The self-focusing condition of a charged particle beam in a resistive plasma has been studied. When plasma heating is weak, the beam focusing is intensified by increasing the beam density or velocity. However, when plasma heating is strong, the beam focusing is only determined by the beam velocity. Especially, in weak heating conditions, the beam trends to be focused into the centre as a whole, and in strong heating conditions, a double-peak structure with a hollow centre is predicted to appear. Furthermore, it is found that the beam radius has a significant effect on focusing distance: a larger the beam radius will result in a longer focusing distance. Simulation results also show that when the beam radius is large enough, filamentation of the beam appears. Our results will serve as a reference for relevant beam–plasma experiments and theoretical analyses, such as heavy ion fusion and ion-beam-driven high energy density physics.

We construct a structure-preserving finite element method and time-stepping scheme for compressible barotropic magnetohydrodynamics both in the ideal and resistive cases, and in the presence of viscosity. The method is deduced from the geometric variational formulation of the equations. It preserves the balance laws governing the evolution of total energy and magnetic helicity, and preserves mass and the constraint $\text {div}B = 0$ to machine precision, both at the spatially and temporally discrete levels. In particular, conservation of energy and magnetic helicity hold at the discrete levels in the ideal case. It is observed that cross-helicity is well conserved in our simulation in the ideal case.

We present two generalized hybrid kinetic-Hall magnetohydrodynamics (MHD) models describing the interaction of a two-fluid bulk plasma, which consists of thermal ions and electrons, with energetic, suprathermal ion populations described by Vlasov dynamics. The dynamics of the thermal components are governed by standard fluid equations in the Hall MHD limit with the electron momentum equation providing an Ohm's law with Hall and electron pressure terms involving a gyrotropic electron pressure tensor. The coupling of the bulk, low-energy plasma with the energetic particle dynamics is accomplished through the current density (current coupling scheme; CCS) and the ion pressure tensor appearing in the momentum equation (pressure coupling scheme; PCS) in the first and the second model, respectively. The CCS is a generalization of two well-known models, because in the limit of vanishing energetic and thermal ion densities, we recover the standard Hall MHD and the hybrid kinetic-ions/fluid-electron model, respectively. This provides us with the capability to study in a continuous manner, the global impact of the energetic particles in a regime extending from vanishing to dominant energetic particle densities. The noncanonical Hamiltonian structures of the CCS and PCS, which can be exploited to study equilibrium and stability properties through the energy-Casimir variational principle, are identified. As a first application here, we derive a generalized Hall MHD Grad–Shafranov–Bernoulli system for translationally symmetric equilibria with anisotropic electron pressure and kinetic effects owing to the presence of energetic particles using the PCS.

The derivation and numerical implementation of a linearized version of the gyrokinetic (GK) Coulomb collision operator (Jorge et al., J. Plasma Phys., vol. 85, 2019, 905850604) and of the widely used linearized GK Sugama collision operator (Sugama et al., Phys. Plasmas, vol. 16, 2009, 112503) is reported. An approach based on a Hermite–Laguerre moment expansion of the perturbed gyrocentre distribution function is used, referred to as gyromoment expansion. This approach allows the considering of arbitrary perpendicular wavenumber and expressing the two linearized GK operators as a linear combination of gyromoments where the expansion coefficients are given by closed analytical expressions that depend on the perpendicular wavenumber and on the temperature and mass ratios of the colliding species. The drift-kinetic (DK) limits of the GK linearized Coulomb and Sugama operators are also obtained. Comparisons between the gyromoment approach and the DK Coulomb and GK Sugama operators in the continuum GK code GENE are reported, focusing on the ion-temperature-gradient instability and zonal flow damping, finding an excellent agreement. It is confirmed that stronger collisional damping of the zonal flow residual by the Sugama GK model compared with the GK linearized Coulomb (Pan et al., Phys. Plasmas, vol. 27, 2020, 042307) persists at higher collisionality. Finally, we show that the numerical efficiency of the gyromoment approach increases with collisionality, a desired property for boundary plasma applications.

