The propagation of extraordinary and upper-hybrid waves in spin quantum magnetoplasmas with vacuum polarization effect is investigated. Based on the quantum magnetohydrodynamics model including Bohm potential, arbitrary relativistic degeneracy pressure and spin force, and Maxwell's equations modified by the spin current and vacuum polarization current, the dispersion relations of extraordinary and upper-hybrid waves are derived. The analytical and numerical results show that quantum effects (Bohm potential, degeneracy pressure and spin magnetization energy) and the vacuum polarization effect modify the propagation of the extraordinary wave. Under the action of a strong magnetic field, the plasma frequency is obviously increased by the vacuum polarization effect.

This paper proposes a metric bracket for representing Coulomb collisions in the so-called guiding-centre Vlasov–Maxwell–Landau model. The bracket is manufactured to preserve the same energy and momentum functionals as does the Vlasov–Maxwell part and to simultaneously satisfy a revised version of the H-theorem, where the equilibrium distributions with respect to collisional dynamics are identified as Maxwellians. This is achieved by exploiting the special projective nature of the Landau collision operator and the simple form of the system's momentum functional. A discussion regarding a possible extension of the results to electromagnetic drift-kinetic and gyrokinetic systems is included. We anticipate that energy conservation and entropy dissipation can always be manufactured whereas guaranteeing momentum conservation is a delicate matter yet to be resolved.

Motivated by recent discussions on the possible role of quantum computation in plasma simulations, here, we present different approaches to Koopman's Hilbert-space formulation of classical mechanics in the context of Vlasov–Maxwell kinetic theory. The celebrated Koopman–von Neumann construction is provided with two different Hamiltonian structures: one is canonical and recovers the usual Clebsch representation of the Vlasov density, the other is non-canonical and appears to overcome certain issues emerging in the canonical formalism. Furthermore, the canonical structure is restored for a variant of the Koopman–von Neumann construction that carries a different phase dynamics. Going back to van Hove's prequantum theory, the corresponding Koopman–van Hove equation provides an alternative Clebsch representation which is then coupled to the electromagnetic fields. Finally, the role of gauge transformations in the new context is discussed in detail.

In the scrape-off layer and the edge region of a tokamak, the plasma is strongly turbulent and scatters the radiofrequency (RF) electromagnetic waves that propagate through this region. It is important to know the spectral properties of these scattered RF waves, whether used for diagnostics or for heating and current drive. The spectral changes influence the interpretation of the obtained diagnostic data, and the current and heating profiles. A full-wave, three-dimensional (3-D) electromagnetic code ScaRF (see Papadopoulos et al., J. Plasma Phys., vol. 85, issue 3, 2019, 905850309) has been developed for studying the RF wave propagation through turbulent plasma. ScaRF is a finite-difference frequency-domain (FDFD) method used for solving Maxwell's equations. The magnetized plasma is defined through the cold plasma by the anisotropic permittivity tensor. As a result, ScaRF can be used to study the scattering of any cold plasma RF wave. It can also be used for the study of the scattering of electron cyclotron waves in ITER-type and medium-sized tokamaks such as TCV, ASDEX-U and DIII-D. For the case of medium-sized tokamaks, there is experimental evidence that drift waves and rippling modes are present in the edge region (see Ritz et al., Phys. Fluids, vol. 27, issue 12, 1984, pp. 2956–2959). Hence, we have studied the scattering of RF waves by periodic density interfaces (plasma gratings) in the form of a superposition of spatial modes with varying periodicity and random amplitudes (see Papadopoulos et al., J. Plasma Phys., vol. 85, issue 3, 2019, 905850309). The power reflection coefficient (a random variable) is calculated for different realizations of the density interface. In this work, the uncertainty of the power reflection coefficient is rigorously quantified by use of the Polynomial Chaos Expansion (see Xiu & Karniadakis, SIAM J. Sci. Comput., vol. 24, issue 2, 2002, pp. 619–644) method in conjunction with the Smolyak sparse-grid integration (see Papadopoulos et al., Appl. Opt., vol. 57, issue 12, 2018, pp. 3106–3114), which is known as the PCE-SG method. The PCE-SG method is proven to be accurate and more efficient (roughly a 2-orders of magnitude shorter execution time) compared with alternative methods such as the Monte Carlo (MC) approach.

