The presence of multi-component protons with their distinct features is confirmed by various space missions in the Earth’s outer magnetosphere regions. Isotropic cold protons and anisotropic hot protons significantly influence/modify the dispersion behaviour of various modes and instabilities and regulate the magnetospheric dynamics effectively. Our present study pays attention to the left-hand-polarised proton cyclotron mode, which gets unstable in the large proton temperature anisotropy condition, i.e. $T_{\perp p}\gt T_{\parallel p}$. Such favourable thermal conditions for protons are extensively observed during the compression of the solar wind against the Earth’s magnetic field. To reveal the wave dynamics in more detail, i.e. time-scale variations in the cold and hot proton temperatures and resulting wave-energy density, we further allow the time evolution of our model bi-Maxwellian distribution function in response to the proton cyclotron instability. Based on velocity-moment techniques, we formulated a set of equations comprising an instantaneous dispersion relation, dynamical perpendicular and parallel temperature relations and a wave-energy density equation. For the graphical illustrations of our mathematical results, we choose initial conditions that are relevant to magnetospheric space environments and reported in various experimental studies. Our exact numerical analysis shows the notable impact of hot proton temperature anisotropy and relative density on the real frequency, growth rate, evolution of initial distributions and wave-energy density of the proton cyclotron instability. Such detailed outcomes will be quite helpful for global/local magnetospheric experimental and simulation studies.

Dusty plasmas typically contain various species of dust particles, though most studies have focused on homogeneous systems. This paper investigates the propagation of dust acoustic waves in an inhomogeneous dusty plasma with an interface, analysing how plasma inhomogeneity influences wave behaviour. Using scattering and reductive perturbation methods, we show that both transmitted and reflected waves depend strongly on the mass ratio between regions. Dust acoustic waves cannot propagate through a dust lattice when the wavelength is smaller than the lattice constant. At a discontinuous interface, at least one transmitted solitary wave is generated, with its amplitude determined by the mass ratio, while at most one reflected solitary wave can exist. These results underscore the critical role of the mass ratio in wave propagation and suggest a method for estimating dust particle masses and properties by analysing the incident, transmitted and reflected waves.

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.

Landau’s collisionless result for a weakly damped plasma wave is precisely recovered in a weakly collisional, steady state plasma by treating the physics of the narrow collisional boundary layer associated with the resonant electrons. To recover Landau’s results, the collision frequency must be large enough that islands are unable to form and/or the wave amplitude must be small enough to allow linearization. However, the Landau treatment fails once the collision frequency becomes too weak and/or the wave amplitude too large. Remarkably, Landau’s weakly damped plasma wave results require collisions and are shown to be inappropriate in the collisionless limit for a nonlinear, finite amplitude, steady state wave!

We study the evolution of collisionless plasmas that, due to their macroscopic evolution, are susceptible to the firehose instability, using both analytic theory and hybrid-kinetic particle-in-cell simulations. We establish that, depending on the relative magnitude of the plasma $\beta$, the characteristic time scale of macroscopic evolution and the ion-Larmor frequency, the saturation of the firehose instability in high-$\beta$ plasmas can result in three qualitatively distinct thermodynamic (and electromagnetic) states. By contrast with the previously identified ‘ultra-high-beta’ and ‘Alfvén-inhibiting’ states, the newly identified ‘Alfvén-enabling’ state, which is realised when the macroscopic evolution time $\tau$ exceeds the ion-Larmor frequency by a $\beta$-dependent critical parameter, can support linear Alfvén waves and Alfvénic turbulence because the magnetic tension associated with the plasma’s macroscopic magnetic field is never completely negated by anisotropic pressure forces. We characterise these states in detail, including their saturated magnetic-energy spectra. The effective collision operator associated with the firehose fluctuations is also described; we find it to be well approximated in the Alfvén-enabling state by a simple quasi-linear pitch-angle scattering operator. The box-averaged collision frequency is $\nu _{\textrm {eff}} \sim \beta /\tau$, in agreement with previous results, but certain subpopulations of particles scatter at a much larger (or smaller) rate depending on their velocity in the direction parallel to the magnetic field. Our findings are essential for understanding low-collisionality astrophysical plasmas including the solar wind, the intracluster medium of galaxy clusters and black hole accretion flows. We show that all three of these plasmas are in the Alfvén-enabling regime of firehose saturation and discuss the implications of this result.

