This work tackles a significant challenge in dynamo theory: the possibility of long-term amplification and maintenance of an axisymmetric magnetic field. We introduce a novel model that allows for non-trivial axially symmetric steady-state solutions for the magnetic field, particularly when the dynamo operates primarily within a ‘nearly spherical’ toroidal volume inside a fluid shell surrounding a solid core. In this model, Ohm’s law is generalised to include the dissipative force, arising from electron collisions, that tends to align the velocity of the shell with the rotational speed of the inner core and outer mantle. Our findings reveal that, in this context, Cowling’s theorem and the neutral point argument are modified, leading to magnetic energy growth for a suitable choice of toroidal flow. The global equilibrium magnetic field that emerges from our model exhibits a dipolar character. The central insight of the model developed here is that if an additional force is incorporated into Ohm’s law, symmetric dynamos become possible.

Insight into plasma dynamics under usual pulsed laser deposition (PLD) conditions for NiO thin film growth is provided by implementing angle- and time-resolved Langmuir probe (LP) methods. The selective separation generated an acceleration region that separates ions based on nature and ionisation state. A maximum of the kinetic energy for most plasma components was found for 0.5–2 Pa Ar, while the time-resolved analysis revealed a multipeak evolution of the electron temperature, which widened and shifted with increasing pressure. Evidence of two temperature structures for NiO plasma is presented, and the estimation of the accelerating field generated between the two plasma structures reveals selective in acceleration in the first microsecond. The acceleration field has a maximum value for the O2 atmosphere at approximately 2 Pa, which shows the separation between drift-dominated kinetics and reaction-based dynamics. Further investigation in this 2 Pa region revealed the appearance of a perturbation consistent with the formation of a plasma fireball on the probe. The dynamics of these perturbations is affected by the nature of the gas having different incubation times.

For small-shear helical-axis stellarators, linear ideal-magnetohydrodynamic (MHD) stability calculations and full-torus, nonlinear, electromagnetic gyrokinetic (GK) simulations (the latter with this unprecedented combination of objectives in stellarator GKs) in their linear phase are shown to yield well agreeing spatio-temporal structures of unstable, globally extended perturbations. Likewise, good agreement is found for their dependence on the plasma pressure and the vacuum-field magnetic well in plasma equilibria with identical gradient lengths of the temperature and density profiles. In the nonlinear phase, these perturbations with MHD signatures entail deformations of the magnetic surfaces, growing magnetic islands which rotate in the electron diamagnetic direction and, eventually, lead to ergodisation of a larger part of the magnetic surfaces.

In this work, we present a detailed assessment of fusion-born alpha-particle confinement, their wall loads and stability of Alfvén eigenmodes driven by these energetic particles in the Infinity Two Fusion Pilot Plant baseline plasma design, a four-field-period quasi-isodynamic stellarator to operate in deuterium–tritium fusion conditions. Using the Monte Carlo codes, SIMPLE, ASCOT5 and KORC-T, we study the collisionless and collisional dynamics of guiding-centre and full-orbit alpha-particles in the core plasma. We find that core energy losses to the wall are less than 4 %. Our simulations shows that peak power loads on the wall of this configuration are approximately 2.5 MW m-$^2$ and are spatially localised, toroidally and poloidaly, in the vicinity of x-points of the magnetic island chain $n/m = 4/5$ outside the plasma volume. Also, an exploratory analysis using various simplified walls shows that shaping and distance of the wall from the plasma volume can help reduce peak power loads. Our stability assessment of Alfvén eigenmodes using the STELLGAP and FAR3d codes shows the absence of unstable modes driven by alpha-particles in Infinity Two due to the relatively low alpha-particle beta at the envisioned 800 MW operating scenario.

