In magnetic confinement fusion devices close to axisymmetry, such as tokamaks, a key element is the winding profile of the magnetic field lines, or its inverse, the safety profile $q=q_{\boldsymbol {B}}$. A corresponding profile, $q_{\boldsymbol {J}}$, can be defined for the current density field lines. Ampère's law relates any mode of current perturbation $\delta \boldsymbol {J}_{m,n}$ with a mode of magnetic perturbation $\delta \boldsymbol {B}_{m,n}$. It is shown that the knowledge of the pair $(q_{\boldsymbol {B}},q_{\boldsymbol {J}})$ allows us then to characterize the resonant, or non-resonant, nature of the modes for both the magnetic and current density field lines. The expression of $q_{\boldsymbol {J}}$ in the flux coordinate is derived. Including this calculation in real-time Grad–Shafranov equilibrium reconstruction codes would yield a comprehensive view of the magnetics. The monitoring of the pair $(q_{\boldsymbol {B}},q_{\boldsymbol {J}})$ would then allow us to investigate the role played by the resonant modes for the current density, that are current filamentary modes, in the plasma small-scale turbulence. By driving the magnetic and current density profiles apart so that the images of $q_{\boldsymbol {B}}$ and $q_{\boldsymbol {J}}$ are disjoint, these filamentary modes would not impact the magnetic field topology, being not associated with magnetic islands but with non-resonant magnetic modes. It remains to be explored to what extent such a configuration, where the spectrum of tiny current density filaments produces a spectrum of magnetic modes that has practically no effect on heat transport, is beneficial.

We present a stellarator configuration optimized for a large threshold (‘critical gradient’) for the onset of the ion temperature gradient (ITG) driven mode, which achieves the largest critical gradient we have seen in any stellarator. Above this threshold, gyrokinetic simulations show that the configuration has low turbulence levels over an experimentally relevant range of the drive strength. The applied optimization seeks to maximize the drift curvature, leading to enhanced local-shear stabilization of toroidal ITG modes, and the associated turbulence. These benefits are combined with excellent quasi-symmetry, yielding low neoclassical transport and vanishingly small alpha particle losses. Analysis of the resulting configuration suggests a trade-off between magnetohydrodynamic (MHD) and ITG stability, as the new configuration possesses a vacuum magnetic hill.

In a recent publication (Toler et al., J. Plasma Phys., vol. 89, issue 2, 2023, p. 905890210), we demonstrated that for axisymmetric geometries, the Kapur–Rokhlin quadrature rule provided an efficient and high-order accurate method for computing the normal component, on the plasma surface, of the magnetic field due to the toroidal current flowing in the plasma, via the virtual-casing principle. The calculation was indirect, as it required the prior computation of the magnetic vector potential from the virtual-casing principle, followed by the computation of its tangential derivative by Fourier differentiation, to obtain the normal component of the magnetic field. Our approach did not provide the other components of the virtual-casing magnetic field. In this letter, we show that a more direct and more general approach is available for the computation of the virtual-casing magnetic field. The Kapur–Rokhlin quadrature rule accurately calculates the principal value integrals in the expression for all the components of the magnetic field on the plasma boundary, and the numerical error converges at a rate nearly as high as the indirect method we presented previously.

Linearized gravity around a rotating black hole or compact object introduces the concept of a gravitomagnetic field, which originates from the matter–current in the rotating object. Plasma in proximity to this object is subsequently subjected to motion guided by this gravitomagnetic term (where mass serves as the effective charge) in addition to the conventional magnetic field. Such an interplay of fields complicates the accessible plasma waves of the system and thus merits exploration to delineate this interplay, to identify any observable signatures of the gravitomagnetic field in weakly magnetized systems, and to motivate future numerical work in a fully relativistic setting where the effects may be stronger. In this work we analyse the dispersion of the upper and lower hybrid electrostatic waves in a plasma immersed in both magnetic and gravitomagnetic fields. In particular, we discuss the effective augmentation or cancellation of the two fields under the right conditions for the upper hybrid wave. In contrast, the lower hybrid wave experiences a frequency up-shift from the gravitomagnetic field regardless of whether it is parallel or antiparallel to the magnetic field for the studied field strengths.

