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.

Accurate reduced models of turbulence are desirable to facilitate the optimisation of magnetic-confinement fusion reactor designs. As a first step towards higher-dimensional turbulence applications, we use reservoir computing, a machine-learning (ML) architecture, to develop a closure model for a limiting case of electrostatic gyrokinetics. We implement a pseudo-spectral Eulerian code to solve the one-dimensional Vlasov–Poisson system on a basis of Fourier modes in configuration space and Hermite polynomials in velocity space. When cast onto the Hermite basis, the Vlasov equation becomes an infinitely coupled hierarchy of fluid moments, presenting a closure problem. We exploit the locality of interactions in the Hermite representation to introduce an ML closure model of the small-scale dynamics in velocity space. In the linear limit, when the kinetic Fourier–Hermite solver is augmented with the reservoir closure, the closure permits a reduction of the velocity resolution, with a relative error within 2 % for the Hermite moment where the reservoir closes the hierarchy. In the strongly nonlinear regime, the ML closure model more accurately resolves the low-order Fourier and Hermite spectra when compared with a naive closure by truncation and reduces the required velocity resolution by a factor of 16.

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.

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.

The kinetic stability of collisionless, sloshing beam-ion ($45^\circ$ pitch angle) plasma is studied in a three-dimensional (3-D) simple magnetic mirror, mimicking the Wisconsin high-temperature superconductor axisymmetric mirror experiment. The collisional Fokker–Planck code CQL3D-m provides a slowing-down beam-ion distribution to initialize the kinetic-ion/fluid-electron code Hybrid-VPIC, which then simulates free plasma decay without external heating or fuelling. Over $1$–$10\;\mathrm{\unicode{x03BC} s}$, drift-cyclotron loss-cone (DCLC) modes grow and saturate in amplitude. The DCLC scatters ions to a marginally stable distribution with gas-dynamic rather than classical-mirror confinement. Sloshing ions can trap cool (low-energy) ions in an electrostatic potential well to stabilize DCLC, but DCLC itself does not scatter sloshing beam-ions into the said well. Instead, cool ions must come from external sources such as charge-exchange collisions with a low-density neutral population. Manually adding cool $\mathord {\sim } 1\;\mathrm{keV}$ ions improves beam-ion confinement several-fold in Hybrid-VPIC simulations, which qualitatively corroborates prior measurements from real mirror devices with sloshing ions.

Using two counter-propagating ultra-intense laser interactions with a solid target, we conducted a study on the generation of electron-positron pairs via the multi-photon Breit–Wheeler (BW) process and trident process. These processes were simulated using the particle-in-cell (PIC) code EPOCH. Our proposed scheme involves irradiating two targets with two counter-propagating lasers. High-energy photons are produced when hot electrons collide with the reflected laser pulse at the target's front, leading to electron and positron pair production. In the single-target scenario, electron bunches are extracted from the target by the p-polarized laser electromagnetic field and accelerated by the laser ponderomotive force before colliding with the counter-propagating laser. However, using two targets enhances pair creation compared with the single-target set-up. We observed that in two-target configurations, the increased number of high-energy gamma-rays contributes to higher-energy electron–positron generation. Additionally, the generation of hot electrons is also more pronounced in this scheme. Consequently, the laser demonstrates higher efficiency in generating gamma photons and positrons in the dual-target set-up, which is beneficial for investigating high-energy pair production and gamma-ray emission. The generated positrons exhibit a density of the order of $10^{27}\,\text {m}^{-3}$ and can be accelerated to energies of 1.5 GeV. The involvement of hot electrons in the target is crucial for generating high-energy photons and positrons. The maximum pair yield reaches $8 \times 10^9$ for the BW process and $10^8$ for the trident process. Notably, the total laser energy conversion efficiencies to electrons, $\gamma$-rays and positrons show improvement in the dual-target configuration. Specifically, the laser energy absorbed by positrons increases from 11.62 % in Case A to 13.12 % in Case B. These enhancements in conversion efficiency and electron/positron density have significant practical implications in experimental set-ups. In both the BW and trident processes, the two-target set-up dominates, highlighting its effectiveness. We also compared the strengths of both approaches, suggesting that these simple models of implementing two targets can be used in experiments as well.