Curvature-driven instabilities are ubiquitous in magnetised fusion plasmas. By analysing the conservation laws of the gyrokinetic system of equations, we demonstrate that the well-known spatial localisation of these instabilities to regions of ‘bad magnetic curvature’ can be explained using the conservation law for a sign-indefinite quadratic quantity that we call the gyrokinetic field invariant. Its evolution equation allows us to define the local effective magnetic curvature whose sign demarcates the regions of ‘good’ and ‘bad’ curvature, which, under some additional simplifying assumptions, can be shown to correspond to the inboard (high-field) and outboard (low-field) sides of a tokamak plasma, respectively. We find that, given some reasonable assumptions, electrostatic curvature-driven modes are always localised to the regions of bad magnetic curvature, regardless of the specific character of the instability. More importantly, we also deduce that any mode that is unstable in the region of good magnetic curvature must be electromagnetic in nature. As a concrete example, we present the magnetic-drift mode, a novel good-curvature electromagnetic instability, and compare its properties with the well-known electron-temperature-gradient instability. Finally, we discuss the relevance of the magnetic drift mode for high-$\beta$ fusion plasmas, and in particular its relationship with microtearing modes.

Standard approaches to neoclassical theory do not extend into regions of strong gradients in tokamaks such as the pedestal and internal transport barriers. Here, we calculate the modifications to neoclassical electron physics inside strong gradient regions of large aspect ratio tokamaks in the banana regime. We show that these modifications are due to the different ion flow and the strong poloidal variation of the potential. We also provide a physical interpretation of the mechanisms that drive poloidal asymmetries and hence a poloidal electric field. We apply our model to two specific example cases of pedestal profiles, calculating the neoclassical electron flux and the bootstrap current. We find that, depending on the ion flow, weak gradient neoclassical theory overestimates or underestimates the neoclassical electron transport and the bootstrap current in regions with strong gradients. We show that the determination of the mean parallel flow is more complex than in weak gradient neoclassical theory. For vanishing turbulence, we can determine the radial electric field for a given flow profile in the pedestal.

This study reports on a set of experiments designed to clarify the impact of the rotational transform on confinement quality at the TJ-II stellarator. For this purpose, the net plasma current is controlled using external coils, resulting in the modification of the rotational transform profile. Significant and systematic variations of the edge electron density gradients (up to $50\,\%{-}60\,\%$) and the plasma energy content ($20\,\%{-}30\,\%$) are achieved. The explanation of this behaviour relies on the placement of low-order rational surfaces in relation to the edge gradient region, which affect local turbulence fluctuation levels, facilitating the formation of zonal flows and concomitant transport barriers. This hypothesis is confirmed experimentally on the basis of a broad array of diagnostic measurements. Calculations based on a resistive magnetohydrodynamic turbulence model provide qualitative support for this hypothesis, clarifying the impact on confinement of specific rational surfaces and highlighting the complex nature of magnetically confined fusion plasmas.

Magnetic reconnection, a fundamental plasma process, is pivotal in understanding energy conversion and particle acceleration in astrophysical systems. While extensively studied in two-dimensional (2-D) configurations, the dynamics of reconnection in three-dimensional (3-D) systems remains under-explored. In this work, we extend the classical tearing mode instability to three dimensions by introducing a modulation along the otherwise uniform direction in a 2-D equilibrium, given by $g(y)$, mimicking a flux-tube-like configuration. We perform linear stability analysis (both analytically and numerically) and direct numerical simulations to investigate the effects of three-dimensionality. Remarkably, we find that a tearing-like instability arises in three dimensions as well, even without the presence of guide fields. Further, our findings reveal that the 3-D tearing instability exhibits reduced growth rates compared with two dimensions by a factor of $\int g(y)^{1/2} {\rm d}y\,/\int {\rm d}y$, with the dispersion relation maintaining similar scaling characteristics. We show that the modulation introduces spatially varying resistive layer properties, which influence the reconnection dynamics.

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.

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.

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.

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.

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.