The self-consistent propagation of electrical impulses and of the accompanying distortions of the electron surface in the framework of a cold plasma model with a sharp boundary has been described with help of a derived system of two equations. The method of ‘shallow water theory’ has been applied for the case of bounded plasma and deriving an equation with which to link the spatial and temporal structures and evolution of the boundary curvature and the surface charge. Under certain conditions, such perturbations can propagate along the boundary without changing their shape for a long distance. An approximate analytical solution has been found, and numerical calculations have been performed. Mutual connections between basic parameters of the considered perturbations (velocity components, electrostatic field, etc.) have been presented.

We study the underlying physics of cosmic ray (CR)-driven instabilities that play a crucial role for CR transport across a wide range of scales, from interstellar to galaxy cluster environments. By examining the linear dispersion relation of CR-driven instabilities in a magnetised electron–ion background plasma, we establish that both the intermediate and gyroscale instabilities have a resonant origin, and show that these resonances can be understood via a simple graphical interpretation. These instabilities destabilise wave modes parallel to the large-scale background magnetic field at significantly distinct scales and with very different phase speeds. Furthermore, we show that approximating the electron–ion background plasma with either magnetohydrodynamics (MHD) or Hall-MHD fails to capture the fastest-growing instability in the linear regime, namely the intermediate-scale instability. This finding highlights the importance of accurately characterising the background plasma for resolving the most unstable wave modes. Finally, we discuss the implications of the different phase speeds of unstable modes on particle–wave scattering. Further work is needed to investigate the relative importance of these two instabilities in the nonlinear, saturated regime and to develop a physical understanding of the effective CR transport coefficients in large-scale CR hydrodynamics theories.

This paper presents a magnetohydrodynamic model that describes the small-amplitude fluctuations with wavelengths comparable to ion inertial length in the presence of a relativistically strong mean magnetic field. The set of derived equations is virtually identical to the non-relativistic Hall reduced magnetohydrodynamics (Schekochihin et al., J. Plasma Phys., vol. 85, 2019, 905850303), differing only by a few constants that take into account the relativistic corrections. This means that all the properties of kinetic Alfvén turbulence and ion cyclotron turbulence inherent in the non-relativistic Hall regime persist unchanged even in a magnetically dominated regime.

On the basis of the energy invariants for the Weibel instability in a collisionless non-relativistic plasma, an analytical relation is obtained between the instantaneous values of the space-averaged energy density of the magnetic field, its dominant wavenumber and the average plasma anisotropy parameter. The relation is valid for arbitrary particle velocity distribution functions, including ones that vary with time at the nonlinear stage of instability. It is obtained under the assumption that the plasma is homogeneous along a certain axis, determined, for example, by an external magnetic field, and taking into account only the modes with wavevectors orthogonal to this axis. We give an estimate of the maximum magnetic field energy achievable during the Weibel instability and show that its ratio to the initial longitudinal energy of particles, even for a large initial plasma anisotropy parameter, cannot exceed the value approximately equal to 0.2. The obtained analytical relation is verified using two-dimensional particle-in-cell simulations.

When a particle crosses a region of space where the curvature radius of the magnetic field line shrinks below its gyroradius $r_{g}$, it experiences a non-adiabatic (magnetic moment violating) change in pitch angle. The present paper carries that observation into magnetohydrodynamic (MHD) turbulence to examine the influence of intermittent, sharp bends of the magnetic field lines on particle transport. On the basis of dedicated measurements in a simulation of incompressible turbulence, it is argued that regions of sufficiently large curvature exist in sufficient numbers on all scales to promote scattering. The parallel mean free path predicted by the power-law statistics of the curvature strength scales in proportion to $r_{g}^{0.3}\,\ell _{c}^{0.7}$ ($\ell _{c}$ is the coherence scale of the turbulence), which is of direct interest for cosmic-ray phenomenology. Particle tracking in that numerical simulation confirms that the magnetic moment diffuses through localized, violent interactions, in agreement with the above picture. Correspondingly, the overall transport process is non-Brownian up to length scales $\gtrsim \ell _{c}$.

The transport phenomena of dust particles have been widely observed in fusion plasmas. In this article, we report the observations of dust fragmentations in the Experimental Advanced Superconducting Tokamak (EAST). A dust particle splits into two daughter particles and their motions are recorded before and after the breakup with a fast video camera. The trajectories of the daughter particles in the experiment are consistent with equation-of-motion simulations. The stability of a rotating charged particle in the plasma is briefly discussed.

