The use of ultrathin solid foils offers optimal conditions for accelerating protons to high energies from laser–matter interactions. When the target is thin enough that relativistic self-induced transparency sets in, all of the target electrons get heated to high energies by the laser, which maximizes the accelerating electric field and therefore the final ion energy. In this work, we first investigate how ion acceleration by ultraintense femtosecond laser pulses in transparent CH$_2$ solid foils is modified when turning from normal to oblique ($45^\circ$) incidence. Due to stronger electron heating, we find that higher proton energies can be obtained at oblique incidence but in thinner optimum targets. We then show that proton acceleration can be further improved by splitting the laser pulse into two half-pulses focused at opposite incidence angles. An increase by ${\sim }30\,\%$ in the maximum proton energy and by a factor of ${\sim }4$ in the high-energy proton charge is reported compared to the reference case of a single normally incident pulse.

The plasma channel formation in the focus of a knife-like nanosecond laser pulse irradiating a gas target is studied theoretically, and in gas-dynamics computer simulations. The distribution of the electromagnetic field in the focus region, obtained analytically, is used to calculate the energy deposition in the plasma, which then is implemented in the magnetohydrodynamic computer code. The modelling of the channel evolution shows that the plasma profile, which can guide the laser pulse, is formed by the tightly focused short knife-like lasers. The results of the simulations show that a proper choice of the convergence angle of a knife-like laser beam (determined by the focal length of the last cylindrical lens), and laser pulse duration may provide a sufficient degree of azimuthal symmetry of the formed plasma channel.

This paper reports the recent development of a full-scale particle-in-cell (PIC) simulation package highlighting an efficient electro-statics (ES)-PIC implementation for spacecraft charging problems. Numerical simulations are crucial in studying plasma flows because analytical solutions are rare, and experiments are expensive. There are many types of plasma flow that need various numerical methods for efficient and accurate simulations; as such, how to implement and organize those different methods into one comprehensive simulation package is challenging. This work adopted several modern software design patterns and developed a versatile package that includes various PIC schemes. This package has an open architecture, clean interfaces with both serial and parallel simulation capabilities. Two benchmark test cases are included to demonstrate the capabilities of this package. Then two plasma flows around a positively charged probe are simulated, and the results are discussed. The simulation results are consistent with past simulation results, and new insights are obtained. This work can lead to the development and organization of more sophisticated plasma simulation solvers in the future.

A new optimized quasi-helically symmetric configuration is described that has the desirable properties of improved energetic particle confinement, reduced turbulent transport by three-dimensional shaping and non-resonant divertor capabilities. The configuration presented in this paper is explicitly optimized for quasi-helical symmetry, energetic particle confinement, neoclassical confinement and stability near the axis. Post optimization, the configuration was evaluated for its performance with regard to energetic particle transport, ideal magnetohydrodynamic stability at various values of plasma pressure and ion temperature gradient instability induced turbulent transport. The effects of discrete coils on various confinement figures of merit, including energetic particle confinement, are determined by generating single-filament coils for the configuration. Preliminary divertor analysis shows that coils can be created that do not interfere with expansion of the vessel volume near the regions of outgoing heat flux, thus demonstrating the possibility of operating a non-resonant divertor.

We have investigated the influence of a strong magnetic field on various aspects of a quantum Fermi plasma. Due to the strong magnetic field, the distribution function becomes anisotropic. First, we consider non-degenerate quantum, Landau and Kelly distribution function. It was found that the adiabatic equation is similar to the adiabatic equation for a Maxwell distribution function, when we include the magnetic field in the energy expression. Using the Kelly distribution for a degenerate, quantum Fermi gas, parallel and perpendicular components of the pressure were derived. It was found that perpendicular component of pressure never becomes zero and three-dimensional system always stay three-dimensional. Lastly, we investigated electron emission from metals and have shown the influence of the magnetic field. We calculated thermionic emission, the so-called Richardson effect. In addition, we investigate the influence of external electromagnetic radiation on the electron current density (Hallwachs effect) from metals.

Absorbing boundary conditions or layers are used in simulations to reduce or eliminate wave reflections from the boundary; one of the most widely used absorbing layers is Berenger's perfectly matched layer (PML). In this paper, PML is extended to a compound absorbing layer which has multiple effects of damping and deceleration, and is applied to linear and nonlinear Schrödinger equations. The deceleration extends the time to damp out the modes with higher phase velocities, leading to remarkably reduced total reflection for dispersive waves. By invoking the two effects independently, the flexibility and performance are enhanced. Since this method is based on the WKB formalism, it requires an absorbing layer of a moderate size.