Electron-only reconnection (E-REC) is a process recently observed in the Earth’s magnetosheath, where magnetic reconnection occurs at electron kinetic scales, and ions do not couple to the reconnection process. Electron-only reconnection is likely to have a significant impact on the energy conversion and dissipation of turbulence cascades at kinetic scales in some settings. This paper investigates E-REC under different intensities of strong guide fields (the ratio between the guide field and the in-plane asymptotic field strength is 5, 10 and 20, respectively) via two-dimensional fully kinetic particle-in-cell simulations, focusing on electron heating. The simulations are initialized with a force-free current sheet equilibrium under various intensities of strong guide fields. Similarly to previous experimental studies, electron temperature anisotropy along separatrices is observed, which is found to be mainly caused by the variations of parallel temperature. Both regions of anisotropy and parallel temperature increase/decrease along separatrices become thinner with increasing guide fields. Besides, we find a transition from a quadrupolar to a hexapolar (six-polar) to an octopolar (eight-polar) structure in temperature anisotropy and parallel temperature as the guide field intensifies. Non-Maxwellian electron velocity distribution functions (EVDFs) at different locations in the three simulations are observed. Our results show that parallel electron velocity varies notably with different guide field intensities and finite parallel electron heat flux density is observed. The three simulations exhibit features of the Chew–Goldberger–Low theory, with the level of consistency increasing as the guide field strength increases. This explains the electron parallel temperature variations and the shape of the EVDFs observed along the separatrices. This work may provide insights into the understanding of electron heating and parallel heat flux density in E-REC observed in the turbulent magnetosheath.

Collisionless shocks are frequently analysed using the magnetohydrodynamic (MHD) formalism, even though the required collisionality hypothesis is not fulfilled. In a previous work (Bret & Narayan, 2018 J. Plasma Phys. vol. 84, p. 905840604), we presented a model of collisionless shock displaying an important departure from the expected MHD behaviour, in the case of a strong flow aligned magnetic field. This model was non-relativistic. Here, it is extended to the relativistic regime, considering zero upstream pressure and upstream Lorentz factor $\gg 1$. The result agrees satisfactorily with Particle-in-Cell simulations and shows a similar, and important, departure from the MHD prediction. In the strong field regime, the density jump $r$, seen in the downstream frame, behaves like $r \sim 2 + 1/\gamma _{\mathrm{up}}$, while MHD predicts 4 ($\gamma _{\mathrm{up}}$ is the Lorentz factor of the upstream measured in the downstream frame). Only pair plasmas are considered.

We have investigated the modified Jeans instability and gravitational collapse in uniformly rotating, anisotropic quantum plasmas, including the effects of intrinsic magnetisation, viscosity tensor and Ohmic diffusivity. The closure of the Chew, Goldberger and Low and quantum magnetohydrodynamic fluid models describes the dynamical properties and modified dispersion characteristics of the system. The modified Jeans instability criteria and Jeans wavenumbers for the onset conditions of gravitational collapse are obtained, which are significantly modified due to spin magnetisation, quantum corrections and rotation of the system. Strong magnetisation and electrical resistivity are found to enhance the growth rate of Jeans instability, making the system more gravitationally unstable. The magnetic field shows both stabilising (in weak magnetisation limit) and destabilising (in strong magnetisation limit) influence on the growth rate by affecting the gravitational collapse mechanism of dense stars. The growth rate of pressure-anisotropy-driven firehose instability is destabilised due to pressure anisotropy, rotation and spin magnetisation effects. The results are discussed in order to understand the Jeans instability and gravitational collapse of low-mass strongly magnetised white dwarfs.

A theoretical investigation on the space–time evolution of low-frequency dust acoustic waves (DAWs) in opposite polarity dusty plasmas reveals that they undergo phase mixing for arbitrary initial amplitudes, causing them to suffer a gradual loss in coherency. Both positively and negatively charged dynamical dust grains have been considered to coexist in the plasma, in addition to Maxwell–Boltzmann distributed hot electrons and ions. A perturbative analysis of the governing fluid-Maxwell equations leads us to conclude that the competing dynamics of the opposite polarity dust grains is what causes the DAWs to phase mix. An estimate for the phase-mixing time has also been obtained, which has been found to be profoundly influenced by the values of the various plasma parameters, such as the equilibrium densities of the plasma species, the masses of the opposite polarity dust grains and the electron and ion temperatures. The investigation has also been extended to include phase mixing of DAWs in electron-depleted dusty plasmas. The findings of this study are expected to have relevance in various astrophysical and laboratory plasma environments.