Bootstrap current plays a crucial role in the equilibrium of magnetically confined plasmas, particularly in quasi-symmetric stellarators and in tokamaks, where it can represent bulk of the electric current density. Accurate modeling of this current is essential for understanding the magnetohydrodynamic (MHD) equilibrium and stability of these configurations. This study expands the modeling capabilities of M3D-C1, an extended-MHD code, by implementing self-consistent physics models for bootstrap current. It employs two analytical frameworks: a generalized Sauter model (Sauter et al. 1999 Phys. Plasmas vol. 6, no. 7, pp. 2834–2839), and a revised Sauter-like model (Redl et al. 2021 Phys. Plasmas vol. 28, no. 2, pp. 022502). The isomorphism described by Landreman et al. (2022 Phys. Rev. Lett. vol. 128, pp. 035001) is employed to apply these models to quasi-symmetric stellarators. The implementation in M3D-C1 is benchmarked against neoclassical codes, including NEO, XGCa and SFINCS, showing excellent agreement. These improvements allow M3D-C1 to self-consistently calculate the neoclassical contributions to plasma current in axisymmetric and quasi-symmetric configurations, providing a more accurate representation of the plasma behavior in these configurations. A workflow for evaluating the neoclassical transport using SFINCS with arbitrary toroidal equilibria calculated using M3D-C1 is also presented. This workflow enables a quantitative evaluation of the error in the Sauter-like model in cases that deviate from axi- or quasi-symmetry (e.g. through the development of an MHD instability).

The linear theory of the kinetic-ballooning-mode (KBM) instability is extended to capture a weakly driven regime in general toroidal geometry where the destabilization is caused by the magnetic-drift resonance of the ions. Such resonantly destabilized KBMs are characterized by broad eigenfunctions along the magnetic-field line and near-marginal positive growth rates, even well below the normalized-plasma-pressure ($\beta$) threshold of their non-resonant counterparts. This unconventional (or sub-threshold) KBM (stKBM), when destabilized, has been shown to catalyze an enhancement of turbulent transport in the Wendelstein 7-X (W7-X) stellarator (Mulholland et al. 2023 Phys. Rev. Lett. vol. 131, 185101; 2025 Nucl. Fusion vol. 65, 016022). Simplifying the energy dependence of key resonant quantities allows for an analytical treatment of this KBM using the physics-based ordering from the more general equations of Tang et al. (1980 Nucl. Fusion vol. 20, 1439). Results are then compared with high-fidelity gyrokinetic simulations for the (st)KBM in W7-X and the conventional KBM in a circular tokamak at both high and low magnetic shear, where good agreement is obtained in all cases. This reduced KBM model provides deeper insight into (sub-threshold) KBMs and their relationship with geometry, and shows promise for aiding in transport model development and geometry-based turbulence optimization efforts going forward.

We develop a phenomenological model of strong imbalanced magnetohydrodynamic (MHD) turbulence that accounts for intermittency and the reflection of Alfvén waves by spatial variations in the Alfvén speed. Our model predicts the slopes of the inertial-range Elsasser power spectra, the scaling exponents of the higher-order Elsasser structure functions and the way in which the parallel (to the magnetic field) length scale of the fluctuations varies with the perpendicular length scale. These predictions agree reasonably well with measurements of solar-wind turbulence from the Parker Solar Probe (PSP). In contrast to previous models of intermittency in balanced MHD turbulence, we find that intermittency in reflection-driven MHD turbulence increases the parallel wavenumbers of the energetically dominant fluctuations at small perpendicular length scales. This, like the PSP measurements with which our model agrees, suggests that turbulence in the solar wind and solar corona may lead to more ion cyclotron heating than previously realized.

