Isolated, undamped geodesic-acoustic-mode (GAM) packets have been demonstrated to obey a (focusing) nonlinear Schrödinger equation (NLSE) (E. Poli, Phys. Plasmas, 2021). This equation predicts susceptibility of GAM packets to the modulational instability (MI). The necessary conditions for this instability are analysed analytically and numerically using the NLSE model. The predictions of the NLSE are compared with gyrokinetic simulations performed with the global particle-in-cell code ORB5, where GAM packets are created from initial perturbations of the axisymmetric radial electric field $E_r$. An instability of the GAM packets with respect to modulations is observed both in cases in which an initial perturbation is imposed and when the instability develops spontaneously. However, significant differences in the dynamics of the small scales are discerned between the NLSE and gyrokinetic simulations. These discrepancies are mainly due to the radial dependence of the strength of the nonlinear term, which we do not retain in the solution of the NLSE, and to the damping of higher radial spectral components $k_r$. The damping of the high-$k_r$ components, which develop as a consequence of the nonlinearity, can be understood in terms of Landau damping. The influence of the ion Larmor radius $\rho _i$ as well as the perturbation wavevector $k_\text {pert}$ on this effect is studied. For the parameters considered here the aforementioned damping mechanism hinders the MI process significantly from developing to its full extent and is strong enough to stabilize some of the (according to the undamped NLSE model) unstable wavevectors.

We apply a continuation method to recently optimized stellarator equilibria with excellent quasi-axisymmetry to generate new equilibria with a wide range of rotational transform profiles. Using these equilibria, we investigate how the rotational transform affects fast-particle confinement, the maximum coil–plasma distance, the maximum growth rate in linear gyrokinetic ion-temperature gradient simulations and the ion heat flux in corresponding nonlinear simulations. We find values of two-term quasi-symmetry error comparable to or lower than those of the similar Landreman–Paul (Phys. Rev. Lett., vol. 128, 2022, 035001) configuration for values of the mean rotational transform $\bar {\iota }$ between $0.12$ and $0.75$. The fast-particle confinement improves with $\bar {\iota }$ until $\bar {\iota } = 0.73$, at which point the degradation in quasi-symmetry outweighs the benefits of further increasing $\bar {\iota }$. The required coil–plasma distance only varies by about ${\pm }10\,\%$ for the configurations under consideration, and is between $2.8$ and $3.3\ \mathrm {m}$ when the configuration is scaled up to reactor size (minor radius $a=1.7\ \mathrm {m}$ and volume-averaged magnetic field strength of $5.86\ \mathrm {T}$). The maximum growth rate from linear gyrokinetic simulations increases with $\bar {\iota }$, but also shifts towards higher $k_y$ values. The maximum linear growth rate is sensitive to the choice of flux tube at rational $\bar {\iota }$, but this can be compensated for by taking the maximum over several flux tubes. The corresponding ion heat fluxes from nonlinear simulations display a non-monotonic relation to $\bar {\iota }$. Sufficiently large positive shear is destabilizing. This is reflected in both linear growth rates and nonlinear heat fluxes.

A quasi-linear reduced transport model is developed from a database of high-$\beta$ electromagnetic nonlinear gyrokinetic simulations performed with spherical tokamak for energy production (STEP) relevant parameters. The quasi-linear model is fully electromagnetic and accounts for the effect of equilibrium flow shear using a novel approach. Its flux predictions are shown to agree quantitatively with predictions from local nonlinear gyrokinetic simulations across a broad range of STEP-relevant local equilibria. This reduced transport model is implemented in the T3D transport solver that is used to perform the first flux-driven simulations for STEP to account for transport from hybrid kinetic ballooning mode turbulence, which dominates over a wide region of the core plasma. Nonlinear gyrokinetic simulations of the final transport steady state from T3D return turbulent fluxes that are consistent with the reduced model, indicating that the quasi-linear model may also be appropriate for describing the transport steady state. Within the assumption considered here, our simulations support the existence of a transport steady state in STEP with a fusion power comparable to that in the burning flat top of the conceptual design, but do not demonstrate how this state can be accessed.