We investigate the influence of charged dust on the incoherent scatter from the D-region ionosphere. Incoherent scatter is observed with high-power, large aperture radars and results from electromagnetic waves scattering at electrons that are coupled to other charged components through plasma oscillations. The influence of charged dust can hence be considered an effect of dusty plasma. The D-region contains meteoric smoke particles that are of nanometre size and form from incoming ablating meteors. Detection of such charged dust in the incoherent scatter spectrum from the D-region has previously been proposed and studied to some degree. We here present model calculations to investigate the influence of the charged dust component with a size distribution, instead of the one size dust components assumed in other works. The developed code to calculate the incoherent scatter spectrum from the D-region including dust particles with different sizes and different positive and negative charge states is made available (https://doi.org/10.18710/GHZIIY). We investigate how sizes, number density and charge state of the dust influence the spectrum during different ionospheric conditions. We consider the ionospheric parameters for the location of the EISCAT VHF radar during a year and find that conditions are most suitable for dust detection in winter below 80 km at times with increased electron densities. The prospects to derive dust parameters increase, when the incoherent scatter observations are combined with those of other instruments to provide independent information on electron density, neutral density and temperature.

In stellarator optimization studies, the boundary of the plasma is usually described by Fourier series that are not unique: several sets of Fourier coefficients describe approximately the same boundary shape. A simple method for eliminating this arbitrariness is proposed and shown to work well in practice.

Radio frequency (RF) sheaths occur under a wide variety of conditions when RF waves, material surfaces and plasma coexist. RF sheaths are of special importance in describing the interaction of ion cyclotron range of frequency (ICRF) waves with the boundary plasma in tokamaks, stellarators and other magnetic confinement devices. In this article the basic physics of RF sheaths is discussed in the context of magnetic fusion research. Techniques for modelling RF sheaths, their interaction with RF wave fields and the resulting consequences are highlighted. The article is intended as a guide for the early-career ICRF researcher, but it may equally well serve to provide an overview of basic RF sheath concepts and modelling directions for any interested fusion scientist.

General nonlinear equations describing reversed shear Alfvén eigenmode (RSAE) self-modulation via zero-frequency zonal structure (ZFZS) generation are derived using nonlinear gyrokinetic theory, which are then applied to study the spontaneous ZFZS excitation as well as RSAE nonlinear saturation. It is found that both electrostatic zonal flow and electromagnetic zonal current can be preferentially excited by finite-amplitude RSAE, depending on specific plasma parameters. The modification to local shear Alfvén wave continuum is evaluated using the derived saturation level of zonal current, which is shown to play a comparable role in saturating RSAE with the ZFZS scattering.

Pressure anisotropy is a commonly observed phenomenon in tokamak plasmas, due to external heating methods such as neutral beam injection and ion-cyclotron resonance heating. Equilibrium models for tokamaks are constructed by solving the Grad–Shafranov equation; such models, however, do not account for pressure anisotropy since ideal magnetohydrodynamics assumes a scalar pressure. A modified Grad–Shafranov equation can be derived to include anisotropic pressure and toroidal flow by including drift-kinetic effects from the guiding-centre model of particle motion. In this work, we have studied the mathematical well-posedness of these two problems by showing the existence and uniqueness of solutions to the Grad–Shafranov equation both in the standard isotropic case and when including pressure anisotropy and toroidal flow. A new fixed-point approach is used to show the existence of solutions in the Sobolev space $H_0^1$ to the Grad–Shafranov equation, and sufficient criteria for their uniqueness are derived. The conditions required for the existence of solutions to the modified Grad–Shafranov equation are also constructed.

Rotational Fresnel drag – or orbital Faraday rotation – in a rotating magnetised plasma is uncovered and studied analytically for Trivelpiece–Gould and whistler–helicon waves carrying orbital angular momentum (OAM). Plasma rotation is shown to introduce a non-zero phase shift between OAM-carrying eigenmodes with opposite helicities, similarly to the phase shift between spin angular momentum eigenmodes associated with the classical Faraday effect in a magnetised plasma at rest. By examining the dispersion relation for these two low-frequency modes in a Brillouin rotating plasma, this Faraday–Fresnel rotation effect is traced back to the combined effects of Doppler shift, centrifugal forces and Coriolis forces. In addition, the longitudinal group velocity in the presence of rotation is shown to depend both on rotation and azimuthal mode, therefore predicting the Faraday–Fresnel splitting of the envelope of a wave packet containing a superposition of OAM-carrying eigenmodes with opposite helicities.

