We compare three different approaches to describe a magnetic island in a generic toroidal plasma: (i) perturbative, from the perspective of the equilibrium magnetic field and the related action in a variational principle formulation; (ii) again perturbative, based on the integrability of a system with a single resonant mode and the application of a canonical transformation onto a new island equilibrium system; and (iii) non-perturbative, making use of a full geometric description of the island considered as a stand-alone plasma domain. For the three approaches, we characterize some observables and discuss the respective limits.

The Earth magnetopause, when sufficiently plane and stationary at a local scale, can be considered as a ‘quasi-tangential’ discontinuity, since the normal component of the magnetic field B_n$B_n$ is typically very small but not zero. Contrary to observations, the ‘classic theory of discontinuities’ predicts that rotational and compressional jumps should be mutually exclusive in the general case B_n \ne 0$B_n \ne 0$, but allows only one exception: the tangential discontinuity provided that B_n$B_n$ is strictly zero. Here we show that finite Larmor radius (FLR) effects play an important role in the quasi-tangential case, whenever the ion Larmor radius is not fully negligible with respect to the magnetopause thickness. By including FLR effects, the results suggest that a rotational discontinuity undergoes a change comparable to the change of a shear Alfvén into a kinetic Alfvén wave when considering linear modes. For this new kind of discontinuity, the co-existence of rotational and compressional variations at the magnetopause does no more imply that this boundary is a strict tangential discontinuity, even in one-dimensional (1-D)-like regions far from X lines if any. This result may lead to important consequences concerning the oldest and most basic questions of magnetospheric physics: how can the magnetopause be open, where and when? While the role of FLR is established theoretically, in this paper we show that it can be proved experimentally. For this, we make use of magnetospheric multiscale mission (MMS) data and process them with the most recent available four spacecraft tools. First, we present the different processing techniques that we use to estimate spatial derivatives, such as grad(B)$grad(B)$ and div(P)$div(P)$, and the magnetopause normal direction. We point out why this normal direction must be determined with extremely high accuracy to make the conclusions unambiguous. Then, the results obtained by these techniques are presented in a detailed case study and on a statistical basis.

Dispersion relations of electrostatic surface waves propagating in magnetized plasmas contained in an infinite duct and in an infinite cylindrical column surrounded by vacuum are derived by means of a Vlasov equation and fluid equations, respectively. The kinematic boundary condition imposed on the distribution function, the specular reflection conditions on the four sides of a duct, can be satisfied by placing infinite number of fictitious surface charge sheets spaced by the duct widths. The Vlasov equation that includes these surface charge sheets is solved by summing up the contribution due to the infinite charge sheets. The method of placing appropriate fictitious surface charge sheets enables one to treat the surface waves in bounded plasmas of Cartesian structure with mathematical efficiency, kinetically. The kinetic duct dispersion relation is compared with the dispersion relation for the magnetized cylindrical plasma column. When the square duct cross-sectional area as well as the cylinder radius become infinity, both dispersion relations become the dispersion relation of the upper-hybrid wave.

A new approach for constructing polar-like boundary-conforming coordinates inside a toroid with strongly shaped cross-sections is presented. A coordinate mapping is obtained through a variational approach, which involves identifying extremal points of a proposed action in the mapping space from [0, 2{\rm \pi} ]^2 \times [0, 1]$[0, 2{\rm \pi} ]^2 \times [0, 1]$ to a toroidal domain in \mathbb {R}^3$\mathbb {R}^3$. This approach employs an action built on the squared Jacobian and radial length. Extensive testing is conducted on general toroidal boundaries using a global Fourier–Zernike basis via action minimisation. The results demonstrate successful coordinate construction capable of accurately describing strongly shaped toroidal domains. The coordinate construction is successfully applied to the computation of three-dimensional magnetohydrodynamic equilibria in the GVEC code where the use of traditional coordinate construction by interpolation from the boundary failed.

Young stellar objects (YSOs) are protostars that exhibit bipolar outflows fed by accretion disks. Theories of the transition between disk and outflow often involve a complex magnetic field structure thought to be created by the disk coiling field lines at the jet base; however, due to limited resolution, these theories cannot be confirmed with observation and thus may benefit from laboratory astrophysics studies. We create a dynamically similar laboratory system by driving a \sim$\sim$1 MA current pulse with a 200 ns rise through a \approx$\approx$2 mm-tall Al cylindrical wire array mounted to a three-dimensional (3-D)-printed, stainless steel scaffolding. This system creates a plasma that converges on the centre axis and ejects cm-scale bipolar outflows. Depending on the chosen 3-D-printed load path, the system may be designed to push the ablated plasma flow radially inwards or off-axis to make rotation. In this paper, we present results from the simplest iteration of the load which generates radially converging streams that launch non-rotating jets. The temperature, velocity and density of the radial inflows and axial outflows are characterized using interferometry, gated optical and ultraviolet imaging, and Thomson scattering diagnostics. We show that experimental measurements of the Reynolds number and sonic Mach number in three different stages of the experiment scale favourably to the observed properties of YSO jets with Re\sim 10^5\unicode{x2013}10^9$Re\sim 10^5\unicode{x2013}10^9$ and M\sim 1\unicode{x2013}10$M\sim 1\unicode{x2013}10$, while our magnetic Reynolds number of Re_M\sim 1\unicode{x2013}15$Re_M\sim 1\unicode{x2013}15$ indicates that the magnetic field diffuses out of our plasma over multiple hydrodynamical time scales. We compare our results with 3-D numerical simulations in the PERSEUS extended magnetohydrodynamics code.

