Near-future experiments with Petawatt class lasers are expected to produce a high flux of gamma-ray photons and electron–positron pairs through strong field quantum electrodynamical processes. Simulations of the expected regime of laser–matter interaction are computationally intensive due to the disparity of the spatial and temporal scales, and because quantum and classical descriptions need to be accounted for simultaneously (classical for collective effects and quantum for nearly instantaneous events of hard photon emission and pair creation). We study the stochastic cooling of an electron beam in a strong, constant, uniform magnetic field, both its particle distribution functions and their energy momenta. We start by obtaining approximate closed-form analytical solutions to the relevant observables. Then, we apply the quantum-hybrid variational quantum imaginary time evolution to the Fokker–Planck equation describing this process and compare it against theory and results from particle-in-cell simulations and classical partial differential equation solvers, showing good agreement. This work will be useful as a first step towards quantum simulation of plasma physics scenarios where diffusion processes are important, particularly in strong electromagnetic fields.

From the near-Earth solar wind to the intracluster medium of galaxy clusters, collisionless, high-beta, magnetized plasmas pervade our universe. Energy and momentum transport from large-scale fields and flows to small-scale motions of plasma particles is ubiquitous in these systems, but a full picture of the underlying physical mechanisms remains elusive. The transfer is often mediated by a turbulent cascade of Alfvénic fluctuations as well as a variety of kinetic instabilities; these processes tend to be multi-scale and/or multi-dimensional, which makes them difficult to study using spacecraft missions and numerical simulations alone. Meanwhile, existing laboratory devices struggle to produce the collisionless, high ion beta ($\beta _i \gtrsim 1$), magnetized plasmas across the range of scales necessary to address these problems. As envisioned in recent community planning documents, it is therefore important to build a next generation laboratory facility to create a $\beta _i \gtrsim 1$, collisionless, magnetized plasma in the laboratory for the first time. A working group has been formed and is actively defining the necessary technical requirements to move the facility towards a construction-ready state. Recent progress includes the development of target parameters and diagnostic requirements as well as the identification of a need for source-target device geometry. As the working group is already leading to new synergies across the community, we anticipate a broad community of users funded by a variety of federal agencies (including National Aeronautics and Space Administration, Department of Energy and National Science Foundation) to make copious use of the future facility.

Magnetic geometry has a significant effect on the level of turbulent transport in fusion plasmas. Here, we model and analyse this dependence using multiple machine learning methods and a dataset of ${\gt}200\,000$ nonlinear gyrokinetic simulations of ion-temperature-gradient turbulence in diverse non-axisymmetric geometries. The dataset is generated using a large collection of both optimised and randomly generated stellarator equilibria. At fixed gradients and other input parameters, the turbulent heat flux varies between geometries by several orders of magnitude. Trends are apparent among the configurations with particularly high or particularly low heat flux. Regression and classification techniques from machine learning are then applied to extract patterns in the dataset. Due to a symmetry of the gyrokinetic equation, the heat flux and regressions thereof should be invariant to translations of the raw features in the parallel coordinate, similar to translation invariance in computer vision applications. Multiple regression models including convolutional neural networks (CNNs) and decision trees can achieve reasonable predictive power for the heat flux in held-out test configurations, with highest accuracy for the CNNs. Using Spearman correlation, sequential feature selection and Shapley values to measure feature importance, it is consistently found that the most important geometric lever on the heat flux is the flux surface compression in regions of bad curvature. The second most important geometric feature relates to the magnitude of geodesic curvature. These two features align remarkably with surrogates that have been proposed based on theory, while the methods here allow a natural extension to more features for increased accuracy. The dataset, released with this publication, may also be used to test other proposed surrogates, and we find that many previously published proxies do correlate well with both the heat flux and stability boundary.

