We carry out three-dimensional and two-dimensional particle-in-cell simulations of the expansion of a magnetized plasma that initially uniformly fills a half-space and contains a semicylindrical region of heated electrons elongated along the surface of the plasma boundary. This geometry is related, for instance, to ablation of a plane target by a femtosecond laser beam under quasi-cylindrical focusing. We find that a decay of the inhomogeneous plasma–vacuum discontinuity is strongly affected by an external magnetic field parallel to its boundary. We observe various transient phenomena, including an anisotropic scattering of electrons and an accompanying Weibel instability, and reveal various spatial structures of the arising magnetic field and current, including multiple flying-apart filaments of a Z-pinch type and slowly evolving current sheets with different orientations. The magnitude of the self-generated magnetic field can be of the order of, or significantly exceed that of, the external one. Such phenomena are expected in the laser and cosmic plasmas, including the explosive processes in the planetary magnetospheres and stellar coronal arches.

We report a generation of energetic protons by the interaction of a high-energy electron driving beam with an underdense plasma slab. After an interaction period of approximately 4000 fs, a proton beam with maximum energy greater than 250 MeV can be achieved by applying a driving beam with energy 1.0 GeV to a 200 $\mathrm {\mu }$m plasma slab. Our two-dimensional particle-in-cell simulations also show that the proton acceleration process can be divided into two stages. In the first stage, a strong positive longitudinal electric field appears near the rear boundary of the plasma slab after the driving beam has passed through it. This acceleration process is similar to the target normal sheath acceleration scheme by the interaction between intense pulsed laser with overdense plasma targets. In the second stage, the accelerated protons experience a long-range acceleration process with a two-stream instability between the high-energy driving beam and the proton beam. Further analyses show that this accelerated proton beam is equipped with the property of good collimation and high energy. This scheme presents a new way for proton or ion acceleration on some special occasions.

Dissipative processes cause collisionless plasmas in many systems to develop non-thermal particle distributions with broad power-law tails. The prevalence of power-law energy distributions in space/astrophysical observations and kinetic simulations of systems with a variety of acceleration and trapping (or escape) mechanisms poses a deep mystery. We consider the possibility that such distributions can be modelled from maximum-entropy principles, when accounting for generalizations beyond the Boltzmann–Gibbs entropy. Using a dimensional representation of entropy (related to the Renyi and Tsallis entropies), we derive generalized maximum-entropy distributions with a power-law tail determined by the characteristic energy scale at which irreversible dissipation occurs. By assuming that particles are typically energized by an amount comparable to the free energy (per particle) before equilibrating, we derive a formula for the power-law index as a function of plasma parameters for magnetic dissipation in systems with sufficiently complex topologies. The model reproduces several results from kinetic simulations of relativistic turbulence and magnetic reconnection.

Collisionless shocks undergo structural changes with the increase of Mach number. Observations and numerical simulations indicate development of time-dependent rippling. It is not known at present what causes the rippling. However, effects of such rippling on the field pattern and ion motion and distributions can be studied without precise knowledge of the causes and detailed shape. It is shown that deviations of the normal component of the magnetic field from the constant value indicate certain spatial dependence of the rippling. Deviations of the motional electric field from the constant value indicate time dependence. It is argued that whistler waves should propagate towards upstream and downstream regions from the rippled ramp. It is shown that the downstream pattern of the fields and ion distributions should follow the rippling pattern, while collisionless relaxation should be faster than in the stationary planar case.

Fluctuation measurements reveal the outward electromagnetic energy flux needed to drive the dynamo electromotive force supporting magnetic self-organization in a reversed-field pinch plasma. The radial Poynting flux due to tearing mode fluctuations is measured with an insertable probe during magnetic relaxation. This flux corresponds to transient power levels much larger than the input power and comparable to the global equilibrium magnetic energy transient loss rate. The probe measurements of this flux are roughly as predicted by a simple Poynting's theorem model upon substitution of equilibrium measurement data.