Laser-plasma instabilities (LPI) play a detrimental role in energy coupling to the target in inertial confinement fusion (ICF). The recent development of applied strong magnetic fields for use in ICF and laboratory astrophysics experiments has opened opportunities to investigate the role of external magnetic fields on LPIs. Recent numerical studies have shown that stimulated Raman scattering (SRS) can be mitigated by external magnetic fields in the kinetic regime of the instability and warrant systematic experimental studies to validate modelling. To this end, we design experiments at the OMEGA-EP laser facility to investigate the effect of an external perpendicular $B$-field of 5–30 T on the backscattered light spectrum from a gas-jet target. We present measurements from a proof-of-principle experiment, where the backward-SRS (BSRS) is in the kinetic regime, for which the magnetization is expected to produce the greatest effects on instability growth. New simulations motivated by this experiment are used to inform the proposal of an upgraded experimental design. Our simulation predictions show that the new design is suited to experimentally demonstrating BSRS mitigation by an external magnetic field, despite the magnetization effects on the hydrodynamics, as well as the inherent temporal and spatial variations in plasma conditions.

The Hosking integral, which characterizes magnetic helicity fluctuations in subvolumes, is known to govern the decay of magnetically dominated turbulence. Here, we show that, when the evolution of the magnetic field is controlled by the motion of electrons only, as in neutron star crusts, the decay of the magnetic field is still controlled by the Hosking integral, but now it has effectively different dimensions than in ordinary magnetohydrodynamic (MHD) turbulence. This causes the correlation length to increase with time $t$ like $t^{4/13}$ instead of $t^{4/9}$ in MHD. The magnetic energy density decreases like $t^{-10/13}$, which is slower than in MHD, where it decays like $t^{-10/9}$. These new analytic results agree with earlier numerical simulations for the non-helical Hall cascade.

A single-field-period quasi-isodynamic stellarator configuration is presented. This configuration, which resembles a twisted strip, is obtained by the method of direct construction, that is, it is found via an expansion in the distance from the magnetic axis. Its discovery, however, relied on an additional step involving numerical optimization, performed within the space of near-axis configurations defined by a set of adjustable magnetic field parameters. This optimization, completed in 30 s on a single CPU core using the SIMSOPT code, yields a solution with excellent confinement, as measured by the conventional figure of merit for neoclassical transport, effective ripple, at a modest aspect ratio of eight. The optimization parameters that led to this configuration are described, its confinement properties are assessed and a set of magnetic field coils is found. The resulting transport at low collisionality is much smaller than that of W7-X, and the device needs significantly fewer coils because of the reduced number of field periods.

In a magnetised plasma on scales well above ion kinetic scales, any constant-magnitude magnetic field, accompanied by parallel Alfvénic flows, forms a nonlinear solution in an isobaric, constant-density background. These structures, which are also known as spherically polarised Alfvén waves, are observed ubiquitously in the solar wind, presumably created by the growth of small-amplitude fluctuations as they propagate outwards in the corona. Here, we present a computational method to construct such solutions of arbitrary amplitude with general multidimensional structure, and explore some of their properties. The difficulty lies in computing a zero-divergence, constant-magnitude magnetic field, which leaves a single, quasi-free function to define the solution, while requiring strong constraints on any individual component of the field. Motivated by the physical process of wave growth in the solar wind, our method circumvents this issue by starting from low-amplitude Alfvénic fluctuations dominated by a strong mean field, then ‘growing’ magnetic perturbations into the large-amplitude regime. We present example solutions with non-trivial structure in one, two and three dimensions, demonstrating a clear tendency to form very sharp gradients or discontinuities, unless the solution is one-dimensional. As well as being useful as an input for other calculations, particularly the study of parametric decay, our results provide a natural explanation for the extremely sharp field discontinuities observed across magnetic field switchbacks in the low solar wind.

Weakly collisional plasmas are subject to nonlinear relaxation processes, which can operate at rates much faster than the particle collision frequencies. This causes the plasma to respond like a magnetised fluid despite having long particle mean free paths. In this Letter the effective collisional mechanisms are modelled in the plasma kinetic equation to produce density, pressure and magnetic-field responses to compare with spacecraft measurements of the solar wind compressive fluctuations at 1 AU. This enables a measurement of the effective mean free path of the solar wind protons, found to be ${\approx }4 \times 10^{5}$ km, which is approximately $10^{3}$ times shorter than the collisional mean free path. These measurements are shown to support the effective fluid behaviour of the solar wind at scales above the proton gyroradius and demonstrate that effective collision processes alter the thermodynamics and transport of weakly collisional plasmas.

