appears to be collisionless even though collisions play a central role in narrow collisional boundary layers. The order of magnitude estimates, which include nonlinear effects, are shown to provide expressions in agreement with the principal results of recent toroidal Alfvén eigenmode (TAE), toroidal magnetic field ripple, and heating and current drive treatments. More importantly, the retention of nonlinearities leads to new estimates of the alpha particle energy diffusivity at saturation for TAE modes, and the ripple threshold at which superbanana plateau evaluations of alpha particle transport are modified by nonlinear radial drift effects. In addition, the estimates indicate when quasilinear descriptions for heating and current drive will begin to fail. The phenomenological procedure demonstrates that in magnetic fusion relevant plasmas, narrow collisional boundary layers must be retained for resonant wave–particle interactions as they enhance the role of collisions, and make stochastic particle motion unlikely to be more important than other nonlinear processes.

The process of radiation pressure acceleration (RPA) of ions is investigated with the aim of suppressing the Rayleigh–Taylor-like transverse instabilities in laser–foil interaction. This is achieved by imposing surface and density modulations on the target surface. We also study the efficacy of RPA of ions from density modulated and structured targets in the radiation dominated regime where the radiation reaction effects are important. We show that the use of density modulated and structured targets and the radiation reaction effects can help in achieving the twin goals of high ion energy (in GeV range) and lower energy spread.

We study the influence of the shape of the plasma container on the dynamics of the reversed-field pinch (RFP). The geometries we consider are periodic cylinders with elliptical and circular-shaped cross-sections. Numerical simulations of fully nonlinear viscoresistive magnetohydrodynamics are carried out to illustrate how the plasma dynamics is affected by shaping. It is shown that independent of the plasma shape, the quantity \beta$\beta$, comparing the hydrodynamic pressure to the magnetic pressure, decreases for increasing values of the Lundquist number, but the pressure gradient fluctuations remain roughly constant, when compared to the Lorentz force. Different elliptical shapes of the cross-section of the domain lead to the excitation of different toroidal (or axial) magnetic and dynamic modes. Furthermore, it is found that in a geometry with circular cross-section, a significant local poloidal angular momentum is observed, absent in the geometries with elliptical cross-section. Because the confinement is dominantly determined by plasma movement, and the dynamics of the velocity and magnetic field are modified by the modification of the geometry, shaping can thus affect the performance of RFP devices.

Explanations for the long lifetime of spherically symmetric objects in nature and the short lifetime of laboratory plasma are given. A qualitative description of the relativistic model of ball lightning is also given, which is a spherical electric region with strong electric and magnetic fields. The plasma temperature in the zone of the ball-lightning generation is measured by the spectroscopic method. A large ball lightning, the maximum diameter of which is equal to one meter and which stands in the region of its generation, is also registered after the formation and departure of a high-energy ball lightning. The reason for the low emissive power in the optical range characteristic for the atmospheric ball lightning is explained by the absence of electron transitions in the outer proton-containing shell. The absence of electrical breakdown at ultrahigh electric field between the core and the outer shell of the ball lightning and its destruction at the moment when the resulting force becomes nonzero are also explained.

Recently, the energization of superthermal electrons at the Earth's bow shock was found to be consistent with a new magnetic pumping model derived in the limit where the electron transit time is much shorter than any time scale governing the evolution of the magnetic fields. The new model breaks with the common approach of integrating the kinetic equations along unperturbed orbits. Rather, the fast transit-time limit allows the electron dynamics to be characterized by adiabatic invariants (action variables) accurately capturing the nonlinear effects of electrons becoming trapped in magnetic perturbations. Without trapping, fast parallel streaming along magnetic field lines causes the electron pressure to be isotropized and homogeneous along the magnetic field lines. In contrast, trapping permits spatially varying pressure anisotropy to form along the magnetic field lines, and through a Fermi process this pressure anisotropy in turn becomes the main ingredient that renders magnetic pumping efficient for energizing superthermal electrons. We here present a detailed mathematical derivation of the model.

A three-dimensional fully kinetic particle-in-cell (PIC) simulation strategy has been implemented to simulate the acceleration stage of a magnetically enhanced plasma thruster (MEPT). The study has been performed with the open-source code Spacecraft Plasma Interaction Software (SPIS). The tool has been copiously modified to simulate properly the dynamics of a magnetized plasma plume. A cross-validation of the methodology has been done with Starfish, a two-dimensional open-source PIC software. Two configurations have been compared: (i) in the absence of a magnetic field and (ii) in the presence of a magnetic field generated by a coil with maximum intensity of 300 G at the thruster outlet. The results show a reduction of the plume divergence angle, an increase of ion speed and an increase of the specific impulse in the presence of the magnetic nozzle. The simulations presented in this study are representative of the operative conditions of a 50 W MEPT. Nonetheless, the methodology adopted can be extended to handle the magnetized plasma plume of several other types of thrusters such as electron cyclotron resonance and applied field magnetoplasmadynamic thrusters.