The Dougherty model Fokker–Planck operator is extended to describe nonlinear full-$f$ ( f is the distribution function) collisions between multiple species in plasmas. Simple relations for cross-species primitive moments are developed which obey conservation laws, and reproduce familiar velocity and temperature relaxation rates. This treatment of multispecies Dougherty collisions, valid for arbitrary mass ratios, avoids unphysical temperatures and satisfies the $H$-theorem (H is related to the entropy) unlike an analogous Bhatnagar–Gross–Krook operator. Formulas for both a Cartesian velocity space and a gyroaveraged operator are provided for use in Vlasov as well as long-wavelength gyrokinetic models. We present an algorithm for the discontinuous Galerkin discretization of this operator, and provide results from relaxation and Landau damping benchmarks.

We present a study of the linear properties of the ion-temperature gradient (ITG) modes with collisions modelled for the first time by the linearized gyrokinetic (GK) Coulomb collision operator (Frei et al., J. Plasma Phys., vol. 87, issue 5, 2021, 905870501) in the local limit. The study is based on a Hermite–Laguerre polynomial expansion of the perturbed ion distribution function applied to the linearized GK Boltzmann equation, yielding a hierarchy of coupled equations for the expansion coefficients, referred to as gyromoments. We explore the collisionless and high-collisional limits of the gyromoment hierarchy analytically. Parameter scans revealing the dependence of the ITG growth rate on the collisionality modelled using the GK Coulomb operator are reported, showing strong damping at small scales as the collisionality increases and, therefore, the need for a steeper gradient for the ITG onset at high collisionality to overcome the finite Larmor radius (FLR) collisional stabilization. The predictions on the ITG growth rate by the GK Coulomb operator are compared with other collision operator models, such as the Sugama, the Dougherty, as well as the momentum-conserving pitch-angle scattering and the Hirshman–Sigmar–Clarke collision operators derived for the first time in terms of gyromoments. The importance of FLR terms in the collision operators is pointed out by the appearance of a short wavelength ITG branch when collisional FLR terms are neglected, this branch being completely suppressed by FLR collisional effects. Energy diffusion is shown to be important at high collisionality and at small scale lengths. Among the GK collision operators considered in this work, the GK Sugama collision operator yields, in general, the smallest deviation compared with the GK Coulomb collision operator, while the largest deviations are found with the GK Dougherty operator. Convergence studies of the gyromoment method are reported and show that the drifts associated with the gradient and curvature of the magnetic field increase the required number of gyromoments at low collisionality. Nevertheless, the low number of gyromoments necessary for convergence at high collisionality constitutes an attractive numerical and analytical feature of the gyromoment approach to study the plasma dynamics in the boundary of fusion devices.

The dispersion relation of a surface wave generated by a drifting plasma in an infinite duct surrounded by vacuum is derived non-relativistically by means of the Vlasov equation. The kinematic boundary condition imposed on the distribution function, the specular reflection conditions on the four sides of duct, can be satisfied by placing an infinite number of fictitious surface charge sheets spaced by the duct widths. The surface wave mode is specifically the transverse magnetic mode, often called the surface polariton, which propagates with phasor $\exp ({{\rm i}k_zz-{\rm i}\omega t})$. The method of placing appropriate fictitious surface charge sheets enables one to treat the surface waves in semi-infinite, slab and duct plasmas simultaneously on an equal footing, kinetically. The streaming effect manifests itself through the Doppler-shifted frequency and a correction-like term ${u^2}/{c^2}$, where u is the streaming velocity and c is the speed of light.

An optimized compact stellarator with four simple coils is obtained from direct optimization via a coil shape. The new stellarator consists of two interlocking coils and two vertical field coils similar to those of the Columbia Non-neutral Torus (CNT) (Pedersen et al., Phys. Rev. Lett., vol. 88, 2002, pp. 205002). The optimized configuration has a global magnetic well and a low helical ripple level comparable to that of Wendelstein 7-X (W7-X) (Wolf et al., Nucl. Fusion, vol. 57, 2017, pp. 102020). The two interlocking coils have a smooth three-dimensional shape much simpler than those of advanced stellarators such as W7-X. This result opens up possibilities of future stellarator reactors with simplified coils.