The heating effect of electromagnetic waves in ion cyclotron range of frequencies (ICRFs) in magnetic confinement fusion device is different in different plasma conditions. In order to evaluate the ICRF heating effect in different plasma conditions, we conducted a series of experiments and corresponding TRANSP simulations on the EAST tokamak. Both simulation and experimental results show that the effect of ICRF heating is poor at low core electron density. The decrease in electron density changes the left-handed electric field near the resonant layer, resulting in a significant decrease in the power absorbed by the hydrogen fundamental resonance. However, quite a few experiments must be performed in plasma conditions with low electron density. It is necessary to study how to make ICRF heating best in low electron density plasma. Through a series of simulation scans of the parallel refractive index (n//) of the ICRF antenna, it is concluded that the change of the ICRF antenna n// will lead to the change of the left-handed electric field, which will change the fundamental absorption of ICRF power by the hydrogen minority ions. Fully considering the coupling of ion cyclotron wave at the tokamak boundary and the absorption in the plasma core, optimizing the ICRF antenna structure and selecting appropriate parameters such as parallel refractive index, minority ion concentration, resonance layer position, plasma current and core electron temperature can ensure better heating effect in the ICRF heating experiments in the future EAST upgrade. These results have important implications for the enhancement of the auxiliary heating effect of EAST and other tokamaks.

This paper presents a Hammir tandem mirror confinement performance analysis based on Realta Fusion’s first-of-a-kind model for axisymmetric magnetic mirror fusion performance. This model uses an integrated end plug simulation model including, heating, equilibrium and transport combined with a new formulation of the plasma operation contours (POPCONs) technique for the tandem mirror central cell. Using this model in concert with machine learning optimization techniques, it is shown that an end plug utilizing high temperature superconducting magnets and modern neutral beams enables a classical tandem mirror pilot plant producing a fusion gain Q > 5. The approach here represents an important advance in tandem mirror design. The high-fidelity end plug model enables calculations of heating and transport in the highly non-Maxwellian end plug to be made more accurately. The detailed end plug modelling performed in this work has highlighted the importance of classical radial transport and neutral beam absorption efficiency on end plug viability. The central cell POPCON technique allows consideration of a wide range of parameters in the relatively simple near-Maxwellian central cell, facilitating the selection of more optimal central cell plasmas. These advances make it possible to find more conservative classical tandem mirror fusion pilot plant operating points with lower temperatures, neutral beam energies and end plug performance requirements than designs in the literature. Despite being more conservative, it is shown that these operating points have sufficient confinement performance to serve as the basis of a viable fusion pilot plant provided that they can be stabilized against magnetohydrodynamic and trapped particle modes.

Presented here is a novel formulation of the mean-field dynamo as a modulational instability of magnetohydrodynamic (MHD) turbulence. This formulation, termed mean-field wave kinetics (MFWK), is based on the Weyl symbol calculus and allows describing the interaction between the mean fields (magnetic field and fluid velocity) and turbulence without requiring scale separation that is commonly assumed in the literature. The turbulence is described by the Wigner–Moyal equation for the spectrum of the two-point correlation matrix (Wigner matrix) of magnetic-field and velocity fluctuations and depicts the turbulence as an effective plasma of quantum-like particles that interact via the mean fields. Eddy–eddy interactions, which serve as ‘collisions’ in this effective plasma, are modelled within the standard minimal tau approximation to aid comparison with existing theories. Using MFWK, the non-local electromotive force is calculated for generic turbulence from first principles, modulo the limitations of MFWK. This result is then used to study, both analytically and numerically, the modulational modes of MHD turbulence, which appear as linear instabilities of the said effective quantum-like plasma of fluctuations. The standard $\alpha ^2$-dynamo and other known results are reproduced as special cases. A new dynamo effect is predicted that is driven by correlations between the turbulent flow velocity and the turbulent current.