The relaxation of relativistic hot electron–positron plasma is investigated by incorporating the effect of non-zero photon mass, and a quadruple Beltrami (QB) relaxed state for the magnetic vector potential is derived. The QB state is a linear superposition of four single force-free fields and is characterized by four self-organized structures of different length scales. The analysis of QB states shows that for certain values of generalized helicities at lower relativistic temperatures, plasma shows diamagnetic behaviour. It is also noteworthy that the inclusion of non-zero photon mass naturally provides the possibility of multiscale structure formation in the relaxed state. In this scenario, one of the field structures is significantly larger than the Compton wavelength of photons, while the other three structures are on the scale of the electron skin depth. The potential implications of this QB state for astrophysical environments are also discussed.

In moderately coupled plasmas, a significant fraction of the internal energy resides in electric fields. As these plasmas are heated or compressed, the shifting partition of energy between particles and fields leads to surprising effects, particularly when ions and electrons have different temperatures. In this work, quasi-equations of state (quasi-EOS) are derived for two-temperature moderately coupled plasma in a thermodynamic framework and expressed in a simple form. These quasi-EOS readily yield expressions for correlation heating, in which heating of the electrons causes a rapid increase in ion temperature even in the absence of collisional energy exchange between species. It is also shown that, remarkably, compression of moderately coupled plasma drives a temperature difference between electrons and ions, even when the species start at equal temperatures. These additional channels for ion heating may be relevant in designing ignition schemes for inertial confinement fusion.

All-optical Compton sources combine laser-wakefield accelerators and intense scattering pulses to generate ultrashort bursts of backscattered radiation. The scattering pulse plays the role of a small-period undulator (${\sim }1\,\mathrm {\mu }{\rm m}$) in which relativistic electrons oscillate and emit X-ray radiation. To date, most of the working laser-plasma accelerators operate preferably at energies of a few hundreds of megaelectronvolts and the Compton sources developed so far produce radiation in the range from hundreds of kiloelectronvolts to a few megaelectronvolts. However, for such applications as medical imaging and tomography the relevant energy range is 10–100 keV. In this article, we discuss different scattering geometries for the generation of X-rays in this range. Through numerical simulations, we study the influence of electron beam parameters on the backscattered photons. We find that the spectral bandwidth remains constant for beams of the same emittance regardless of the scattering geometry. A shallow interaction angle of $30^{\circ }$ or less seems particularly promising for imaging applications given parameters of existing laser-plasma accelerators. Finally, we discuss the influence of the radiation properties for potential applications in medical imaging and non-destructive testing.

While it is important to design stellarators with high magnetohydrodynamic stability $\beta$-limit, it is also crucial to ensure that good magnetic surfaces exist in a large range of $\beta$ values. As $\beta$ increases, pressure-driven currents perturb the vacuum magnetic field and often lead to the emergence of magnetic field line chaos, which can worsen the confinement and is the cause of another kind of $\beta$-limit, the so-called equilibrium $\beta$-limit. In this paper, we explore numerically the dependence of the equilibrium $\beta$-limit on the bootstrap current strength in a classical stellarator geometry using the stepped pressure equilibrium code. We develop a diagnostic to determine whether or not magnetic islands are expected to participate significantly to radial transport, and we build an analytical model to predict the expected equilibrium $\beta$-limit, which recovers the main features of the numerical results. This research opens the possibility to include additional targets in stellarator optimization functions, provides additional understanding on the existence of magnetic surfaces at large $\beta$, and is a step forward in the understanding of the equilibrium $\beta$-limit.

The Wisconsin high-temperature superconductor axisymmetric mirror experiment (WHAM) will be a high-field platform for prototyping technologies, validating interchange stabilization techniques and benchmarking numerical code performance, enabling the next step up to reactor parameters. A detailed overview of the experimental apparatus and its various subsystems is presented. WHAM will use electron cyclotron heating to ionize and build a dense target plasma for neutral beam injection of fast ions, stabilized by edge-biased sheared flow. At 25 keV injection energies, charge exchange dominates over impact ionization and limits the effectiveness of neutral beam injection fuelling. This paper outlines an iterative technique for self-consistently predicting the neutral beam driven anisotropic ion distribution and its role in the finite beta equilibrium. Beginning with recent work by Egedal et al. (Nucl. Fusion, vol. 62, no. 12, 2022, p. 126053) on the WHAM geometry, we detail how the FIDASIM code is used to model the charge exchange sources and sinks in the distribution function, and both are combined with an anisotropic magnetohydrodynamic equilibrium solver method to self-consistently reach an equilibrium. We compare this with recent results using the CQL3D code adapted for the mirror geometry, which includes the high-harmonic fast wave heating of fast ions.