The propagation and absorption of the slow waves in the plasma of the Joint European Torus (JET) tokamak have been investigated by ray tracing. The study aims to obtain a qualitative notion of the penetration into the plasma and absorption of the slow wave excited by the A2 ITER-like antenna. The slow waves are radiated by antennas in the ion cyclotron resonance frequency inverted minority heating or mode conversion heating regimes. It has been discovered that the rays propagate in the toroidal direction over a significant distance, up to 6 × 103 cm, from the antenna. Spreading in the peripheral plasma, mainly between the separatrix and the wall, they slowly shift in the poloidal direction and can reach the divertor region. The change in equilibrium of the JET tokamak has a strong influence on both the propagation and absorption of slow waves. Absorption of the slow waves is caused by ion–electron collisions and Landau damping. In the minority heating regimes, the slow waves are strongly damped in the cyclotron resonance of minority ions even at very low minority density.

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.

The shear Alfvén wave (SAW) continuum plays a critical role in the stability of energetic particle-driven Alfvén eigenmodes. We develop a theoretical framework to analyze the SAW continuum in three-dimensional (3-D) quasisymmetric magnetic fields, focusing on its implications for stellarator design. By employing a near-axis model and degenerate perturbation theory, the continuum equation is solved, highlighting unique features in 3-D configurations, such as the interactions between spectral gaps. Numerical examples validate the theory, demonstrating the impact of flux-surface shaping and quasisymmetric field properties on continuum structure. The results provide insights into optimizing stellarator configurations to minimize resonance-driven losses of energetic particles. This work establishes a basis for incorporating Alfvénic stability considerations into the stellarator design process, demonstrated through optimization of a quasihelical configuration to avoid high-frequency spectral gaps.

We simulate the dynamics, including laser cooling, of three-dimensional (3-D) ion crystals confined in a Penning trap using a newly developed molecular dynamics-like code. The numerical integration of the ions’ equations of motion is accelerated using the fast multipole method to calculate the Coulomb interaction between ions, which allows us to efficiently study large ion crystals with thousands of ions. In particular, we show that the simulation time scales linearly with ion number, rather than with the square of the ion number. By treating the ions’ absorption of photons as a Poisson process, we simulate individual photon scattering events to study laser cooling of 3-D ellipsoidal ion crystals. Initial simulations suggest that these crystals can be efficiently cooled to ultracold temperatures, aided by the mixing of the easily cooled axial motional modes with the low frequency planar modes. In our simulations of a spherical crystal of 1000 ions, the planar kinetic energy is cooled to several millikelvin in a few milliseconds while the axial kinetic energy and total potential energy are cooled even further. This suggests that 3-D ion crystals could be well suited as platforms for future quantum science experiments.

One of the critical challenges in future high-current tokamaks is the avoidance of runaway electrons during disruptions. Here, we investigate disruptions mitigated with combined deuterium and noble gas injection in SPARC. We use multi-objective Bayesian optimisation of the densities of the injected material, taking into account limits on the maximum runaway current, the transported fraction of the heat loss and the current quench time. The simulations are conducted using the numerical framework Dream (disruption runaway electron analysis model). We show that during deuterium operation, runaway generation can be avoided with material injection, even when we account for runaway electron generation from deuterium–deuterium induced Compton scattering. However, when including the latter, the region in the injected-material-density space corresponding to successful mitigation is reduced. During deuterium–tritium operation, acceptable levels of runaway current and transported heat losses are only obtainable at the highest levels of achievable injected deuterium densities. Furthermore, disruption mitigation is found to be more favourable when combining deuterium with neon, compared with deuterium combined with helium or argon.