We present the first experimental observations of the dust acoustic wave where the wave was observed to propagate in the directions of gravity and magnetic field when these directions were not aligned. The experiments were conducted in the Magnetized Dusty Plasma eXperiment facility using a novel electrode system that allows for the angle between gravity and the magnetic field to be varied in a controlled way. This letter reports on measurements in an rf glow discharge argon plasma environment where the angle between direction of gravity and the magnetic field is 45$^{\circ }$. When there was no applied magnetic field, the wave was observed to propagate in the direction of gravity. However, as the magnetic field increased and the ions transitioned from flowing in the direction of gravity to the direction of the magnetic field, a second wave emerged and two distinct waves were observed to simultaneously propagate, one in the direction of gravity and one in the direction of the magnetic field. As the magnetic field was further increased, the wave that propagated in the direction of gravity was suppressed and the wave was only observed to propagate in the direction of the applied magnetic field. We also observe that the speed and the kinetic temperature of the dust for the mode that propagated in the direction of gravity decreased with increasing magnetic field while the speed and the kinetic temperature of the dust for the mode that propagated in the direction of the magnetic field increased with increasing magnetic field. These measurements suggest that an ion-dust streaming instability is at least partially responsible for the high temperatures that have previously been observed in dusty plasmas when the dust acoustic wave is present.

Using two counter-propagating ultra-intense laser interactions with a solid target, we conducted a study on the generation of electron-positron pairs via the multi-photon Breit–Wheeler (BW) process and trident process. These processes were simulated using the particle-in-cell (PIC) code EPOCH. Our proposed scheme involves irradiating two targets with two counter-propagating lasers. High-energy photons are produced when hot electrons collide with the reflected laser pulse at the target's front, leading to electron and positron pair production. In the single-target scenario, electron bunches are extracted from the target by the p-polarized laser electromagnetic field and accelerated by the laser ponderomotive force before colliding with the counter-propagating laser. However, using two targets enhances pair creation compared with the single-target set-up. We observed that in two-target configurations, the increased number of high-energy gamma-rays contributes to higher-energy electron–positron generation. Additionally, the generation of hot electrons is also more pronounced in this scheme. Consequently, the laser demonstrates higher efficiency in generating gamma photons and positrons in the dual-target set-up, which is beneficial for investigating high-energy pair production and gamma-ray emission. The generated positrons exhibit a density of the order of $10^{27}\,\text {m}^{-3}$ and can be accelerated to energies of 1.5 GeV. The involvement of hot electrons in the target is crucial for generating high-energy photons and positrons. The maximum pair yield reaches $8 \times 10^9$ for the BW process and $10^8$ for the trident process. Notably, the total laser energy conversion efficiencies to electrons, $\gamma$-rays and positrons show improvement in the dual-target configuration. Specifically, the laser energy absorbed by positrons increases from 11.62 % in Case A to 13.12 % in Case B. These enhancements in conversion efficiency and electron/positron density have significant practical implications in experimental set-ups. In both the BW and trident processes, the two-target set-up dominates, highlighting its effectiveness. We also compared the strengths of both approaches, suggesting that these simple models of implementing two targets can be used in experiments as well.

Ion cyclotron resonance heating is a versatile heating method that has been demonstrated to be able to efficiently couple power directly to the ions via the fast magnetosonic wave. However, at temperatures relevant for reactor grade devices such as DEMO, electron damping becomes increasingly important. To reduce electron damping, it is possible to use an antenna with a power spectrum dominated by low parallel wavenumbers. Moreover, using an antenna with a unidirectional spectrum, such as a travelling wave array antenna, the parallel wavenumber can be downshifted by mounting the antenna in an elevated position relative to the equatorial plane. This downshift can potentially enhance ion heating as well as fast wave current drive efficiency. Thus, such a system could benefit ion heating during the ramp-up phase and be used for current drive during flat-top operation. To test this principle, both ion heating and current drive have been simulated in a DEMO-like plasma for a few different mounting positions of the antenna using the FEMIC code. We find that moving the antenna off the equatorial plane makes ion heating more efficient for all considered plasma temperatures at the expense of on-axis heating. Moreover, although current drive efficiency is enhanced, electron damping is reduced for lower mode numbers, thus reducing the driven current in this part of the spectrum.

Upper bounds on the growth of instabilities in gyrokinetic systems have recently been derived by considering the optimal perturbations that maximise the growth of a chosen energy norm. This technique has previously been applied to two-species gyrokinetic systems with fully kinetic ions and electrons. However, in tokamaks and stellarators, the expectation from linear instability analyses is that the most important kinetic electron contribution to ion-scale modes often comes from the trapped electrons, which bounce faster than the time scale upon which instabilities evolve. As a result, a fully kinetic electron response is not required to describe unstable modes in many cases. Here, we apply the optimal mode analysis to a reduced two-species system consisting of fully gyrokinetic ions and bounce-averaged electrons, with the aim of finding a tighter bound on ion-scale instabilities in toroidal geometry. This analysis yields bounds that are greatly reduced in comparison with the earlier two-species result. Moreover, if the energy norm is properly chosen, wave–particle resonance effects can be captured, reproducing the stabilisation of density-gradient-driven instabilities in maximum-$J$ devices. The optimal mode analysis also reveals that the maximum-$J$ property has an additional stabilising effect on ion-temperature-gradient-driven instabilities, even in the absence of an electron free energy source. This effect is explained in terms of the concept of mode inertia, making it distinct from other mechanisms.

