Magnetic reconnection is explored on the Terrestrial Reconnection Experiment (TREX) for asymmetric inflow conditions and in a configuration where the absolute rate of reconnection is set by an external drive. Magnetic pileup enhances the upstream magnetic field of the high-density inflow, leading to an increased upstream Alfvén speed and helping to lower the normalized reconnection rate to values expected from theoretical consideration. In addition, a shock interface between the far upstream supersonic plasma inflow and the region of magnetic flux pileup is observed, important to the overall force balance of the system, thereby demonstrating the role of shock formation for configurations including a supersonically driven inflow. Despite the specialized geometry where a strong reconnection drive is applied from only one side of the reconnection layer, previous numerical and theoretical results remain robust and are shown to accurately predict the normalized rate of reconnection for the range of system sizes considered. This experimental rate of reconnection is dependent on system size, reaching values as high as 0.8 at the smallest normalized system size applied.

The fundamental nature of turbulent density fluctuations in standard Wendelstein 7-X (W7-X) stellarator discharges is investigated experimentally via phase contrast imaging (PCI) in combination with gyrokinetic simulations with the code GENE. We find that density fluctuations are ion-temperature-gradient-driven and radially localised in the outer half of the plasma. It is shown that the line-integrated PCI measurements cover the right range of wavenumbers and a favourable toroidal and poloidal location to capture some of the strongest density fluctuations in W7-X. Due to the radial localisation of fluctuations, measured wavenumber–frequency spectra exhibit a dominant phase velocity, which can be related to the $\boldsymbol {E\times B}$ rotation velocity at the radial position of a well in the neoclassical radial electric field. The match is robust against variations of heating power and line-integrated density, which is partly due to the localisation of fluctuations and partly due to effects of the radial gradient in the $\boldsymbol {E\times B}$ velocity profile on the wavenumber–frequency spectrum. The latter effect is studied with a newly built synthetic PCI diagnostic and global gyrokinetic simulations with GENE-3D.

A first-principles method to calculate the critical temperature gradient for the onset of the ion-temperature-gradient mode (ITG) in linear gyrokinetics is presented. We find that conventional notions of the connection length previously invoked in tokamak research should be revised and replaced by a generalized correlation length to explain this onset in stellarators. Simple numerical experiments and gyrokinetic theory show that localized ‘spikes’ in shear, a hallmark of stellarator geometry, are generally insufficient to constrain the parallel correlation length of the mode. ITG modes that localize within bad drift curvature wells that have a critical gradient set by peak drift curvature are also observed. A case study of near-helical stellarators of increasing field period demonstrates that the critical gradient can indeed be controlled by manipulating the magnetic geometry, but underscores the need for a general framework to evaluate the critical gradient. We conclude that average curvature and global shear set the correlation length of resonant ITG modes near the absolute critical gradient, the physics of which is included through direct solution of the gyrokinetic equation. Our method, which handles the general geometry and is more efficient than conventional gyrokinetic solvers, could be applied to future studies of stellarator ITG turbulence optimization.