In this paper, effects of discharge parameters and modulation frequency on the signal of laser-induced fluorescence measurements of ion velocity distribution functions are investigated in the LIF Test Source. A maximum modulation frequency is found for each given set of parameters, beyond which the signal gradually declines. Meanwhile, this maximum modulation frequency occurred consistently at ~1/10 of the theoretical frequency limit and photon counts received by a photomultiplier tube, which indicates that as modulation frequency and the associated per-pulse-excitation-event count decrease, the transition from the macroscopic statistical signal to the microscopic probabilistic signal is a gradual process.

Energetic-particle-induced geodesic acoustic modes, EGAMs (Fu, Phys. Rev. Let., vol. 101, 2008, pp. 185002), driven by neutral beam injection (NBI), have been observed in many DIII-D tokamak experiments (Nazikian et al., Phys. Rev. Lett., vol. 101, 2008, pp. 185001). This mechanism has been theoretically investigated in (Qiu et al., Plasma Phys. Control. Fusion, vol. 52, 2010, pp. 095003), using a sharp energetic particle distribution function, and in (Qu et al., Plasma Phys. Control. Fusion, vol. 59, 2017, pp. 055018), where the dispersion relation and eigenmode behaviour were obtained for the situation of early beam scenario, that is, for times smaller than the beam slowing down time. In this work, we extend these studies determining the eigenmode for beyond the slowing down time, in a scenario with reverse safety factor $q$ profile, where a small concentration of energetic ions can produce an off-axis maximum in the GAM dispersion relation. The characteristics of EGAM are analytically studied with the drift kinetic equation together with the MHD code NOVA. The toroidal energetic ion transit frequency, coupled with the GAM frequency, produces the maximum in the dispersion relation where the eigenmode can be found. The quantitative correspondence of experimental results with the predictions of the proposed model is analysed.

Recent experiments on the collective interaction of gigawatt electron beams with plasma at the GOL-PET facility have shown that the power of the electromagnetic radiation at the plasma frequency increases tens of times if the starting plasma is created with quasiperiodic radial density gradients. One of the mechanisms capable of providing highly efficient conversion of an unstable beam-driven wave into an electromagnetic one in the presence of periodic density perturbations is the mechanism of plasma antenna. However, earlier this mechanism was considered only for strictly longitudinal modulation of the plasma density, when its efficiency dropped drastically if the transverse size of the plasma significantly exceeded the radiation wavelength. In this work, based on both analytical theory and particle-in-cell modelling, we will show that the presence of oblique modulation of the plasma density makes the antenna mechanism effective even in a thick plasma, if the long-wavelength satellite of the most unstable beam-driven wave falls into resonance with natural plasma oscillations.

The first experimental campaigns have proven that, due to the optimization of the magnetic configuration with respect to neoclassical transport, the contribution of turbulence is essential to understand and predict the total particle and energy transport in Wendelstein 7-X (W7-X). This has spurred much work on gyrokinetic modelling for the interpretation of the available experimental results and for the preparation of the next campaigns. At the same time, new stellarator gyrokinetic codes have just been or are being developed. It is therefore desirable to have a sufficiently complete, documented and verified set of gyrokinetic simulations in W7-X geometry against which new codes or upgrades of existing codes can be tested and benchmarked. This paper attempts to provide such a set of simulations in the form of a comprehensive benchmark between the recently developed code stella and the well-established code GENE. The benchmark consists of electrostatic gyrokinetic simulations in the W7-X magnetic geometry and includes different flux tubes, linear ion-temperature-gradient (ITG) and trapped-electron-mode stability analyses, computation of linear zonal-flow responses and calculation of ITG-driven heat fluxes.