In hydrodynamic (HD) turbulence, an exact decomposition of the energy flux across scales has been derived that identifies the contributions associated with vortex stretching and strain self-amplification (Johnson, Phys. Rev. Lett., vol. 124, 2020 104501; J. Fluid Mech., vol. 922, 2021, A3) to the energy flux across scales. Here, we extend this methodology to general coupled advection–diffusion equations and, in particular, to homogeneous magnetohydrodynamic (MHD) turbulence. We show that several MHD subfluxes are related to each other by kinematic constraints akin to the Betchov relation in HD. Applied to data from direct numerical simulations, this decomposition allows for an identification of physical processes and for the quantification of their respective contributions to the energy cascade, as well as a quantitative assessment of their multi-scale nature through a further decomposition into single- and multi-scale terms. We find that vortex stretching is strongly depleted in MHD compared with HD, and the kinetic energy is transferred from large to small scales almost exclusively by the generation of regions of small-scale intense strain induced by the Lorentz force. In regions of large strain, current sheets are stretched by large-scale straining motion into regions of magnetic shear. This magnetic shear in turn drives extensional flows at smaller scales. Magnetic energy is transferred from large to small scales predominantly by the aforementioned current-sheet thinning in regions of high strain. The contributions from current-filament stretching – the analogue to vortex stretching – and from bending of magnetic field-lines into current filaments by vortical motion are both almost negligible, although the latter induces strong backscatter of magnetic energy. Consequences of these results for subgrid-scale turbulence modelling are discussed.

The regulation of electron heat transport in high-$\beta$, weakly collisional, magnetized plasma is investigated. A temperature gradient oriented along a mean magnetic field can induce a kinetic heat-flux-driven whistler instability (HWI), which back-reacts on the transport by scattering electrons and impeding their flow. Previous analytical and numerical studies have shown that the heat flux for the saturated HWI scales as $\beta _e^{-1}$. These numerical studies, however, had limited scale separation and consequently large fluctuation amplitudes, which calls into question their relevance at astrophysical scales. To this end, we perform a series of particle-in-cell simulations of the HWI across a range of $\beta _e$ and temperature-gradient length scales under two different physical set-ups. The saturated heat flux in all of our simulations follows the expected $\beta _e^{-1}$ scaling, supporting the robustness of the result. We also use our simulation results to develop and implement several methods to construct an effective collision operator for whistler turbulence. The results point to an issue with the standard quasi-linear explanation of HWI saturation, which is analogous to the well-known $90^{\circ }$ scattering problem in the cosmic-ray community. Despite this limitation, the methods developed here can serve as a blueprint for future work seeking to characterize the effective collisionality caused by kinetic instabilities.

Using the ONEDFEL code we perform free electron laser simulations in the astrophysically important guide-field dominated regime. For wigglers’ (Alfvén waves) wavelengths of tens of kilometres and beam Lorentz factor ${\sim }10^3$, the resulting coherently emitted waves are in the centimetre range. Our simulations show a growth of the wave intensity over fourteen orders of magnitude, over the astrophysically relevant scale of approximately a few kilometres. The signal grows from noise (unseeded). The resulting spectrum shows fine spectral substructures, reminiscent of those observed in fast radio bursts.

Magnetic reconnection leads to the formation of island-shaped magnetic structure(s). Due to disagreement between theoretical evaluations of the characteristic reconnection time and observations, it is commonly accepted that the collisionality (or resistivity) is too low to explain magnetic reconnection phenomena in fusion plasmas. Thus, magnetic reconnection still raises many open questions. The work presented here aims to improve the fundamental knowledge about ‘the life of a magnetic island’. Here, in the light of the many works of the last 70 years, a new paradigm for understanding magnetic reconnection in fusion plasmas is proposed. The life of a magnetic island (whatever its scale) follows three phases: the origin, the growth and the saturation. The possible physical mechanisms at play in these three phases will be investigated. First, for the island origin, typical time scales in link with magnetic reconnection will be evaluated for three tokamaks of different sizes (TCV, WEST and JET) to verify if magnetic reconnection is such an unexplained phenomenon in fusion plasmas. Second, for the island drive, the richness of possible mechanisms leading to ‘rapid’ magnetic island growth in fusion devices will be presented for small and large scales. Third comes the island saturation step. Results on the prediction of a large island width at saturation are presented and discussed.