The variation of pressure-gradient-driven turbulence with plasma $\beta$ (up to $\beta \approx 15\,\%$) is investigated in linear, magnetized plasma. The magnitude of magnetic fluctuations is observed to increase substantially with increasing $\beta$. More importantly, parallel magnetic fluctuations are observed to dominate at higher $\beta$ values, with $\delta B_\parallel / \delta B_\perp \approx 2$ and $\delta B / B_0 \approx 1\,\%$. Parallel magnetic fluctuations are strongly correlated with density fluctuations and the two are observed to be out of phase. The relative magnitude of and cross-phase between density and parallel magnetic field fluctuations are consistent with the dynamic pressure balance ($P+{B_{0}^2}/{2\mu _0} = \textrm {constant}$). A local slab model theory for electromagnetic, modified drift Alfvén waves, including parallel magnetic fluctuations, shows partial agreement with experimental observations.

In part 1 (V. S. Dharodi and A. Das, J. Plasma Phys. 87 (02), 905870216 (2021)), we simulated the individual dynamics of a bubble (a localized low-density region) and a droplet (a localized high-density region) in a strongly coupled dusty plasma. We observed that under the influence of gravity, the result of a pair of counter-rotating vorticity lobes causes the bubble to rise and droplet to fall. With an interest to understand the hetero- (bubble–droplet) interactions between them, we extend this study to their combined evolution through the following two arrangements. First, both are placed side-by-side in a row at the same height. We observe that the overall dynamics is governed by the competition between the net vertical motion induced by gravity and rotational motion induced by the pairing between two co-rotating inner vorticity lobes. In the second arrangement, the vertically aligned bubble (below) and droplet (above) after collision exchange their partners and subsequently start to move horizontally in opposite directions away from each other. This horizontal movement becomes slower with increasing coupling strength. For these arrangements, we consider varying the distance between the fixed-size bubble and droplet, and varying the coupling strength. To visualize the bubble–droplet interactions, a series of two-dimensional simulations have been conducted in the framework of an incompressible generalized hydrodynamic viscoelastic fluid model.

The stepped-pressure equilibrium code (SPEC) (Hudson et al., Phys. Plasmas, vol. 19, issue 11, 2012, 112502) is extended to allow the computation of multi-region, relaxed magnetohydrodynamics (MRxMHD) equilibria at prescribed toroidal current profile. Toroidal currents are expressed in the framework of the MRxMHD theory, exhibiting spatial separation between pressure driven and externally driven currents. Additionally, analytical force balance derivatives at constant toroidal current are deployed in order to maintain SPEC's advantageous speed. The newly implemented capability is verified in screw pinch and classical stellarator geometries, and is applied to obtain the equilibrium $\beta$-limit of a classical stellarator without net toroidal currents. This new capability opens the possibility to study the effect of toroidal current on three-dimensional equilibria with the SPEC code.

Hall instability in electron magnetohydrodynamics is interpreted as the shear-Hall instability driven jointly by helicoidal oscillations and shear in the electron current velocity. This explanation suggests an antiparallel orientation of the background magnetic field and vorticity of the current velocity as the necessary condition for Hall instability. The condition is tested and generally confirmed by numerical computations in plane slab geometry. Unstable eigenmodes are localized in the spatial regions of the antiparallel field and vorticity. Computations of the tearing-type mode of the instability are complemented by (and generally agree with) asymptotic analytical estimations for large Hall numbers. The stabilizing effect of perfect conductor boundary conditions is found and explained. For large Hall numbers, the growth rates approach the power-law dependence $\sigma \propto B^\alpha \eta ^{1-\alpha }$ on the magnetic field ($B$) and diffusivity ($\eta$). Almost all computations give the power index $\alpha = 3/4$ with one exception of the tearing-type mode with vacuum boundary conditions for which case $\alpha = 2/3$.

In the ion cyclotron range of frequencies, electromagnetic surface waves are physically relevant for wave–filament interactions, parasitic edge losses and sheath–plasma waves. They are also important numerically, where non-physical surface waves may occur as side effects of slab-geometry approximations. We give new, completely general, mathematical techniques to construct dispersion relations for electromagnetic surface waves between any two media, isotropic or anisotropic, and first-order corrections for when the material interface is steep but continuous. We discuss numerical issues (localized non-convergence, undesired power generation) that arise in numerical calculations due to the presence of surface waves.