We show that the saturation of resistive tearing modes in a cylindrical tokamak, as well as the corresponding island width, can be directly calculated with a magnetohydrodynamics (MHD) equilibrium code without solving the dynamics and without considering resistivity. The results are compared with initial-value resistive MHD simulations and to an analytical nonlinear theory. For small enough islands, the agreement is remarkable. For sufficiently large islands, the equilibrium calculations, which assume a flat current profile inside the island, overestimate the saturation amplitude. On the other hand, excellent agreement between nonlinear resistive MHD simulations and nonlinear theory is observed for all the considered tearing unstable equilibria.

The structure of a collisionless shock affects ion motion in the shock front and is affected by the formed ion distribution. In high-Mach-number shocks, a significant fraction of incident ions are reflected by the macroscopic electric and magnetic fields in the shock front. Ions are non-specularly reflected by the combined electric deceleration and magnetic deflection. Here, a first analytical description of the non-specular reflection is presented. The contribution of the increasing magnetic field is evaluated and shown to enhance reflection. The distribution of non-specularly reflected ions ahead of the ramp is calculated and their velocities at the re-entry to the shock are found numerically. Dependence on the angle between the shock normal and the upstream magnetic field vector is illustrated.

We present a novel method for numerically finding quasi-isodynamic stellarator magnetic fields with excellent fast-particle confinement and extremely small neoclassical transport. The method works particularly well in configurations with only one field period. We examine the properties of these newfound quasi-isodynamic configurations, including their transport coefficients, particle confinement and available energy for trapped-electron-instability-driven turbulence, as well as the degree to which they change when a finite pressure profile is added. We finally discuss the differences between the magnetic axes of the optimized solutions and their respective initial conditions, and conclude with the prospects for future quasi-isodynamic optimization.

When a particle crosses a region of space where the curvature radius of the magnetic field line shrinks below its gyroradius $r_{g}$, it experiences a non-adiabatic (magnetic moment violating) change in pitch angle. The present paper carries that observation into magnetohydrodynamic (MHD) turbulence to examine the influence of intermittent, sharp bends of the magnetic field lines on particle transport. On the basis of dedicated measurements in a simulation of incompressible turbulence, it is argued that regions of sufficiently large curvature exist in sufficient numbers on all scales to promote scattering. The parallel mean free path predicted by the power-law statistics of the curvature strength scales in proportion to $r_{g}^{0.3}\,\ell _{c}^{0.7}$ ($\ell _{c}$ is the coherence scale of the turbulence), which is of direct interest for cosmic-ray phenomenology. Particle tracking in that numerical simulation confirms that the magnetic moment diffuses through localized, violent interactions, in agreement with the above picture. Correspondingly, the overall transport process is non-Brownian up to length scales $\gtrsim \ell _{c}$.

In designing stellarators, any design decision ultimately comes with a trade-off. Improvements in particle confinement, for instance, may increase the burden on engineers to build more complex coils, and the tightening of financial constraints may simplify the design and worsen some aspects of transport. Understanding trade-offs in stellarator designs is critical in designing high performance devices that satisfy the multitude of physical, engineering and financial criteria. In this study, we show how multi-objective optimization (MOO) can be used to investigate trade-offs and develop insight into the role of design parameters. We discuss the basics of MOO, as well as practical solution methods for solving MOO problems. We apply these methods to bring insight into the selection of two common design parameters: the aspect ratio of an ideal magnetohydrodynamic equilibrium and the total length of the electromagnetic coils.

The multi-cell Penning–Malmberg trap concept has been proposed as a way to accumulate and confine unprecedented numbers of antiparticles, an attractive but challenging goal. We report on the commissioning and first results (using electron plasmas) of the World's second prototype of such a trap, which builds and improves on the findings of its predecessor. Reliable alignment of both ‘master’ and ‘storage’ cells with the axial magnetic field has enabled confinement of plasmas, without use of the ‘rotating wall’ (RW) compression technique, for over an hour in the master cell and tens of seconds in the storage cells. In the master cell, attachment to background neutrals is found to be the main source of charge loss, with an overall charge-confinement time of 8.6 h. Transfer to on-axis and off-axis storage cells has been demonstrated, with an off-axis transfer rate of $50\,\%$ of the initial particles, and confinement times in the storage cells in the tens of seconds (again, without RW compression). This, in turn, has enabled the first simultaneous plasma confinement in two off-axis cells, a milestone for the multi-cell trap concept.