Between the base of the solar corona at $r=r_\textrm {b}$ and the Alfvén critical point at $r=r_\textrm {A}$, where $r$ is heliocentric distance, the solar-wind density decreases by a factor $ \mathop > \limits_\sim 10^5$, but the plasma temperature varies by a factor of only a few. In this paper, I show that such quasi-isothermal evolution out to $r=r_\textrm {A}$ is a generic property of outflows powered by reflection-driven Alfvén-wave (AW) turbulence, in which outward-propagating AWs partially reflect, and counter-propagating AWs interact to produce a cascade of fluctuation energy to small scales, which leads to turbulent heating. Approximating the sub-Alfvénic region as isothermal, I first present a brief, simplified calculation showing that in a solar or stellar wind powered by AW turbulence with minimal conductive losses, $\dot {M} \simeq P_\textrm {AW}(r_\textrm {b})/v_\textrm {esc}^2$, $U_{\infty } \simeq v_\textrm {esc}$, and $T\simeq m_\textrm {p} v_\textrm {esc}^2/[8 k_\textrm {B} \ln (v_\textrm {esc}/\delta v_\textrm {b})]$, where $\dot {M}$ is the mass outflow rate, $U_{\infty }$ is the asymptotic wind speed, $T$ is the coronal temperature, $v_\textrm {esc}$ is the escape velocity of the Sun, $\delta v_\textrm {b}$ is the fluctuating velocity at $r_\textrm {b}$, $P_\textrm {AW}$ is the power carried by outward-propagating AWs, $k_\textrm {B}$ is the Boltzmann constant, and $m_\textrm {p}$ is the proton mass. I then develop a more detailed model of the transition region, corona, and solar wind that accounts for the heat flux $q_\textrm {b}$ from the coronal base into the transition region and momentum deposition by AWs. I solve analytically for $q_\textrm {b}$ by balancing conductive heating against internal-energy losses from radiation, $p\,\textrm {d} V$ work, and advection within the transition region. The density at $r_\textrm {b}$ is determined by balancing turbulent heating and radiative cooling at $r_\textrm {b}$. I solve the equations of the model analytically in two different parameter regimes. In one of these regimes, the leading-order analytic solution reproduces the results of the aforementioned simplified calculation of $\dot {M}$, $U_\infty$, and $T$. Analytic and numerical solutions to the model equations match a number of observations.

In preparation for extending the JOREK nonlinear magnetohydrodynamics (MHD) code to stellarators, a hierarchy of stellarator-capable reduced and full MHD models has been derived and tested. The derivation was presented at the EFTC 2019 conference. Continuing this line of work, we have implemented the reduced MHD model (Nikulsin et al., Phys. Plasmas, vol. 26, 2019, 102109) as well as an alternative model which was newly derived using a different set of projection operators for obtaining the scalar momentum equations from the full MHD vector momentum equation. With the new operators, the reduced model matches the standard JOREK reduced models for tokamaks in the tokamak limit and conserves energy exactly, while momentum conservation is less accurate than in the original model whenever field-aligned flow is present.

In an earlier paper we showed that the combination of azimuthal magnetic fields and super-rotation in Taylor–Couette flows of conducting fluids can be unstable against non-axisymmetric perturbations if the magnetic Prandtl number of the fluid is $\textrm {Pm}\neq 1$. Here we demonstrate that the addition of a weak axial field component allows axisymmetric perturbation patterns for $\textrm {Pm}$ of order unity depending on the boundary conditions. The axisymmetric modes only occur for magnetic Mach numbers (of the azimuthal field) of order unity, while higher values are necessary for the non-axisymmetric modes. The typical growth time of the instability and the characteristic time scale of the axial migration of the axisymmetric mode are long compared with the rotation period, but short compared with the magnetic diffusion time. The modes travel in the positive or negative $z$ direction along the rotation axis depending on the sign of $B_\phi B_z$. We also demonstrate that the azimuthal components of flow and field perturbations travel in phase if $|B_\phi |\gg |B_z|$, independent of the form of the rotation law. Within a short-wave approximation for thin gaps it is also shown (in an appendix) that for ideal fluids the considered helical magnetorotational instability only exists for rotation laws with negative shear.

An adjoint method to calculate the gradient of island width in stellarators is presented and applied to a set of magnetic field configurations. The underlying method for calculation of the island width is that of Cary & Hanson (Phys. Fluids B, vol. 3, issue 4, 1991, pp. 1006–1014) (with a minor modification), and requires that the residue of the island centre be small. Therefore, the gradient of the residue is calculated in addition. Both the island width and the gradient calculations are verified using an analytical magnetic field configuration introduced by Reiman & Greenside (Comput. Phys. Commun., vol. 43, issue 1, 1986, pp. 157–167). The method is also applied to the calculation of the shape gradient of the width of a magnetic island in a National Compact Stellarator Experiment (NCSX) vacuum configuration with respect to positions on a coil. A gradient-based optimization is applied to a magnetic field configuration studied by Hanson & Cary (Phys. Fluids, vol. 27, issue 4, 1984, pp. 767–769) to minimize stochasticity by adding perturbations to a pair of helical coils. Although only vacuum magnetic fields and an analytical magnetic field model are considered in this work, the adjoint calculation of the island width gradient could also be applied to a magnetohydrodynamic (MHD) equilibrium if the derivative of the magnetic field, with respect to the equilibrium parameters, is known. Using the island width gradient calculation presented here, more general gradient-based optimization methods can be applied to design stellarators with small magnetic islands. Moreover, the sensitivity of the island size may itself be optimized to ensure that coil tolerances, with respect to island size, are kept as high as possible.