We construct a mean-field model that describes the nonlinear dynamics of a spin-polarized electron gas interacting with fixed, positively charged ions possessing a magnetic moment that evolves in time. The mobile electrons are modelled by a four-component distribution function in the two-dimensional phase space $(x,v)$, obeying a Vlasov–Poisson set of equations. The ions are modelled by a Landau–Lifshitz equation for their spin density, which contains ion–ion and electron–ion magnetic exchange terms. We perform a linear response study of the coupled Vlasov–Poisson–Landau–Lifshitz (VPLL) equations for the case of a Maxwell–Boltzmann equilibrium, focussing in particular on the spin dispersion relation. Conditions of stability or instability for the spin modes are identified, which depend essentially on the electron spin polarization rate $\eta$ and the electron–ion magnetic coupling constant $K$. We also develop an Eulerian grid-based computational code for the fully nonlinear VPLL equations, based on the geometric Hamiltonian method first developed by Crouseilles et al. (J. Plasma Phys., vol. 89, no. 2, 2023, p. 905890215). This technique allows us to achieve great accuracy for the conserved quantities, such as the modulus of the ion spin vector and the total energy. Numerical tests in the linear regime are in accordance with the estimations of the linear response theory. For two-stream equilibria, we study the interplay of instabilities occurring in both the charge and the spin sectors. The set of parameters used in the simulations, with densities close to those of solids (${\approx }10^{29}\ {\rm m}^{-3}$) and temperatures of the order of 10 eV, may be relevant to the warm dense matter regime appearing in some inertial fusion experiments.

Fully relativistic particle-in-cell (PIC) simulations are crucial for advancing our knowledge of plasma physics. Modern supercomputers based on graphics processing units (GPUs) offer the potential to perform PIC simulations of unprecedented scale, but require robust and feature-rich codes that can fully leverage their computational resources. In this work, this demand is addressed by adding GPU acceleration to the PIC code Osiris. An overview of the algorithm, which features a CUDA extension to the underlying Fortran architecture, is given. Detailed performance benchmarks for thermal plasmas are presented, which demonstrate excellent weak scaling on NERSC's Perlmutter supercomputer and high levels of absolute performance. The robustness of the code to model a variety of physical systems is demonstrated via simulations of Weibel filamentation and laser-wakefield acceleration run with dynamic load balancing. Finally, measurements and analysis of energy consumption are provided that indicate that the GPU algorithm is up to ${\sim }$14 times faster and $\sim$7 times more energy efficient than the optimized CPU algorithm on a node-to-node basis. The described development addresses the PIC simulation community's computational demands both by contributing a robust and performant GPU-accelerated PIC code and by providing insight into efficient use of GPU hardware.

An ionized gas medium (plasma state) turns to a complex state of plasma or dusty plasma if micrometre- to submicrometre-sized solid dust particles are introduced in it. The dusty plasma medium exhibits fluid- as well as solid-like characteristics at different background plasma conditions. It supports various linear and nonlinear dynamical structures because of external perturbation and internal instabilities. The vortical or coherent structure in the dusty plasma medium is a kind of self-sustained dynamical structure that is formed either by instabilities or by external forcing. In this review article, the author discusses the past theoretical, experimental and computational investigations on vortical and coherent structures in unmagnetized and magnetized dusty plasmas. The possible mechanisms of the formation of vortices in a dust-grain medium are discussed in detail. The studies on the evolution of vortices and their correlation with turbulence are also reviewed.

It is common wisdom that collisionless shocks become non-planar and non-stationary at sufficiently high Mach numbers. Whatever the shock structure, the upstream and downstream fluxes of the mass, momentum and energy should be equal. At low Mach numbers, these conservation laws are satisfied when the shock front is planar and stationary. When this becomes impossible, inhomogeneity and time dependence, presumably in the form of rippling, develop. In this study, we show that the shock structure changes as a kind of ‘phase transition’ when the Mach number is increased while other shock parameters are kept constant.