We present a geometric particle-in-cell (PIC) algorithm on unstructured meshes for studying electrostatic perturbations with frequency lower than electron gyrofrequency in magnetized plasmas. In this method, ions are treated as fully kinetic particles and electrons are described by the adiabatic response. The PIC method is derived from a discrete variational principle on unstructured meshes. To preserve the geometric structure of the system, the discrete variational principle requires that the electric field is interpolated using Whitney 1-forms, the charge is deposited using Whitney 0-forms and the electric field is computed by discrete exterior calculus. The algorithm has been applied to study the ion Bernstein wave (IBW) in two-dimensional magnetized plasmas. The simulated dispersion relations of the IBW in a rectangular region agree well with theoretical results. In a two-dimensional circular region with fixed boundary condition, the spectrum and eigenmode structures of the IBW are obtained from simulations. We compare the energy conservation property of the geometric PIC algorithm derived from the discrete variational principle with that of previous PIC methods on unstructured meshes. The comparison shows that the new PIC algorithm significantly improves the energy conservation property.

The parallel expansion of a dense, pellet-produced plasmoid is modelled with parameters relevant to pellet fuelling experiments in the Wendelstein7-X stellarator. Good agreement is found between the analytical theory and more detailed modelling. In particular, much of the energy deposited in the pellet by the ambient plasma is transferred to the pellet ions by the ambipolar electric field during the expansion. The validity of the hydrodynamic treatment of the plasmoid and the ambient plasma is discussed.

We derive the local dispersion relation of energetic-particle-induced geodesic acoustic modes (EGAMs) for both trapped and circulating ion beams with single pitch angle slowing-down and Maxwellian distributions, as well as a bump-on-tail distribution in tokamak plasmas. For slowing-down and Maxwellian particles, the solutions of the local dispersion relation give the spectrum, growth rate and thresholds of excitation as functions of the pitch angle, beam density and frequency of the energetic particles bounce motion. For circulating ions there is only one unstable branch with frequency below the GAM continuum and a threshold of excitation in the pitch angle, for both the slowing-down and single pitch Maxwellian distributions. Trapped particles cause no excitation of a mode for neither slowing-down nor Maxwellian ion beams, but they can excite a mode with a bump-on-tail distribution when the mean velocity of the beam is larger than the threshold and the energetic particle bounce frequency is high enough.

In order to predict and analyse turbulent transport in tokamaks, it is important to model transport that arises from microinstabilities. For this task, quasilinear codes have been developed that seek to calculate particle, angular momentum and heat fluxes, both quickly and accurately. In this tutorial, we present a derivation of one such code known as QuaLiKiz, a quasilinear gyrokinetic transport code. The goal of this derivation is to provide a self-contained and complete description of the underlying physics and mathematics of QuaLiKiz from first principles. This work serves both as a comprehensive overview of QuaLiKiz specifically as well as an illustration for deriving quasilinear models in general.

Quasi-periodic plasmoid formation at the tip of magnetic streamer structures is observed to occur in experiments on the Big Red Ball as well as in simulations of these experiments performed with the extended magnetohydrodynamics code, NIMROD. This plasmoid formation is found to occur on a characteristic time scale dependent on pressure gradients and magnetic curvature in both experiment and simulation. Single mode, or laminar, plasmoids exist when the pressure gradient is modest, but give way to turbulent plasmoid ejection when the system drive is higher, which produces plasmoids of many sizes. However, a critical pressure gradient is also observed, below which plasmoids are never formed. A simple heuristic model of this plasmoid formation process is presented and suggested to be a consequence of a dynamic loss of equilibrium in the high-$\beta$ region of the helmet streamer. This model is capable of explaining the periodicity of plasmoids observed in the experiment and simulations, and produces plasmoid periods of 90 minutes when applied to two-dimensional models of solar streamers with a height of $3R_\odot$. This is consistent with the location and frequency at which periodic plasma blobs have been observed to form by Large Angle and Spectrometric Coronograph and Sun Earth Connection Coronal and Heliospheric Investigation instruments.

Electron energization during merging of magnetized plasmas is studied using the OMEGA and OMEGA EP laser facilities by colliding two plasma plumes, each containing a Biermann-battery self-generated magnetic field. Two neighbouring plasma plumes are produced by intense laser beams, and the anti-parallel Biermann fields merge and reconnect in the process of the plumes’ expansion and collision. To isolate the merging as an acceleration source, the electron energy spectra obtained from two-plume collision shots are compared with the spectra from single-plume shots. Single-plume shots exhibit an energized electron tail with energies up to ${\sim }250\ \textrm {keV}$. The electrons in merging experiments are additionally accelerated by ${\sim }50\text {--}100$ keV compared to single-plume shots.