In this paper, we review recent and ongoing work by our group on numerical simulations of relativistic jets. Relativistic outflows in astrophysics are related to dilute, high energy plasmas, with physical conditions out of the reach of current laboratory capabilities. Simulations are thus imperative for the study of these objects. We present a number of such scenarios that have been studied by our group at the Universitat de València. In particular, we have focused on the evolution of extragalactic outflows through galactic and intergalactic environments, deceleration by interaction with stars or clouds or the propagation of jets in X-ray binaries and interaction with stellar winds from massive companions. All also share their role as particle acceleration sites and production of non-thermal radiation throughout the electromagnetic spectrum. Therefore, our work is not only aimed at understanding the impact of outflows on their environments and thus their role in galaxy and cluster evolution, but also the nature and capabilities of these sites as generators of high- and very-high-energy radiation and cosmic rays.

In the classical treatment the screening phenomenon of electric fields in a plasma is solely caused by charged particles, i.e. electrons and ions. In contrast, the present consideration focuses on the role of neutrals in a situation when the correlations between the charged and neutral components of the plasma medium turn rather significant. The consideration is entirely based on the renormalization procedure for interparticle interactions, which takes into account collective events in the generalized Poisson–Boltzmann equation relating the true microscopic potentials with their effective macroscopic counterparts. A meaningful approach is proposed to analytically derive the screening length from an appropriate assumption on the asymptotic behaviour of the macroscopic potential at large interparticle separations. It is clearly demonstrated that the neutral component really affects the screening length when the plasma reaches states corresponding to warm dense matter conditions. It is also shown that, at certain critical values of the plasma parameters, the character of the screening changes from exponential to oscillatory decay.

This paper investigates energetic electron transport in magnetized toroidal plasmas with magnetic fields characterized by island chains and regions of stochastic field lines produced by coil perturbations. We report on experiments performed in the DIII-D tokamak, which utilize electron cyclotron heating and current drive pulses to ‘tag’ electron populations within different locations across the discharge. The cross-field transport of these populations is then inferred from electron cyclotron emission measurements and gamma emission signals from scintillator detectors. Two types of energetic particles are distinguished and discussed: non-relativistic suprathermal electrons and relativistic runaway electrons. The magnetic field topology in each discharge is reconstructed with field-line tracing codes, which are also used to determine the location and scale of magnetic islands and stochastic regions. Comparison of simulations and experiments suggests that suprathermal transport is suppressed when the tagging is performed at a smaller radial location than the location of the $q = 1$ island chain and enhanced otherwise. Here q is the safety factor. We further demonstrate that increasing the width of the stochastic region within the edge plasma yields enhancement of the suprathermal electron transport.

The multiple-recycle fuel cycle for uranium-238 considered here, if practically realized, can bring revolutionary changes in nuclear energy. A full use of uranium-238 implies a practically infinite resource for power generation. Besides the energy, the fuel cycle net output is only fission products, which are co-products rather than waste. For the same amount of energy produced, the amount of fission products is two orders of magnitude less compared with the amount of spent nuclear fuel generated in currently exploited nuclear energy production scenarios. Using the simplest isotope balance model, key features of the multiple-recycle fuel cycle for uranium-238 are investigated. The repetition of this cycle results in smooth transformation of the initial fuel to ‘stationary’ fuel without strong variations in the fractional isotope content. Deficit of delayed neutrons is a threat of the fuel cycle considered as well as other fuel cycles that use plutonium. It has a dramatic impact on reactor controllability and safety. A solution to this threat could be a subcritical nuclear reactor with an external neutron source. In this paper, use of a stellarator–mirror (SM) fusion–fission hybrid for the multiple-recycle fuel cycle for uranium-238 is analysed. A summary of the experimental and theoretical studies on the SM hybrid is given. Preliminary results for principal design of a SM hybrid nuclear reactor for the multiple-recycle fuel cycle for uranium-238 are presented.