Mercier’s criterion is typically enforced as a hard operational limit in stellarator design. At the same time, past experimental and numerical studies have shown that this limit may often be surpassed, though the exact mechanism behind this nonlinear stability is not well understood. This work aims to contribute to our current understanding by comparing the nonlinear evolution of Mercier unstable Wendelstein stellarators with that of nonlinearly stable quasi-interchange modes in tokamaks. A high mirror, very low $\iota$, W7-X-like configuration is first simulated. Broad flow structures are observed, which produce a similar magnetohydrodynamic (MHD) dynamo term to that in hybrid tokamak discharges, leading to flux pumping. Unlike in tokamaks, there is no net toroidal current to counterbalance this dynamo, and it is unclear if it can be sustained to obtain a similar quasistationary nonlinear state. In the simulation, partial reconnection induced by the overlap of multiple interchange instabilities leads to a core temperature crash. A second case is then considered using experimental reconstructions of intermediate $\beta$ W7-AS discharges, where saturated low-n modes were observed experimentally, with sustained MHD signatures over tens of milliseconds. It is shown that these modes do not saturate in a benign quasistationary way in current simulations even in the presence of background equilibrium $\boldsymbol{E} \times \boldsymbol{B}$ flow shear. This leads to a burst of MHD behaviour, inconsistent with the sustained MHD signatures in the experiment. Nevertheless, the (1, 2) mode is observed at the experimental Spitzer resistivity, and its induced anomalous transport can be overcome using an experimentally relevant heat source, reproducing these aspects of the dynamics. The possible reasons for the discrepancies between experiment and simulation, and the observation of partial reconnection in contrast to flux pumping are discussed, in view of reproducing and designing for operation of stellarators beyond the Mercier stability limit.

The generation and radial structure of zonal flows are studied in competing collisional drift waves and interchange turbulence using the reduced flux-driven nonlinear model Tokam1D. Zonal flows are generated in both the interchange dominated and adiabatic regimes with the former favoring radially structured flows and avalanche transport. The distance to the instability threshold proves to be key, with a more stable radial flow structure emerging near the threshold and increased energy stored in the flows for interchange turbulence. The avalanches are shown to perturb zonal flow structures in drift-wave turbulence and to reactivate them in the interchange regime. Finally, the ExB staircases with radially structured, stable in time zonal flows are proved beneficial for the overall confinement.

Ion-acoustic waves in a dusty plasma are investigated where it is assumed that the ions follow a Cairns distribution and the electrons are Boltzmann distributed. Two theoretical methods are applied: Sagdeev pseudopotential analysis (SPA) and reductive perturbation theory (RPT). Since SPA incorporates all nonlinearities of the model it is the most accurate but deriving soliton profiles requires numerical integration of Poisson’s equation. By contrast, RPT is a perturbation method which at second order yields the Gardner equation incorporating both the quadratic nonlinearity of the Korteweg–de Vries (KdV) equation and the cubic nonlinearity of the modified KdV equation. For consistency with the perturbation scheme the coefficient of the quadratic term needs to be at least an order of magnitude smaller than the coefficient of the cubic term. Solving the Gardner equation yields an analytic expression of the soliton profile. Selecting an appropriate set of compositional parameters, the soliton solutions obtained from SPA and RPT are analysed and compared.

The Vlasov–Maxwell equations provide kinetic simulations of collisionless plasmas, but numerically solving them on classical computers is often impractical. This is due to the computational resource constraints imposed by the time evolution in the six-dimensional phase space, which requires broad spatial and temporal scales. The novelty of this study is to implement a quantum–classical hybrid Vlasov–Maxwell solver and the rigorous numerical scheme evaluation by numerical simulations. Specifically, the Vlasov solver implements the Hamiltonian simulation based on quantum singular value transformation, coupled with a classical Maxwell solver. We perform numerical simulation of a one-dimensional advection test and a one-spatial-dimension, one-velocity-dimension two-stream instability test on the Qiskit-Aer-GPU quantum circuit emulator with an A100 GPU. The computational complexity of our quantum algorithm can potentially be reduced from the classical $\mathcal{O}(N^6T^2/\epsilon )$ to $\mathcal{O}\left (\text{poly}(\log {N})\left (NT+T\log \left (T/\epsilon \right )\right )\right )$ for the $N$ grid system, simulation time $T$ and error tolerance $\epsilon$ in the limit where the number of queries is large enough and the error is small enough. Furthermore, the numerical analysis reveals that our quantum algorithm is robust under larger time steps compared with classical algorithms with the constraint of Courant–Friedrichs–Lewy condition.