The impact of temperature inhomogeneity, surface charge and surface mass densities on the stability analysis of charged surface waves at the interface between dense, incompressible, radiative, self-gravitating magnetized electron–ion plasma and vacuum is investigated. For such an incompressible plasma system, the temperature inhomogeneity is governed by an energy balance equation. Adopting the one-fluid magnetohydrodynamic (MHD) approximation, a general dispersion relation is obtained for capillary surface waves, which takes into account gravitational, radiative and magnetic field effects. The dispersion relation is analysed to obtain the conditions under which the plasma–vacuum interface may become unstable. In the absence of electromagnetic (EM) pressure, astrophysical objects undergo gravitational collapse through Jeans surface oscillations in contrast to the usual central contraction of massive objects due to enhanced gravity. EM radiation does not affect the dispersion relation much, but actually tends to stabilize the Jeans surface instability. In certain particular cases, pure gravitational radiation may propagate on the plasma vacuum interface. The growth rate of radiative dissipative instability is obtained in terms of the wavevector. Our theoretical model of the Jeans surface instability is applicable in astrophysical environments and also in laboratory plasmas.

The effect of different density profiles on micron-sized hydrogen plasma spheres is investigated when the plasma gets irradiated with an ultrashort circularly polarized laser. In this study, we show that significant improvement in the characteristics of the accelerated protons viz. maximum proton energy, as well as their monoenergetic behaviour, is possible by using a plasma sphere having a tailored density profile. A linear-shaped density inhomogeneity is introduced in the plasma sphere such that the density is peaked at the centre and gradually dropping outwards. The density gradient is tuned by changing the peak density at the centre. The optimum regime of steepness is found for the maximum energy attained by the protons where the target is opaque enough for the radiation pressure to play its role, however not too opaque to inhibit efficient target heating. A novel Gaussian-shaped density profile is suggested which plays an important role in suppressing the sheath field. With a decreased rear-side field, a visible improvement of the monoenergetic feature of the protons is observed.

The possibility of controlling the electrostatic field distribution in plasma has yielded wide prospects for modern technologies. As a magnetic field primarily allows for creating electric fields in plasma, it serves as an additional obstacle for the current flow through a medium. In the present paper, an axially symmetric system is considered in which the magnetic field is directed along the axis and concentric electrodes are located at the ends. The electrodes are negatively biased. A model which solves the problem of the radial distribution of the plasma potential inside the cylindrical plasma column supported by the end electrodes is proposed. The most commonly encountered configurations of the electrical connection for the end electrodes are considered, and the particular solutions to the problem of the radial distribution are presented. The contribution of ions and electrons to the transverse conductivity is evaluated in detail. The influence of a thermionic element on the radial profile of the plasma potential is considered. To verify the proposed model, an experimental study of the reflex discharge is carried out with both cold electrodes and a thermionic element on the axis. A comparison of the computational model results with experimental data is given. The presented model makes it possible to solve the problem concerning the plasma potential distribution in the case of an arbitrary number of end electrodes, and also to take into account the inhomogeneity of the distribution of plasma density, neutral gas pressure and electron temperature along the radius.

We derive the two-dimensional counter-differential rotation equilibria of two-component plasmas, composed of both ion and electron ($e^-$) clouds with finite temperatures, for the first time. In the equilibrium found in this study, as the density of the $e^{-}$ cloud is always larger than that of the ion cloud, the entire system is a type of non-neutral plasma. Consequently, a bell-shaped negative potential well is formed in the two-component plasma. The self-electric field is also non-uniform along the $r$-axis. Moreover, the radii of the ion and $e^{-}$ plasmas are different. Nonetheless, the pure ion as well as $e^{-}$ plasmas exhibit corresponding rigid rotations around the plasma axis with different fluid velocities, as in a two-fluid plasma. Furthermore, the $e^{-}$ plasma rotates in the same direction as that of $\boldsymbol {E \times B}$, whereas the ion plasma counter-rotates overall. This counter-rotation is attributed to the contribution of the diamagnetic drift of the ion plasma because of its finite pressure.