Free energy, widely used as a measure of turbulence intensity in weakly collisional plasmas, has been recently found to be a suitable basis to describe both linear and nonlinear growth in a wide class gyrokinetic systems. The simplicity afforded by this approach is accompanied by some drawbacks, notably the lack of any explicit treatment of wave–particle effects, which makes the theory unable to describe things like stability thresholds or dependence on the geometry of the background magnetic field. As a step toward overcoming these limitations, we propose an extension of the theory based on a generalization of the free energy. With this, it is demonstrated that resonance effects are recovered, and the bounds on growth are significantly reduced. The simplicity and efficient computation of the associated ‘optimal’ growth rates makes the theory potentially applicable to stellarator optimization.

The OMFIT STEP (Meneghini et al., Nucl. Fusion, vol. 10, 2020, p. 1088) workflow has been used to develop inductive and steady-state H-mode core plasma scenario use cases for a $B_0 = 8 \, {\rm T}$, $R_0 = 4 \, {\rm m}$ machine to help guide and inform future higher-fidelity studies of core transport and confinement in compact tokamak reactors. Both use cases are designed to produce 200 MW or more of net electric power in an up-down symmetric plasma with minor radius $a = 1.4 \, {\rm m}$, elongation $\kappa = 2.0$, triangularity $\delta = 0.5$ and effective charge $Z_{{\rm eff}} \simeq 2$. Additional considerations based on the need for compatibility of the core with reactor-relevant power exhaust solutions and external actuators were used to guide and constrain the use case development. An extensive characterization of core transport in both scenarios is presented, the most important feature of which is the extreme sensitivity of the results to the quantitative stiffness level of the transport model used as well as the predicted critical gradients. This sensitivity is shown to arise from different levels of transport stiffness exhibited by the models, combined with the gyroBohm-normalized fluxes of the predictions being an order of magnitude larger than other H-mode plasmas. Additionally, it is shown that although heating in both plasmas is predominantly to the electrons and collisionality is low, the plasmas remain sufficiently well coupled for the ions to carry a significant fraction of the thermal transport. As neoclassical transport is negligible in these conditions, this situation inherently requires long-wavelength ion gyroradius-scale turbulence to be the dominant transport mechanism in both plasmas. These results are combined with other basic considerations to propose a simple heuristic model of transport in reactor-relevant plasmas, along with simple metrics to quantify coupling and core transport properties across burning and non-burning plasmas.

Pressure anisotropy can strongly influence the dynamics of weakly collisional, high-beta plasmas, but its effects are missed by standard magnetohydrodynamics (MHD). Small changes to the magnetic-field strength generate large pressure-anisotropy forces, heating the plasma, driving instabilities and rearranging flows, even on scales far above the particles’ gyroscales where kinetic effects are traditionally considered most important. Here, we study the influence of pressure anisotropy on turbulent plasmas threaded by a mean magnetic field (Alfvénic turbulence). Extending previous results that were concerned with Braginskii MHD, we consider a wide range of regimes and parameters using a simplified fluid model based on drift kinetics with heat fluxes calculated using a Landau-fluid closure. We show that viscous (pressure-anisotropy) heating dissipates between a quarter (in collisionless regimes) and half (in collisional regimes) of the turbulent-cascade power injected at large scales; this does not depend strongly on either plasma beta or the ion-to-electron temperature ratio. This will in turn influence the plasma's thermodynamics by regulating energy partition between different dissipation channels (e.g. electron and ion heat). Due to the pressure anisotropy's rapid dynamic feedback onto the flows that create it – an effect we term ‘magneto-immutability’ – the viscous heating is confined to a narrow range of scales near the forcing scale, supporting a nearly conservative, MHD-like inertial-range cascade, via which the rest of the energy is transferred to small scales. Despite the simplified model, our results – including the viscous heating rate, distributions and turbulent spectra – compare favourably with recent hybrid-kinetic simulations. This is promising for the more general use of extended-fluid (or even MHD) approaches to model weakly collisional plasmas such as the intracluster medium, hot accretion flows and the solar wind.

In this paper, we summarize our recent work on gyrokinetic applications in electron–positron and non-neutral plasma. The electrostatic stability of electron–positron plasmas was investigated in dipole and slab geometries, with and without ion admixture. The gyrokinetic dispersion relation was derived and, for the slab case, extended to non-neutral plasmas. Here, we further extend the gyrokinetic formulation to the relativistic regime. Electron–positron plasmas are found to be remarkably stable as long as perfect symmetry between the two species prevails, but instabilities appear if this symmetry is broken, for instance by the introduction of impurities or magnetic curvature.