Starting from the assumption that saturation of plasma turbulence driven by temperature-gradient instabilities in fusion plasmas is achieved by a local energy cascade between a long-wavelength outer scale, where energy is injected into the fluctuations, and a small-wavelength dissipation scale, where fluctuation energy is thermalised by particle collisions, we formulate a detailed phenomenological theory for the influence of perpendicular flow shear on magnetised-plasma turbulence. Our theory introduces two distinct regimes, called the weak-shear and strong-shear regimes, each with its own set of scaling laws for the scale and amplitude of the fluctuations and for the level of turbulent heat transport. We discover that the ratio of the typical radial and poloidal wavenumbers of the fluctuations (i.e. their aspect ratio) at the outer scale plays a central role in determining the dependence of the turbulent transport on the imposed flow shear. Our theoretical predictions are found to be in excellent agreement with numerical simulations of two paradigmatic models of fusion-relevant plasma turbulence: (i) an electrostatic fluid model of slab electron-scale turbulence, and (ii) Cyclone-base-case gyrokinetic ion-scale turbulence. Additionally, our theory envisions a potential mechanism for the suppression of electron-scale turbulence by perpendicular ion-scale flows based on the role of the aforementioned aspect ratio of the electron-scale fluctuations.

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.

The selection, design and optimization of a suitable blanket configuration for an advanced high-field stellarator concept is seen as a key feasibility issue and has been incorporated as a vital and necessary part of the Infinity Two fusion pilot plant physics basis. The focus of this work was to identify a baseline blanket which can be rapidly deployed for Infinity Two while also maintaining flexibility and opportunities for higher performing concepts later in development. Results from this analysis indicate that gas-cooled solid breeder designs such as the helium-cooled pebble bed (HCPB) are the most promising concepts, primarily motivated by the neutronics performance at applicable blanket build depths, and the relatively mature technology basis. The lithium lead (PbLi) family of concepts, particularly the dual-cooled lithium lead, offer a compelling alternative to solid blanket concepts as they have synergistic developmental pathways while simultaneously mitigating much of the technical risk of those designs. Homogenized three-dimensional neutronics analysis of the Infinity Two configuration indicates that the HCPB achieves an adequate tritium breeding ratio (TBR) (1.30 which enables sufficient margin at low engineering fidelity), and near appropriate shielding of the magnets (average fast fluence of 1.3 ${\times}$ 10$^{18}$ n cm$^{-2}$ per full-power year). The thermal analysis indicates that reasonably high thermal efficiencies (greater than 30 %) are readily achievable with the HCPB paired with a simple Rankine cycle using reheat. Finally, the tritium fuel cycle analysis for Infinity Two shows viability, with anticipated operational inventories of less than one kilogram (approximately 675 g) and a required TBR (TBR$_{\textrm {req}}$) of less than 1.05 to maintain fuel self-sufficiency (approximately 1.023 for a driver blanket with no inventory doubling). Although further optimization and engineering design are still required, at the physics basis stage all initial targets have been met for the Infinity Two configuration.

We present the first experimental observations of the dust acoustic wave where the wave was observed to propagate in the directions of gravity and magnetic field when these directions were not aligned. The experiments were conducted in the Magnetized Dusty Plasma eXperiment facility using a novel electrode system that allows for the angle between gravity and the magnetic field to be varied in a controlled way. This letter reports on measurements in an rf glow discharge argon plasma environment where the angle between direction of gravity and the magnetic field is 45$^{\circ }$. When there was no applied magnetic field, the wave was observed to propagate in the direction of gravity. However, as the magnetic field increased and the ions transitioned from flowing in the direction of gravity to the direction of the magnetic field, a second wave emerged and two distinct waves were observed to simultaneously propagate, one in the direction of gravity and one in the direction of the magnetic field. As the magnetic field was further increased, the wave that propagated in the direction of gravity was suppressed and the wave was only observed to propagate in the direction of the applied magnetic field. We also observe that the speed and the kinetic temperature of the dust for the mode that propagated in the direction of gravity decreased with increasing magnetic field while the speed and the kinetic temperature of the dust for the mode that propagated in the direction of the magnetic field increased with increasing magnetic field. These measurements suggest that an ion-dust streaming instability is at least partially responsible for the high temperatures that have previously been observed in dusty plasmas when the dust acoustic wave is present.