A two-field Hamiltonian gyrofluid model for kinetic Alfvén waves retaining ion finite Larmor radius corrections and parallel magnetic field fluctuations is used to study direct turbulent cascades from the magnetohydrodynamic to the sub-ion scales. For moderate energy imbalance and weak enough magnetic fluctuations, the spectrum of the transverse magnetic field and that of the most energetic wave display a steep transition zone near the ion scale, while the parallel transfer (and thus the parallel dissipation) remains weak. In this regime, the perpendicular flux of generalized cross-helicity displays a significant decay past the ion scale, while the perpendicular energy flux remains almost constant. A phenomenological model suggests that the interactions between co-propagative waves present at the sub-ion scales can play a central role in the development of a transition zone in the presence of a helicity barrier.

The theory of magnetohydrodynamic (MHD) turbulence predicts that Alfvénic and slow-mode-like compressive fluctuations are energetically decoupled at small scales in the inertial range. The partition of energy between these fluctuations determines the nature of dissipation, which, in many astrophysical systems, happens on scales where plasma is collisionless. However, when the magnetorotational instability (MRI) drives the turbulence, it is difficult to resolve numerically the scale at which both types of fluctuations start to be decoupled because the MRI energy injection occurs in a broad range of wavenumbers, and both types of fluctuations are usually expected to be coupled even at relatively small scales. In this study, we focus on collisional MRI turbulence threaded by a near-azimuthal mean magnetic field, which is naturally produced by the differential rotation of a disc. We show that, in such a case, the decoupling scales are reachable using a reduced MHD model that includes differential-rotation effects. In our reduced MHD model, the Alfvénic and compressive fluctuations are coupled only through the linear terms that are proportional to the angular velocity of the accretion disc. We numerically solve for the turbulence in this model and show that the Alfvénic and compressive fluctuations are decoupled at the small scales of our simulations as the nonlinear energy transfer dominates the linear coupling below the MRI-injection scale. In the decoupling scales, the energy flux of compressive fluctuations contained in the small scales is almost double that of Alfvénic fluctuations. Finally, we discuss the application of this result to prescriptions of ion-to-electron heating ratio in hot accretion flows.

We introduce modes of instantaneous optimal growth of free energy for the fully electromagnetic gyrokinetic equations. We demonstrate how these ‘optimal modes’ arise naturally from the free energy balance equation, allowing its convenient decomposition, and yielding a simple picture of energy flows. Optimal modes have a number of other favourable features, such as their low dimensionality, efficiency of computation and the fact that their growth rates provide a rigorous and ‘tight’ upper bound on both the nonlinear growth rate of energy, and the linear growth rate of traditional gyrokinetic (normal mode) instabilities. We provide simple closed-form solutions for the optimal growth rates in a number of asymptotic limits, and compare these with our previous bounds.

Following indirect-drive experiments which demonstrated promising performance for low convergence ratios (below 17), previous direct-drive simulations identified a fusion-relevant regime which is expected to be robust to hydrodynamic instability growth. This paper expands these results with simulated implosions at lower energies of 100 and 270 kJ, and ‘hydrodynamic equivalent’ capsules which demonstrate comparable convergence ratio, implosion velocity and in-flight aspect ratio without the need for cryogenic cooling, which would allow the assumptions of one-dimensional-like performance to be tested on current facilities. A range of techniques to improve performance within this regime are then investigated, including the use of two-colour and deep ultraviolet laser pulses. Finally, further simulations demonstrate that the deposition of electron energy into the hotspot of a low convergence ratio implosion through auxiliary heating also leads to significant increases in yield. Results include break even for 1.1 MJ of total energy input (including an estimated 370 kJ of short-pulse laser energy to produce electron beams for the auxiliary heating), but are found to be highly dependent upon the efficiency with which electron beams can be created and transported to the hotspot to drive the heating mechanism.