We examine the turbulence driven by the ion and electron temperature gradients in selected magnetic configurations of the Wendelstein 7-X (W7-X) stellarator. The inherent flexibility in the configuration space of W7-X enables us to find candidate configurations manifesting low turbulent transport. We follow insights gained by stellarator optimization techniques, in order to identify key geometric features, which are directly related to the ion and electron heat fluxes produced by plasma turbulence. One such a feature is the flux expansion at locations where the curvature is particularly unfavourable. Starting from a configuration routinely used in the W7-X experiment, we end up with an optimized configuration. Based on this equilibrium, we select a configuration from W7-X configuration database with a similar feature as the optimized one. With the help of nonlinear gyrokinetic simulations, we show that the heat flux in this configuration is less stiff than in the initial configuration, both for ion temperature gradient and electron temperature gradient turbulence.

Dissipative processes cause collisionless plasmas in many systems to develop non-thermal particle distributions with broad power-law tails. The prevalence of power-law energy distributions in space/astrophysical observations and kinetic simulations of systems with a variety of acceleration and trapping (or escape) mechanisms poses a deep mystery. We consider the possibility that such distributions can be modelled from maximum-entropy principles, when accounting for generalizations beyond the Boltzmann–Gibbs entropy. Using a dimensional representation of entropy (related to the Renyi and Tsallis entropies), we derive generalized maximum-entropy distributions with a power-law tail determined by the characteristic energy scale at which irreversible dissipation occurs. By assuming that particles are typically energized by an amount comparable to the free energy (per particle) before equilibrating, we derive a formula for the power-law index as a function of plasma parameters for magnetic dissipation in systems with sufficiently complex topologies. The model reproduces several results from kinetic simulations of relativistic turbulence and magnetic reconnection.

We report a generation of energetic protons by the interaction of a high-energy electron driving beam with an underdense plasma slab. After an interaction period of approximately 4000 fs, a proton beam with maximum energy greater than 250 MeV can be achieved by applying a driving beam with energy 1.0 GeV to a 200 $\mathrm {\mu }$m plasma slab. Our two-dimensional particle-in-cell simulations also show that the proton acceleration process can be divided into two stages. In the first stage, a strong positive longitudinal electric field appears near the rear boundary of the plasma slab after the driving beam has passed through it. This acceleration process is similar to the target normal sheath acceleration scheme by the interaction between intense pulsed laser with overdense plasma targets. In the second stage, the accelerated protons experience a long-range acceleration process with a two-stream instability between the high-energy driving beam and the proton beam. Further analyses show that this accelerated proton beam is equipped with the property of good collimation and high energy. This scheme presents a new way for proton or ion acceleration on some special occasions.

We carry out three-dimensional and two-dimensional particle-in-cell simulations of the expansion of a magnetized plasma that initially uniformly fills a half-space and contains a semicylindrical region of heated electrons elongated along the surface of the plasma boundary. This geometry is related, for instance, to ablation of a plane target by a femtosecond laser beam under quasi-cylindrical focusing. We find that a decay of the inhomogeneous plasma–vacuum discontinuity is strongly affected by an external magnetic field parallel to its boundary. We observe various transient phenomena, including an anisotropic scattering of electrons and an accompanying Weibel instability, and reveal various spatial structures of the arising magnetic field and current, including multiple flying-apart filaments of a Z-pinch type and slowly evolving current sheets with different orientations. The magnitude of the self-generated magnetic field can be of the order of, or significantly exceed that of, the external one. Such phenomena are expected in the laser and cosmic plasmas, including the explosive processes in the planetary magnetospheres and stellar coronal arches.

Fluctuation measurements reveal the outward electromagnetic energy flux needed to drive the dynamo electromotive force supporting magnetic self-organization in a reversed-field pinch plasma. The radial Poynting flux due to tearing mode fluctuations is measured with an insertable probe during magnetic relaxation. This flux corresponds to transient power levels much larger than the input power and comparable to the global equilibrium magnetic energy transient loss rate. The probe measurements of this flux are roughly as predicted by a simple Poynting's theorem model upon substitution of equilibrium measurement data.