The formation of a substantial postdisruption runaway electron current in ASDEX Upgrade material injection experiments is determined by avalanche multiplication of a small seed population of runaway electrons. For the investigation of these scenarios, the runaway electron description of the coupled 1.5-D transport solvers ASTRA-STRAHL is amended by a fluid model describing electron runaway caused by the hot-tail mechanism. Applied in simulations of combined background plasma evolution, material injection and runaway electron generation in ASDEX Upgrade discharge #33108, both the Dreicer and hot-tail mechanism for electron runaway produce only ${\sim }$ 3 kA of runaway current. In colder plasmas with core electron temperatures $T_\textrm {e,c}$ below 9 keV, the postdisruption runaway current is predicted to be insensitive to the initial temperature, in agreement with experimental observations. Yet in hotter plasmas with $T_\textrm {e,c}$ above 10 keV, hot-tail runaway can be increased by up to an order of magnitude, contributing considerably to the total postdisruption runaway current. In ASDEX Upgrade high-temperature runaway experiments, however, no runaway current is observed at the end of the disruption, despite favourable conditions for both primary and secondary runaway.

In strong electromagnetic regimes, gyrokinetic simulations have linked a substantial ion-scale turbulence stabilization to the presence of supra-thermal particles, capturing qualitatively well the experimental observations in different devices worldwide. An explanation for the underlying physical mechanism responsible for the fast-ion-induced turbulent transport reduction observed in the numerical simulations has been proposed only recently by Di Siena et al. (Nucl. Fusion, vol. 59, 2019, p. 124001; Nucl. Fusion, vol. 60, 2020, p. 089501). It involves a nonlinear cross-scale coupling (nonlinear interaction involving different modes at different wavenumbers) between ion-temperature-gradient and marginally stable Alfvén eigenmodes, which in turn increases zonal flow activity. In view of an optimization of this turbulence-stabilizing effect, the key parameters controlling the nonlinear cross-scale coupling are here identified. At the same time, these findings provide useful insights for reduced-turbulence models and integrative approaches, which might be trained on the results presented in this paper to grasp the underlying physics and the parameter scaling of the beneficial effects of fast particles on plasma turbulence.

Combined plasma–coil optimization approaches for designing stellarators are discussed and a new method for calculating free-boundary equilibria for multiregion relaxed magnetohydrodynmics (MRxMHD) is proposed. Four distinct categories of stellarator optimization, two of which are novel approaches, are the fixed-boundary optimization, the generalized fixed-boundary optimization, the quasi-free-boundary optimization, and the free-boundary (coil) optimization. These are described using the MRxMHD energy functional, the Biot–Savart integral, the coil-penalty functional and the virtual casing integral and their derivatives. The proposed free-boundary equilibrium calculation differs from existing methods in how the boundary-value problem is posed, and for the new approach it seems that there is not an associated energy minimization principle because a non-symmetric functional arises. We propose to solve the weak formulation of this problem using a spectral-Galerkin method, and this will reduce the free-boundary equilibrium calculation to something comparable to a fixed-boundary calculation. In our discussion of combined plasma–coil optimization algorithms, we emphasize the importance of the stability matrix.