Experimental research into the control of particle charge in dusty plasmas conducted at Auburn University indicates that photocurrents generated by exposing dust to intense, near-ultraviolet light can provide a reliable and novel method of independently controlling dust charge without radically altering the background plasma; the experiment also showed that some particles may respond differently to this photo-discharge, with some exhibiting highly periodic responses to the discharge and others exhibiting chaotic behaviour. Since the dust particles in the experiment were a polydisperse sample of different sizes and shapes, particle geometry may play a role in explaining this difference. Simulations of particle discharge and dynamics are used in an attempt to reproduce experimental results and investigate a possible correlation between particle symmetry and dynamic periodicity.

On the Experimental Advanced Superconducting Tokamak (EAST), the electron cyclotron wave (ECW) and lower hybrid wave (LHW) are actively used to achieve a high-performance plasma. Turbulence associated with the combined heating experiment is studied numerically based on the gyrokinetic toroidal code (GTC). The linear simulation results show that the unstable mode peaks at k_{\theta }\rho _{s}\approx 0.65$k_{\theta }\rho _{s}\approx 0.65$ and k_{\theta }\rho _{s}\approx 1.42$k_{\theta }\rho _{s}\approx 1.42$. Meanwhile, all of the frequencies of these instabilities are positive, which suggests that the collisionless trapped electron mode (CTEM) is the dominant instability. In the process of nonlinear simulations, a higher transport level is locally achieved during the two waves combined heating due to a formation of a steeper electron temperature gradient. In addition, a low-frequency geodesic acoustic mode (GAM) is observed in the nonlinear stage. Effects of the electron beta, the dimensionless ratio of T_e/T_i$T_e/T_i$ and R/L_{T_e}$R/L_{T_e}$ on the growth rate of instability, are also discussed in the paper.

The simplification of collision operators is necessary for quasilinear turbulence modelling used with integrated modelling frameworks, such as the gyrokinetic code QuaLiKiz. The treatment of collisions greatly impacts the accuracy of trapped electron mode (TEM) modelling, which is necessary to predict the electron heat flux and the balance between inward and outward particle fluxes. In particular, accurate particle flux predictions are necessary to successfully model density peaking in the tokamak core. We explored two ways of improving collisional TEM model reduction for tokamak core plasmas. First, we carried out linear GENE simulations to study the complex interplay between collisions and trapped electrons. We then used these simulations to define an effective trapped fraction to characterize the collisional TEM based on two key parameters, the local inverse-aspect ratio \epsilon$\epsilon$ and the collisionality \nu ^\ast$\nu ^\ast$. One aspect missing from analytical TEM research is that the collisional frequency and the bounce-transit frequency are both velocity dependent; this effective trapped fraction takes both into account. In doing so, we determined that two parameters are not enough to model the collisional TEM, as an additional third free parameter was necessary. We determined that this model, as currently formulated, is not suitable for integrated modelling purposes. Second, we directly improved QuaLiKiz's Krook operator, which relies on two free parameters. We determined that these parameters required adjustments against higher-fidelity collisional models. In order to improve density profile predictions when paired with integrated models, we refined the Krook operator by using GENE simulations as a higher-fidelity point of comparison. We then demonstrate strong improvement of density peaking predictions of QuaLiKiz within the integrated modelling framework JETTO.

We study the tearing instability of a current sheet in a relativistic pair plasma with a power-law distribution function. We first estimate the growth rate analytically and then confirm the analytical results by solving numerically the dispersion equation, taking into account all exact particle trajectories within the reconnecting layer. We found that the instability is suppressed when the particle spectrum becomes harder.

Optimising stellarators for quasisymmetry leads to strongly reduced collisional transport and energetic particle losses compared with unoptimised configurations. Although stellarators with precise quasisymmetry have been obtained in the past, it remains unclear how broad the parameter space is where good quasisymmetry may be achieved. We study the range of aspect ratios and rotational transform values for which stellarators with excellent quasisymmetry on the boundary can be obtained. A large number of Fourier harmonics is included in the boundary representation, which is made computationally tractable by the use of adjoint methods to enable fast gradient-based optimisation and by the direct optimisation of vacuum magnetic fields, which converge more robustly compared with solutions from magnetohydrostatics. Several novel configurations are presented, including stellarators with record levels of quasisymmetry on a surface, three field period quasiaxisymmetric stellarators with substantial magnetic shear, and compact quasisymmetric stellarators at low aspect ratios similar to tokamaks.

There is renewed interest in direct-drive inertial confinement fusion, following the milestone December 2022 3.15 MJ ignition result on the National Ignition Facility. A key obstacle is the control of the two-plasmon decay instability. Here, recent advances in inhomogeneous turbulence theory are applied to the broadband parametric instability problem for the first time. A novel dispersion relation is derived for the two-plasmon decay in a uniform plasma valid under broad-bandwidth laser fields with arbitrary power spectra. The effects of temporal incoherence on the instability are then studied. In the limit of large bandwidth, the well-known scaling relations for the growth rate are recovered, but it is shown that the result is more sensitive to the spectral shape of the laser pulse rather than to its coherence time. The range of wavenumbers of the excited plasma waves is shown to be substantially broadened, suggesting that the absolute instability is favoured in regions further away from the quarter critical density. The intermediate-bandwidth regime is explored numerically – the growth rate is reduced to half its monochromatic value for laser intensities of 10^{15} \ \text {W}\ \text {cm}^{-2}$10^{15} \ \text {W}\ \text {cm}^{-2}$ and relatively modest bandwidths of 5 \ \text {THz}$5 \ \text {THz}$. The instability-quenching properties of a spectrum of discrete lines spread over some bandwidth have also been studied. The reduction in the growth rate is found to be somewhat lower compared with the continuous case but is still significant, despite the fact that, formally, the coherence time of such a laser pulse is infinite.