The work presented here revisits the Velikhov-ionisation instability, an instability first discovered in the early 1960s (Velikhov, E. P. 1962 1st International Conference on MHD Electrical Power Generation, Newcastle upon Tyne, England, p. 135). This mode strongly deteriorates the performance of magnetohydrodynamic (MHD) energy convertors in which the seed gas must be at a substantially higher temperature than the high density primary gas, the latter gas carrying almost all the energy. Specifically, a finite temperature difference is necessary for the MHD generator to successfully act as a topping cycle for nuclear (fission and fusion) power plants. The ionisation instability has thus been viewed for many years as a show stopper for MHD nuclear topping cycles. Even so, some experimental observations, never fully exploited, show that nearly full ionisation of the seed gas can stabilise this dangerous instability. One goal of the research presented here is to provide a first-principles theoretical explanation for these experimental observations. The stabilisation can theoretically produce high temperature ratios, of the order of 10, by carefully choosing the density of the unionised seed gas. A second goal of the research is to investigate whether or not the recent development of high-field, high-temperature REBCO (rare-earth barium copper oxide) superconductors can lead to substantially improved power plant efficiency. Here, it is shown that the answer is subtle – no clear conclusions can be drawn, a consequence of the fact that the new stability criterion is a local one. What is needed to assess overall plant efficiency is a global analysis. Additional work has recently been completed on a newly developed global model which answers this question and will be reported on in a future paper.

Next-generation X-ray satellite telescopes such as XRISM, NewAthena and Lynx will enable observations of exotic astrophysical sources at unprecedented spectral and spatial resolution. Proper interpretation of these data demands that the accuracy of the models is at least within the uncertainty of the observations. One set of quantities that might not currently meet this requirement is transition energies of various astrophysically relevant ions. Current databases are populated with many untested theoretical calculations. Accurate laboratory benchmarks are required to better understand the coming data. We obtained laboratory spectra of X-ray lines from a silicon plasma at an average spectral resolving power of $\sim$7500 with a spherically bent crystal spectrometer on the Z facility at Sandia National Laboratories. Many of the lines in the data are measured here for the first time. We report measurements of 53 transitions originating from the K-shells of He-like to B-like silicon in the energy range between $\sim$1795 and 1880 eV (6.6–6.9 Å). The lines were identified by qualitative comparison against a full synthetic spectrum calculated with ATOMIC. The average fractional uncertainty (uncertainty/energy) for all reported lines is ${\sim}5.4 \times 10^{-5}$. We compare the measured quantities against transition energies calculated with RATS and FAC as well as those reported in the NIST ASD and XSTAR’s uaDB. Average absolute differences relative to experimentally measured values are 0.20, 0.32, 0.17 and 0.38 eV, respectively. All calculations/databases show good agreement with the experimental values; NIST ASD shows the closest match overall.

Powerful lasers may be used in the future to produce magnetic fields that would allow us to study turbulent magnetohydrodynamic inverse cascade behaviour. This has so far only been seen in numerical simulations. In the laboratory, however, the produced fields may be highly anisotropic. Here, we present corresponding simulations to show that, during the turbulent decay, such a magnetic field undergoes spontaneous isotropisation. As a consequence, we find the decay dynamics to be similar to that in isotropic turbulence. We also find that an initially pointwise non-helical magnetic field is unstable and develops magnetic helicity fluctuations that can be quantified by the Hosking integral. It is a conserved quantity that characterises magnetic helicity fluctuations and governs the turbulent decay when the mean magnetic helicity vanishes. As in earlier work, the ratio of the magnetic decay time to the Alfvén time is found to be approximately $50$ in the helical and non-helical cases. At intermediate times, the ratio can even reach a hundred. This ratio determines the endpoints of cosmological magnetic field evolution.

We present a number of measures and techniques to characterise and effectively construct quasi-isodynamic stellarators within the near-axis framework, without the need to resort to the computation of global equilibria. These include measures of the reliability of the model (including aspect-ratio limits and the appearance of ripple wells), quantification of omnigeneity through $\epsilon _{\mathrm{eff}}$, measure and construction of MHD-stabilised fields, and the sensitivity of the field to the pressure gradient. The paper presents, discusses and gives examples of all of these, for which expansions to second order are crucial. This opens the door to the exploration of how key underlying choices of the field design govern the interaction of desired properties (‘trade-offs’) and provides a practical toolkit to perform efficient optimisation directly within the space of near-axis quasi-isodynamic configurations.

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.

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.

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.

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.

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.

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.

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.

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.

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.