The axisymmetric visco-resistive magnetohydrodynamic steady states allowing flows (i.e. non-vanishing velocity fields) are computed for a toroidal JET-like geometry. It is shown that a spatially inhomogeneous heating of moderate magnitude leads to an increase of typical toroidal speeds with respect to the situation with uniform temperature with identical mean Hartmann numbers. A symmetry argument is introduced to capture the symmetry breaking, induced by the temperature gradient, that produces a net toroidal plasma flow.

Recent discoveries have demonstrated that matter can be distinguished on the basis of topological considerations, giving rise to the concept of topological phase. Introduced originally in condensed matter physics, the physics of topological phase can also be fruitfully applied to plasmas. Here, the theory of topological phase is introduced, including a discussion of Berry phase, Berry connection, Berry curvature and Chern number. One of the clear physical manifestations of topological phase is the bulk-boundary correspondence, the existence of localized unidirectional modes at the interface between topologically distinct phases. These concepts are illustrated through examples, including the simple magnetized cold plasma. An outlook is provided for future theoretical developments and possible applications.

The electron runaway phenomenon in plasmas depends sensitively on the momentum- space dynamics. However, efficient simulation of the global evolution of systems involving runaway electrons typically requires a reduced fluid description. This is needed, for example, in the design of essential runaway mitigation methods for tokamaks. In this paper, we present a method to include the effect of momentum-dependent spatial transport in the runaway avalanche growth rate. We quantify the reduction of the growth rate in the presence of electron diffusion in stochastic magnetic fields and show that the spatial transport can raise the effective critical electric field. Using a perturbative approach, we derive a set of equations that allows treatment of the effect of spatial transport on runaway dynamics in the presence of radial variation in plasma parameters. This is then used to demonstrate the effect of spatial transport in current quench simulations for ITER-like plasmas with massive material injection. We find that in scenarios with sufficiently slow current quench, owing to moderate impurity and deuterium injection, the presence of magnetic perturbations reduces the final runaway current considerably. Perturbations localised at the edge are not effective in suppressing the runaways, unless the runaway generation is off-axis, in which case they may lead to formation of strong current sheets at the interface of the confined and perturbed regions.

Finding less complicated coils that have adequately low field errors is a crucial step in stellarator development. One coil metric that is of high importance is the maximum curvature of the coil centreline, or coil single filament. Conductors cannot be bent below some threshold minimum radius of curvature. High coil curvatures can cause strains to exceed acceptable levels, especially in superconducting coils. We investigate three ways to optimize coil curvature and find that applying penalty functions to the coil curvature solves for coils that have a constrained maximum curvature and low field error. Penalty functions are implemented in FOCUS and coil solutions optimized for an HSX-like ‘plasma boundary’ are presented.

The first detection of a binary neutron star merger through gravitational waves and photons marked the dawn of multimessenger astronomy with gravitational waves, and it greatly increased our insight in different fields of astrophysics and fundamental physics. However, many open questions on the physical process involved in a compact binary merger still remain and many of these processes concern plasma physics. With the second generation of gravitational wave interferometers approaching their design sensitivity, the new generation under design study and new X-ray detectors under development, the high energy universe will become more and more a unique laboratory for our understanding of plasma in extreme conditions. In this review, we discuss the main electromagnetic signals expected to follow the merger of two compact objects highlighting the main physical processes involved and some of the most important open problems in the field.

Accelerated particles are ubiquitous in the Cosmos and play a fundamental role in many processes governing the evolution of the Universe at all scales, from the sub-AU scale relevant for the formation and evolution of stars and planets to the Mpc scale involved in Galaxy assembly. We reveal the presence of energetic particles in many classes of astrophysical sources thanks to their production of non-thermal radiation, and we detect them directly at the Earth as cosmic rays. In the last two decades both direct and indirect observations have provided us a wealth of new, high-quality data about cosmic rays and their interactions both in sources and during propagation, in the Galaxy and in the Solar System. Some of the new data have confirmed existing theories about particle acceleration and propagation and their interplay with the environment in which they occur. Some others have brought about interesting surprises, whose interpretation is not straightforward within the standard framework and may require a change of paradigm in terms of our ideas about the origin of cosmic rays of different species or in different energy ranges. In this article, we focus on cosmic rays of galactic origin, namely with energies below a few petaelectronvolts, where a steepening is observed in the spectrum of energetic particles detected at the Earth. We review the recent observational findings and the current status of the theory about the origin and propagation of galactic cosmic rays.