The tertiary instability is believed to be important for governing magnetised plasma turbulence under conditions of strong zonal flow generation, near marginal stability. In this work, we investigate its role for a collisionless strongly driven fluid model, self-consistently derived as a limit of gyrokinetics. It is found that a region of absolute stability above the linear threshold exists, beyond which significant nonlinear transport rapidly develops. Characteristically, this range exhibits a complex pattern of transient zonal evolution before a stable profile can arise. Nevertheless, the Dimits transition itself is found to coincide with a tertiary instability threshold, so long as linear effects are included. Through a simple and readily extendable procedure, tracing its origin to St-Onge (J. Plasma Phys., vol. 83, issue 05, 2017, 905830504), the stabilising effect of the typical zonal profile can be approximated, and the accompanying reduced mode estimate is found to be in good agreement with nonlinear simulations.

The mechanism of harmonic generation in both O- and X-mode configurations for a magnetized plasma has been explored here in detail with the help of particle-in-cell simulations. A detailed characterization of both the reflected and transmitted electromagnetic radiation propagating in the bulk of the plasma has been carried out for this purpose. The efficiency of harmonic generation is shown to increase with the incident laser intensity. A dependency of harmonic efficiency has also been found on magnetic field strength. This work demonstrates that there is an optimum value of the magnetic field at which the efficiency of harmonic generation maximizes. The observations are in agreement with theoretical analysis. For the O-mode configuration, this is compelling as the harmonic generation provides for a mechanism by which laser energy can propagate inside an overdense plasma region.

The interaction of radio-frequency (RF) waves with edge turbulence modifies the incident wave spectrum, and can significantly affect RF heating and current drive in tokamaks. Previous lower hybrid (LH) scattering models have either used the weak-turbulence approximation, or treated more realistic, filamentary turbulence in the ray tracing limit. In this work, a new model is introduced which retains full-wave effects of RF scattering in filamentary turbulence. First, a Mie-scattering technique models the interaction of an incident wave with a single Gaussian filament. Next, an effective differential scattering width is derived for a statistical ensemble of filaments. Lastly, a Markov chain solves for the transmitted wave spectrum in slab geometry. This model is applied to LH launching for current drive. The resulting wave spectrum is asymmetrically broadened in angular wavenumber space. This asymmetry is not accounted for in previous LH scattering models. The modified wave spectrum is coupled to a ray tracing/Fokker–Planck solver (GENRAY/CQL3D) to study its impact on current drive. The resulting current profile is greatly altered, and there is significant increase in the on-axis current and decrease in the off-axis peaks. This is attributed to a portion of the modified wave spectrum that is strongly dampened on-axis during the first pass.

The quantum effects in plasmas can be described by the hydrodynamics containing the continuity and Euler equations. However, novel quantum phenomena are found via the extended set of hydrodynamic equations, where the pressure evolution equation and the pressure flux third-rank tensor evolution equation are included. These give the quantum corrections to the Coulomb interaction. The spectra of the Langmuir waves and the spin-electron acoustic waves are calculated. The application of the pressure evolution equation ensures that the contribution of pressure in the Langmuir wave spectrum is proportional to $(3/5)v_{\textrm {Fe}}^{2}$ rather than $(1/3)v_{\textrm {Fe}}^{2}$, where $v_{\textrm {Fe}}$ is the Fermi velocity.

Alfvén waves as excited in black hole accretion disks and neutron star magnetospheres are the building blocks of turbulence in relativistic, magnetized plasmas. A large reservoir of magnetic energy is available in these systems, such that the plasma can be heated significantly even in the weak turbulence regime. We perform high-resolution three-dimensional simulations of counter-propagating Alfvén waves, showing that an $E_{B_{\perp }}(k_{\perp }) \propto k_{\perp }^{-2}$ energy spectrum develops as a result of the weak turbulence cascade in relativistic magnetohydrodynamics and its infinitely magnetized (force-free) limit. The plasma turbulence ubiquitously generates current sheets, which act as locations where magnetic energy dissipates. We show that current sheets form as a natural result of nonlinear interactions between counter-propagating Alfvén waves. These current sheets form owing to the compression of elongated eddies, driven by the shear induced by growing higher-order modes, and undergo a thinning process until they break-up into small-scale turbulent structures. We explore the formation of current sheets both in overlapping waves and in localized wave packet collisions. The relativistic interaction of localized Alfvén waves induces both Alfvén waves and fast waves, and efficiently mediates the conversion and dissipation of electromagnetic energy in astrophysical systems. Plasma energization through reconnection in current sheets emerging during the interaction of Alfvén waves can potentially explain X-ray emission in black hole accretion coronae and neutron star magnetospheres.