The propagation of radio-frequency (RF) waves in tokamaks can be affected by filamentary structures, or blobs, that are present in the edge plasma and the scrape-off layer. The difference in the permittivity between the surrounding plasma and interior of a filament leads to reflection, refraction and diffraction of the waves. This, in turn, can affect the power flow into the core of the plasma and reduce the efficiency of heating and/or current generation. The scattering of RF waves, lower hybrid, helicon and ion cyclotron waves, by a single cylindrical filament, embedded in a background plasma, is studied using a full-wave analytical theory developed previously (Ram & Hizanidis, Phys. Plasmas, vol. 23, 2016, 022504). The theory assumes that the plasma in and around a filament is homogeneous and cold. A detailed scattering analysis reveals a variety of common features that exist among the three distinctly different RF waves. These common attributes can be inferred intuitively based on an examination of the cold plasma dispersion relation. The physical intuition is a useful step to understanding experimental observations on scattering, as well as results from simulations that include general forms of edge plasma turbulence. While a filament can affect the propagation of RF waves, the radiation force exerted by the waves can influence the filament. The force on a filament is determined using the Maxwell stress tensor. In 1905, Poynting was the first to evaluate and measure the radiation force on an interface separating two different dielectric media (Poynting, London Edinburgh Dublin Philos. Mag. J. Sci., vol. 9, 1905, pp. 393–406). For ordinary light propagating in vacuum and incident on a glass surface, Poynting noted that the surface is ‘pulled’ towards the vacuum. In a magnetized cold plasma, there are two independent wave modes. Even if only one of these modes is excited by an RF antenna, a filament will couple power to the other mode: a consequence of electromagnetic boundary conditions. This facet of scattering has consequences on the radiation force that go beyond Poynting's seminal contribution. The direction of the force depends on the polarization of the incident wave and on the mode structure of the waves inside and in the vicinity of a filament. It can either pull the filament toward the RF source or push it away. For slow lower hybrid waves, filaments with densities greater than the ambient density are pulled in, while filaments with lower densities are pushed out, thereby enhancing the density in front of the antenna. In the case of fast helicon and ion cyclotron waves, the direction of the force depends on the plasma and wave parameters; in particular, on the ambient density. The radiation force, in all three frequency ranges, is large enough to affect the motion of a filament and could be measured experimentally. This also suggests the possibility of modifying the edge turbulence using RF waves.

Magnetic reconnection, a plasma process converting magnetic energy to particle kinetic energy, is often invoked to explain magnetic energy releases powering high-energy flares in astrophysical sources including pulsar wind nebulae and black hole jets. Reconnection is usually seen as the (essentially two-dimensional) nonlinear evolution of the tearing instability disrupting a thin current sheet. To test how this process operates in three dimensions, we conduct a comprehensive particle-in-cell simulation study comparing two- and three-dimensional evolution of long, thin current sheets in moderately magnetized, collisionless, relativistically hot electron–positron plasma, and find dramatic differences. We first systematically characterize this process in two dimensions, where classic, hierarchical plasmoid-chain reconnection determines energy release, and explore a wide range of initial configurations, guide magnetic field strengths and system sizes. We then show that three-dimensional (3-D) simulations of similar configurations exhibit a diversity of behaviours, including some where energy release is determined by the nonlinear relativistic drift-kink instability. Thus, 3-D current sheet evolution is not always fundamentally classical reconnection with perturbing 3-D effects but, rather, a complex interplay of multiple linear and nonlinear instabilities whose relative importance depends sensitively on the ambient plasma, minor configuration details and even stochastic events. It often yields slower but longer-lasting and ultimately greater magnetic energy release than in two dimensions. Intriguingly, non-thermal particle acceleration is astonishingly robust, depending on the upstream magnetization and guide field, but otherwise yielding similar particle energy spectra in two and three dimensions. Although the variety of underlying current sheet behaviours is interesting, the similarities in overall energy release and particle spectra may be more remarkable.