The decay of a turbulent magnetic field is slower with helicity than without. Furthermore, the magnetic correlation length grows faster for a helical than a non-helical field. Both helical and non-helical decay laws involve conserved quantities: the mean magnetic helicity density and the Hosking integral. Using direct numerical simulations in a triply periodic domain, we show quantitatively that in the fractionally helical case the mean magnetic energy density and correlation length are approximately given by the maximum of the values for the purely helical and purely non-helical cases. The time of switchover from one to the other decay law can be obtained on dimensional grounds and is approximately given by $I_{H}^{1/2}I_{M}^{-3/2}$, where $I_{H}$ is the Hosking integral and $I_{M}$ is the mean magnetic helicity density. An earlier approach based on the decay time is found to agree with our new result and suggests that the Hosking integral exceeds naive estimates by the square of the same resistivity-dependent factor by which also the turbulent decay time exceeds the Alfvén time. In the presence of an applied magnetic field, the mean magnetic helicity density is known to be not conserved, and we show that then also the Hosking integral is not conserved.

Kinetic theory of particles near resonances is a current topic of discussion in plasma physics and astrophysics. We extend this discussion to the kinetic theory of the interaction between alpha particles (energetic particles predicted to exist in large quantities in next-generation fusion experiments) and a neoclassical tearing mode (NTM), a resistively-driven perturbation which sometimes exists in a tokamak. We develop a quasilinear treatment of the interaction between alpha particles and an NTM, showing why an NTM can be a source of significant passing alpha particle transport in tokamaks. The limitations on quasilinear theory constrain our theory's applicability to small amplitude NTMs, highlighting the importance of nonlinear studies.

This paper presents a theoretical model of plasma equilibrium in the diamagnetic confinement mode in an axisymmetric mirror device with neutral beam injection. The hot ionic component is described within the framework of the kinetic theory, since the Larmor radius of the injected ions appears to be comparable to or even larger than the characteristic scale of the magnetic field inhomogeneity. The electron drag of the hot ions is taken into account, while the angular scattering of the hot ions due to Coulomb collisions is neglected. The background warm plasma, on the contrary, is considered to be in local thermal equilibrium, i.e. has a Maxwellian distribution function and is described in terms of magnetohydrodynamics. The density of the hot ions is assumed to be negligible compared with that of the warm plasma. Both the conventional gas-dynamic loss and the non-adiabatic loss specific to the diamagnetic confinement mode are taken into account. In this work, we do not consider the effects of the warm plasma rotation as well as the inhomogeneity of the electrostatic potential. A self-consistent theoretical model of the plasma equilibrium is constructed. In the case of the cylindrical bubble, this model is reduced to a simpler one. The numerical solutions in the limit of a thin transition layer of the diamagnetic bubble are found. Examples of the equilibria corresponding to the gas-dynamic multiple-mirror trap device are considered.

We investigate the global stability properties of an electron–positron pair plasma in the linear regime. The plasma is confined by the magnetic field of an infinitely long wire. This configuration is the large-aspect-ratio limit of the levitated dipole experiment of the APEX collaboration. The stability is governed by the diocotron mode and the interchange mode. The diocotron mode dominates in the case of a cold, non-neutral plasma. For specific density profiles we find analytic solutions. We derive a necessary condition for instability and find unstable solutions if the plasma forms a thin shell around the wire. Solutions for arbitrary density profiles with finite temperature are obtained numerically. We find that finite-temperature effects stabilise the diocotron mode. The interchange mode, on the other hand, dominates if the plasma is neutral and has a finite temperature. This mode becomes unstable for a steep-enough density gradient, that is aligned with the gradient of the magnetic field strength and is stabilised by the equilibrium $E\times B$ drift of a non-neutral plasma.

This study investigates the impact of local thermal non-equilibrium on the stability analysis of partially ionized plasma within a porous medium. The plasma, heated from below, is enclosed by various combinations of bounding surfaces. Both nonlinear (via the energy method) and linear (utilizing the normal mode analysis method) analyses are performed. Eigenvalue problems for both analyses are formulated and solved using the Galerkin method. The study also explores the effects of compressibility, medium permeability and magnetic fields on system stability. The collisional frequency among plasma components and the thermal diffusivity ratio significantly influence energy decay. The results reveal that the Rayleigh–Darcy number is identical for both nonlinear and linear analyses, thus eliminating the possibility of a subcritical region and confirming global stability. The principle of exchange of stabilities is validated, indicating the absence of oscillatory convection modes. Medium permeability, heat-transfer coefficient and compressibility delay the onset of convection, demonstrating stabilizing effects. Conversely, the porosity-modified conductivity ratio hastens the convection process, indicating destabilizing effects. Rigid–rigid bounding surfaces are found to be thermally more stable for confining the partially ionized plasma. Additionally, the magnetic field exerts a stabilizing influence.