The intensity of the turbulence in tokamaks and stellarators depends on its ability to excite and sustain zonal flows. Insight into this physics may be gained by studying the ‘residual’, i.e. the late-time linear response of the system to an initial perturbation. We investigate this zonal-flow residual in the limit of a small magnetic mirror ratio, where we find that the typical quadratic approximation to RH (Rosenbluth & Hinton, 1998 Phys. Rev. Lett. vol. 80, issue 4, pp. 724–727) breaks down. Barely passing particles are in this limit central in determining the resulting level of the residual, which we estimate analytically. The role played by the population with large orbit width provides valuable physical insight into the response of the residual beyond this limit. Applying this result to tokamak, quasi-symmetric and quasi-isodynamic equilibria, using a near-axis approximation, we identify the effect to be more relevant (although small) in the core of quasi-axisymmetric fields, where the residual is smallest. The analysis in the paper also clarifies the relationship between the residual and the geodesic acoustic mode, whose typical theoretical set-ups are similar.

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.

Stability of the ‘rigid’ ($m = 1$) ballooning mode in a mirror axisymmetric trap is studied for the case of oblique neutral beam injection (NBI), which creates an anisotropic population of fast sloshing ions. Since small-scale modes with azimuthal numbers $m>1$ in long thin (paraxial) mirror traps are easily stabilized by finite-Larmor-radius (FLR) effects, suppression of the rigid ballooning and flute modes would mean stabilization of all magnetohydrodynamic (MHD) modes, with the exception of the mirror and firehose disturbances, which are intensively studied in geophysics, but have not yet been identified in mirror traps. Large-scale ballooning mode can, in principle, be suppressed either by the lateral perfectly conducting wall, or by the end MHD anchors such as the cusp, by biased limiters or by a combination of these two methods. The effects of the wall shape, vacuum gap width between the plasma column and the lateral wall, angle of oblique NBI, radial profile of the plasma pressure and axial profile of the vacuum magnetic field are studied. It is confirmed that the lateral conducting wall still creates the upper stability zone, where the ratio $\beta$ of the plasma pressure to the pressure of vacuum magnetic field exceeds the second critical value $\beta_{\text{cr2}}$, $\beta >\beta _{\text {cr2}}$. However, in many cases the upper zone is clamped from above by mirror instability. When the lateral wall is combined with end MHD anchors, a lower stability zone $\beta <\beta _{\text {cr}1}$ appears, where $\beta$ is below the first critical value $\beta_{\text{cr1}}$. These two zones can overlap in the case of a sufficiently smooth radial pressure profile, and/or a sufficiently low mirror ratio and/or a sufficiently narrow vacuum gap between the plasma column and the lateral wall. However, even in this case, the range of permissible values of beta is limited from above by the threshold of mirror instability $\beta_{\text{mm}}$, so that $\beta <\beta _{\text {mm}}<1$, in contrast to the case of transversal NBI, when neutral beams are injected perpendicularly to the magnetic field.

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.

We present a quantum algorithm based on repeated measurement to solve initial-value problems for nonlinear ordinary differential equations (ODEs), which may be generated from partial differential equations in plasma physics. We map a dynamical system to a Hamiltonian form, where the Hamiltonian matrix is a function of dynamical variables. To advance in time, we measure expectation values from the previous time step and evaluate the Hamiltonian function classically, which introduces stochasticity into the dynamics. We then perform standard quantum Hamiltonian simulation over a short time, using the evaluated constant Hamiltonian matrix. This approach requires evolving an ensemble of quantum states, which are consumed each step to measure the required observables. We apply this approach to the classic logistic and Lorenz systems, in both integrable and chaotic regimes. Our analysis shows that the solutions’ accuracy is influenced by both the stochastic sampling rate and the nature of the dynamical system.