The behaviour of a strongly magnetised collisional electron–positron plasma that is optically thin to cyclotron radiation is considered, and the distribution functions accessible to it on the various timescales in the system are calculated. Particular attention is paid to the limit in which the collision time exceeds the radiation emission time, making the electron distribution function strongly anisotropic. Indeed, these are the exact conditions likely to be attained in the first laboratory electron–positron plasma experiments currently being developed, which will typically have very low densities and be confined in very strong magnetic fields. The constraint of strong magnetisation adds an additional complication in that long-range Coulomb collisions, which are usually negligible, must now be considered. A rigorous collision operator for these long-range collisions has never been written down. Nevertheless, we show that the collisional scattering can be accounted for without knowing the explicit form of this collision operator. The rate of radiation emission is calculated and it is found that the loss of energy from the plasma is proportional to the parallel collision frequency multiplied by a factor that only depends logarithmically on plasma parameters. That is, this is a self-accelerating process, meaning that the bulk of the energy will be lost in a few collision times. We show that in a simple case, that of straight field-line geometry, there are no unstable drift waves in such plasmas, despite being far from Maxwellian.

The behaviour of a collisional plasma that is optically thin to cyclotron radiation is considered, and the distribution functions accessible to it on the various time scales in the system are calculated. Particular attention is paid to the limit in which the collision time exceeds the radiation emission time, making the electron distribution function strongly anisotropic. Unusually for plasma physics, the collision operator can nevertheless be calculated analytically although the plasma is far from Maxwellian. The rate of radiation emission is calculated and found to be governed by the collision frequency multiplied by a factor that only depends logarithmically on plasma parameters.

Synchrotron radiation images from runaway electrons (REs) in an ASDEX Upgrade discharge disrupted by argon injection are analysed using the synchrotron diagnostic tool Soft and coupled fluid-kinetic simulations. We show that the evolution of the runaway distribution is well described by an initial hot-tail seed population, which is accelerated to energies between 25–50 MeV during the current quench, together with an avalanche runaway tail which has an exponentially decreasing energy spectrum. We find that, although the avalanche component carries the vast majority of the current, it is the high-energy seed remnant that dominates synchrotron emission. With insights from the fluid-kinetic simulations, an analytic model for the evolution of the runaway seed component is developed and used to reconstruct the radial density profile of the RE beam. The analysis shows that the observed change of the synchrotron pattern from circular to crescent shape is caused by a rapid redistribution of the radial profile of the runaway density.

We present experimental data providing evidence for the formation of transient (${\sim }20\ \mathrm {\mu }\textrm {s}$) plasmas that are simultaneously weakly magnetized (i.e. Hall magnetization parameter $\omega \tau > 1$) and dominated by thermal pressure (i.e. ratio of thermal-to-magnetic pressure $\beta > 1$). Particle collisional mean free paths are an appreciable fraction of the overall system size. These plasmas are formed via the head-on merging of two plasmas launched by magnetized coaxial guns. The ratio $\lambda _{\textrm {gun}}=\mu _0 I_{\textrm {gun}}/\psi _{\textrm {gun}}$ of gun current $I_{\textrm {gun}}$ to applied magnetic flux $\psi _{\textrm {gun}}$ is an experimental knob for exploring the parameter space of $\beta$ and $\omega \tau$. These experiments were conducted on the Big Red Ball at the Wisconsin Plasma Physics Laboratory. The transient formation of such plasmas can potentially open up new regimes for the laboratory study of weakly collisional, magnetized, high-$\beta$ plasma physics; processes relevant to astrophysical objects and phenomena; and novel magnetized plasma targets for magneto-inertial fusion.