In plasmas and in astrophysical systems, particle diffusion faster than normal, namely superdiffusion, has been detected, calling for a generalisation of Fick’s law and of the transport equation. Formally, superdiffusive transport is often described by fractional diffusion equations, where the second-order spatial derivative is changed into a spatial derivative of fractional order less than two, usually in the form of the so-called Riesz derivative. Fractional operators are non-local, so that this involves the contribution of very distant points (far from the particle source) to the particle flux at a given position in the system. To consider the property of non-locality in the case of anomalous transport, we give a simple analytical derivation of the fractional Fick’s law, where the contribution to the flux of distant points is weighted by an inverse power law, and show that this is consistent with use of the Riesz derivative in the transport equation. A numerical procedure for the computation of the non-local flux is presented and applied to both a simple Gaussian density profile and also to density profiles coming from test particle simulations of one-dimensional collisionless shocks. In these simulations, energetic particles can move diffusively or superdiffusively. The latter case naturally gives rise to the emergence of uphill transport in the downstream region, which means a flux of particles in the same direction of the density gradient. This analysis contributes to the interpretation of energetic particle fluxes accelerated at collisionless shock waves in the interplanetary medium.

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.

Presented here is a transcription of the lecture notes from Professor Allan N. Kaufman’s graduate statistical mechanics course Physics 212A and 212B at the University of California Berkeley from the 1972–1973 academic year. 212A addressed equilibrium statistical mechanics with topics: fundamentals (micro-canonical and sub-canonical ensembles, adiabatic law and action conservation, fluctuations, pressure, and virial theorem), classical fluids and other systems (equation of state, deviations from ideality, virial coefficients and van der Waals potential, canonical ensemble and partition function, quasistatic evolution, grand-canonical ensemble and partition function, chemical potential, simple model of a phase transition, quantum virial expansion, numerical simulation of equations of state, and phase transition), chemical equilibrium (systems with multiple species and chemical reactions, law of mass action, Saha equation, chemical equilibrium including ionization and excited states), and long-range interactions (including Coulomb, dipole, and gravitational interactions, Debye–Hückel theory, and shielding). 212B addressed nonequilibrium statistical mechanics with topics: fundamentals (definitions: realizations, moments, characteristic function, and discrete variables), Brownian motion (Langevin equation, fluctuation–dissipation theorem, spatial diffusion, Boltzmann’s H-theorem), Liouville and Klimontovich equations, Landau equation (derivation, elaboration, and H-theorem, and irreversibility), Markov processes and Fokker–Planck equation (derivations of the Fokker–Planck equation and a master equation), linear response and transport theory (linear Boltzmann equation, linear response theory of Kubo and Mori, relation of entropy production to electrical conductivity, transport relations and coefficients, normal mode solutions of the transport equations, sketch of a generalized Langevin equation method for transport theory), and an introduction to nonequilibrium quantum statistical mechanics.

The near-axis description of optimised stellarators, at second order in the expansion, provides important information about the field, both of physical and practical importance for stellarator optimisation. It, however, remains relatively underdeveloped for an important class of such stellarators, called quasi-isodynamic (QI). In this paper we develop the theoretical and numerical framework, applying the second-order omnigeneity conditions derived in Rodríguez & Plunk (2023), to make explicit construction of equilibrium solutions. We find that the case of QI stellarators calls for the careful treatment of continuity, smoothness and periodicity of the various functions involved, especially for so-called half-helicity fields, which feature prominently in existing QI designs. The numerical implementation of necessary elements is described, and several examples are constructed and quantitatively verified in detail. This work establishes a basis for further systematic exploration of the space of QI stellarators, and the development of both theoretical and practical tools to facilitate effective optimisation of QI stellarators.