Transport characteristics and predicted confinement are shown for the Infinity Two fusion pilot plant baseline plasma physics design, a high field stellarator concept developed using modern optimization techniques. Transport predictions are made using high-fidelity nonlinear gyrokinetic turbulence simulations along with drift kinetic neoclassical simulations. A pellet-fuelled scenario is proposed that enables supporting an edge density gradient to substantially reduce ion temperature gradient turbulence. Trapped electron mode turbulence is minimized through the quasi-isodynamic configuration that has been optimized with maximum-J. A baseline operating point with deuterium–tritium fusion power of $P_{{fus,DT}}=800$ MW with high fusion gain $Q_{{fus}}=40$ is demonstrated, respecting the Sudo density limit and magnetohydrodynamic stability limits. Additional higher power operating points are also predicted, including a fully ignited ($Q_{{fus}}=\infty$) case with $P_{{fus,DT}}=1.5$ GW. Pellet ablation calculations indicate it is plausible to fuel and sustain the desired density profile. Impurity transport calculations indicate that turbulent fluxes dominate neoclassical fluxes deep into the core, and it is predicted that impurity peaking will be smaller than assumed in the transport simulations. A path to access the large radiation fraction needed to satisfy exhaust requirements while sustaining core performance is also discussed.

A set of experiments were conducted on the LArge Plasma Device (LAPD) at UCLA to test the operational principles of a traveling wave antenna of the comb-line type. This antenna was designed to launch helicon waves (fast waves in the lower hybrid range of frequencies) on DIII-D. With the order-of-magnitude lower static magnetic field on LAPD, the antenna excites waves in a different regime. Whenever fast waves can propagate in LAPD, slow waves are also supported by the plasma so it is necessary to distinguish between the two cold-plasma branches in evaluating the effectiveness of the launcher. The results show that the launcher couples well to fast waves when the plasma supports fast-wave propagation; control of the principal imposed parallel wavenumber can be achieved through varying the launch frequency on the antenna within its bandwidth of operation; and that the launched waves exhibit strong directionality. We also investigate the role of the plasma profile and wave mode on the loading characteristics. Additionally, a comparison with full-wave modeling of the propagating waves is shown using both a cold-plasma model in COMSOL and a hot-plasma model in RFPisa, which obtain similar results in the present regime.

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.

Plasma-terminating disruptions represent a critical outstanding issue for reactor-relevant tokamaks. ITER will use shattered pellet injection (SPI) as its disruption mitigation system to reduce heat loads, vessel forces and to suppress the formation of runaway electrons. In this paper we demonstrate that reduced kinetic modelling of SPI is capable of capturing the major experimental trends in ASDEX Upgrade SPI experiments, such as dependence of the radiated energy fraction on neon content, or the current quench dynamics. Simulations are also consistent with the experimental observation of no runaway electron generation with neon and mixed deuterium–neon pellet composition. We also show that statistical variations in the fragmentation process only have a notable impact on the disruption dynamics at intermediate neon doping, as was observed in experiments.

In this study, we conducted an electrical analysis of the effects of cold plasma on the properties of distilled water, using a corona discharge in a tip–plane configuration. The discharge was initiated by applying a voltage of 7.17 kV with a 2 mm gap between the tip and the water surface. We investigated the impact of plasma treatment on the total dissolved solids (TDS) and conductivity of 20 mL of distilled water, with exposure times ranging from 2 to 12 min. The results show that plasma treatment leads to a significant increase in conductivity and TDS, with a proportional increase relative to the exposure time. In addition to these measurements, we performed a detailed electrical analysis to evaluate the energy efficiency of the plasma treatment. This analysis involved calculating the useful power and energy efficiency using an equivalent electrical model of the corona discharge reactor, as direct measurement of these parameters is challenging in this context. The model allowed us to calculate energy consumption and analyse the electrical behaviour of the system throughout the treatment process. This study also enables us to monitor, control and optimize the energy during plasma treatment, providing insights into the energy dynamics involved. The findings have potential applications in improving energy efficiency in industrial and environmental processes.