Alfvén wave collisions are the primary building blocks of the non-relativistic turbulence that permeates the heliosphere and low- to moderate-energy astrophysical systems. However, many astrophysical systems such as gamma-ray bursts, pulsar and magnetar magnetospheres and active galactic nuclei have relativistic flows or energy densities. To better understand these high-energy systems, we derive reduced relativistic magnetohydrodynamics equations and employ them to examine weak Alfvénic turbulence, dominated by three-wave interactions, in reduced relativistic magnetohydrodynamics, including the force-free, infinitely magnetized limit. We compare both numerical and analytical solutions to demonstrate that many of the findings from non-relativistic weak turbulence are retained in relativistic systems. But, an important distinction in the relativistic limit is the inapplicability of a formally incompressible limit, i.e. there exists finite coupling to the compressible fast mode regardless of the strength of the magnetic field. Since fast modes can propagate across field lines, this mechanism provides a route for energy to escape strongly magnetized systems, e.g. magnetar magnetospheres. However, we find that the fast-Alfvén coupling is diminished in the limit of oblique propagation.

Particle acceleration via magnetic reconnection is a fundamental process in astrophysical plasmas. Experimental architectures are able to confirm a wide variety of particle dynamics following the two-dimensional Sweet–Parker model, but are limited in their reproduction of the fan-spine magnetic field topology about three-dimensional (3-D) null points. Specifically, there is not yet an experiment featuring driven 3-D torsional magnetic reconnection. To move in this direction, this paper expands on recent work toward the design of an experimental infrastructure for inducing 3-D torsional fan reconnection by predicting feasible particle acceleration profiles. Solutions to the steady-state, kinematic, resistive magnetohydrodynamic equations are used to numerically calculate particle trajectories from a localized resistivity profile using well-understood laboratory plasma parameters. We confine a thin, 10 eV helium sheath following the snowplough model into the region of this localized resistivity and find that it is accelerated to energies of {\approx }2${\approx }2$ keV. This sheath is rapidly accelerated and focused along the spine axis propagating a few centimetres from the reconnection region. These dynamics suggest a novel architecture that may hold promise for future experiments studying solar coronal particle acceleration and for technology applications such as spacecraft propulsion.

Arched magnetized structures are a common occurrence in space and laboratory plasmas. Results from a laboratory experiment on spatio-temporal evolution of an arched magnetized plasma (\beta \approx 10^{-3}$\beta \approx 10^{-3}$, Lundquist number \approx 10^{4}$\approx 10^{4}$, plasma radius/ion gyroradius \approx 20$\approx 20$) in a sheared magnetic configuration are presented. The experiment is designed to model conditions relevant to the formation and destabilization of similar structures in the solar atmosphere. The magnitude of a nearly horizontal overlying magnetic field was varied to study its effects on the writhe and twist of the arched plasma. In addition, the direction of the guiding magnetic field along the arch was varied to investigate its role in the formation of either forward- or reverse-S shaped plasma structures. The electrical current in the arched plasma was well below the current required to make it kink unstable. A significant increase in the writhe of the arched plasma was observed with larger magnitudes of overlying magnetic field. A forward-S shaped arched plasma was observed for a guiding magnetic field oriented nearly antiparallel to the initial arched plasma current, while the parallel orientation yielded the reverse-S shaped arched plasma.

In the ion cyclotron range of frequency (ICRF), the presence of a lower hybrid (LH) resonance can appear in the edge of a tokamak plasma and lead to deleterious edge power depositions. An analytic formula for these losses is derived in the cold plasma approximation and for a slab geometry using an asymptotic approach and an analytical continuation near the LH resonance. The way to minimize these losses in a large machine like ITER is discussed. An internal verification between the power loss computed with the semi-analytical code ANTITER IV for ion cyclotron resonance heating (ICRH) and the analytic result is performed. This allows us to check the precision of the numerical integration of the singular set of cold plasma wave differential equations. The set of cold plasma equations used is general and can be applied in other parameters domain.

An interesting aspect of complex plasma is its ability to self-organize into a variety of structural configurations and undergo transitions between these states. A striking phenomenon is the isotropic-to-string transition observed in electrorheological complex plasma under the influence of a symmetric ion wake field. Such transitions have been investigated using the Plasma Kristall-4 (PK-4) microgravity laboratory on the International Space Station. Recent experiments and numerical simulations have shown that, under PK-4-relevant discharge conditions, the seemingly homogeneous direct current discharge column is highly inhomogeneous, with large axial electric field oscillations associated with ionization waves occurring on microsecond time scales. A multi-scale numerical model of the dust–plasma interactions is employed to investigate the role of the electric field in the charge of individual dust grains, the ion wake field and the order of string-like structures. Results are compared with those for dust strings formed in similar conditions in the PK-4 experiment.