Understanding edge-localised-mode (ELM)-free high-confinement (H-)mode scenarios is vital for developing practical future demonstration reactor scenarios. An argon-seeded EDA H-mode discharge performed in ASDEX Upgrade is computationally studied in detail for the first time with the gyrokinetic GENE code using experimental profiles and magnetic equilibrium as direct code inputs. Linear scans outline dominant instabilities in the regime and reveal distinct ion- and electron-scale wavenumber growth-rate peaks for two local core and two local pedestal top scenarios. Linear ion-scale growth rates are found to be relatively insensitive to the addition of argon, and collisionality scans demonstrate increased sensitivity in the pedestal top. The addition of an argon impurity profile while keeping the input main ion temperature gradient (ITG) largely unchanged is found to reduce ITG-driven turbulence in the outer core. Nonlinear electromagnetic simulations reveal close agreement with experimentally predicted heat fluxes in the core, outline key sensitivities to electron $\beta$ and background $\boldsymbol{E\times B}$ shearing, and reveal gyrokinetic challenges in analysing the quasicoherent mode. Global electrostatic nonlinear simulations reduce local simulated heat transport overpredictions at the pedestal top. A quasilinear analysis finds that there is good core agreement but poor agreement in the pedestal between linear and nonlinear temperature and density fluctuation cross-phases. Local simulation limitations are elucidated and paths forward for future computation are suggested.

This paper focuses on utilizing several different optical diagnostics to experimentally characterize a pure helium atmospheric pressure plasma jet. Axial electric field measurements were carried out along the plasma plume through the use of a non-perturbing method based on polarization-dependent Stark spectroscopy of the helium $492.2$ nm line. The electric field is shown to increase with distance along the plume length, reaching values as high as $24.5$ kV cm$^{-1}$. The rate of increase of the electric field is dependent on the helium gas flow rate, with lower gas flows rising quicker with distance in comparison with larger flow rates, with the typical values remaining within the same range. This sensitivity is linked to gas mixing between the helium and surrounding ambient air. Schlieren imaging of the gas flow is included to support this. The addition of a target is shown to further increase the measured electric field in close range to the target, with the magnitude of this increase being strongly dependent on the distance between the tube exit and target. The relative increase in the electric field is shown to be on average greater for a conducting target of water in comparison with plastic. A minimal equipment optical configuration, which is here referred to as fast two-dimensional monochromatic imaging, is introduced as an approach for estimating excited state densities within the plasma. Densities of the upper helium states for transitions, $1s3s$ $^{3}S_{1}$ $\rightarrow$ $1s2p$ $^{3}P^{0}_{0,1,2}$ at $706.5$ nm and $1s3s$ $^{1}S_{0}$ $\rightarrow$ $1s2p$ $^{1}P^{0}_{1}$ at $728.1$ nm, were estimated using this approach and found to be of the order of $10^{10}$–$10^{11}$ cm$^{-3}$.

Tokamak start-up is characterized by low electron densities and strong electric fields, in order to quickly raise the plasma current and temperature, allowing the plasma to fully ionize and magnetic flux surfaces to form. Such conditions are ideal for the formation of superthermal electrons, which may reduce the efficiency of ohmic heating and prevent the formation of a healthy thermal fusion plasma. This is of particular concern in ITER where engineering limitations put restrictions on the allowable electric fields and limit the prefill densities during start-up. In this study, we present a new 0D burn-through simulation tool called STREAM (STart-up Runaway Electron Analysis Model), which self-consistently evolves the plasma density, temperature and electric field, while accounting for the generation and loss of relativistic runaway electrons. After verifying the burn-through model, we investigate conditions under which runaway electrons can form during tokamak start-up as well as their effects on the plasma initiation. We find that Dreicer generation plays a crucial role in determining whether a discharge becomes runaway-dominated or not, and that a large number of runaway electrons could limit the ohmic heating of the plasma, thus preventing successful burn-through or further ramp-up of the plasma current. The runaway generation can be suppressed by raising the density via gas fuelling, but only if done sufficiently early. Otherwise a large runaway seed may have already been built up, which can avalanche even at relatively low electric fields and high densities.