The transient transmission of an electromagnetic wave through cold, unmagnetized and collisionless plasmas is described both analytically and numerically for its normal incidence from vacuum upon a plasma half-space. Exact formulas for the electromagnetic field are written in integral forms, which are convenient for approximate analysis and comparison with the results of direct numerical simulations. The time when the plasma particle oscillations become self-consistent with the electromagnetic field can be calculated from the simplified formulas for an arbitrary distance from the plasma–vacuum interface. Special attention is paid to the formation of the electrostatic oscillation in the case when the frequency of the incident wave is equal to the plasma frequency. The amplitudes of the vanishing magnetic field and the forming electrostatic oscillation are calculated as functions of time and the distance from the plasma–vacuum interface. The formation of the electrostatic oscillation is a slow process because the electromagnetic power penetrating into the plasma tends to zero with time. The transmitted plasma electromagnetic field is also simulated by the a finite-difference time-domain (FDTD) code. The difficulties of the numerical simulation of the quasi-electrostatic field are discussed. The analytical results can be used for the validation of the FDTD codes for plasma waves.

We report measurements of the time-averaged surface floating potential of magnetic and non-magnetic spherical probes (or large dust particles) immersed in a magnetized capacitively coupled discharge. In this study, the size of the spherical probes is taken greater than the Debye length. The surface potential of a spherical probe first increases, i.e. becomes more negative at low magnetic field ($B < 0.05\ \textrm {T}$), attains a maximum value and decreases with further increase of the magnetic field strength ($B > 0.05\ \textrm {T}$). The rate of change of the surface potential in the presence of a $B$-field mainly depends on the background plasma and types of material of the objects. The results show that the surface potential of the magnetic sphere is higher (more negative) compared with the non-magnetic spherical probe. Hence, the smaller magnetic sphere collects more negative charges on its surface than a bigger non-magnetic sphere in a magnetized plasma. The different sized spherical probes have nearly the same surface potential above a threshold magnetic field ($B > 0.03\ \textrm {T}$), implying a smaller role of size dependence on the surface potential of spherical objects. The variation of the surface potential of the spherical probes is understood on the basis of a modification of the collection currents to their surface due to charge confinement and cross-field diffusion in the presence of an external magnetic field.

We study the propagation of nonlinear waves in non-relativistic electron–positron plasmas. The waves are assumed to propagate at small angles with respect to the equilibrium magnetic field. We derive the equation describing the wave propagation under the assumption that the waves are weakly dispersive and also can weakly depend on spatial variables orthogonal to the equilibrium magnetic field. We obtain solutions of the derived equation describing solitons. Then we study the stability of solitons with respect to transverse perturbations.

A disruption database characterizing the current quench of disruptions with ITER-like tungsten divertor has been developed on EAST. It provides a large number of plasma parameters describing the predisruptive plasma, current quench time, eddy current, and mitigation by massive impurity injection, which shows that the current quench time strongly depends on magnetic energy and post-disruption electron temperature. Further, the energy balance and magnetic energy dissipation during the current quench phase has been well analysed. Magnetic energy is also demonstrated to be dissipated mainly by ohmic reheating and inductive coupling, and both of the two channels have great effects on current quench time. Also, massive gas injection is an efficient method to speed up the current quench and increase the fraction of impurity radiation.

We derive a sufficient condition for the linear stability of plasma equilibria with incompressible flow parallel to the magnetic field, $\boldsymbol{B}$, constant mass density and anisotropic pressure such that the quantity $\unicode[STIX]{x1D70E}_{d}=\unicode[STIX]{x1D707}_{0}(P_{\Vert }-P_{\bot })/B^{2}$, where $P_{\Vert }$ ($P_{\bot }$) is the pressure tensor element parallel (perpendicular) to $\boldsymbol{B}$, remains constant. This condition is applicable to any steady state without geometrical restriction. The condition, generalising the respective condition for magnetohydrodynamic equilibria with isotropic pressure and constant density derived in Throumoulopoulos & Tasso (Phys. Plasmas, vol. 14, 2007, 122104), involves physically interpretable terms related to the magnetic shear, the flow shear and the variation of total pressure perpendicular to the magnetic surfaces. On the basis of this condition we prove that, if a given equilibrium is linearly stable, then the ones resulting from the application of Bogoyavlenskij symmetry transformations are linearly stable too, provided that a parameter involved in those transformations is positive. In addition, we examine the impact of pressure anisotropy, flow and torsion of a helical magnetic axis, for a specific class of analytic equilibria. In this case, we find that the pressure anisotropy and the flow may have either stabilising or destabilising effects. Also, helical configurations with small torsion and large pitch seem to have more favourable stability properties.

We have recently demonstrated that by expanding in small distance from the magnetic axis compared with the major radius, stellarator shapes with low neoclassical transport can be generated efficiently. To extend the utility of this new design approach, here we evaluate measures of magnetohydrodynamic interchange stability within the same expansion. In particular, we evaluate the magnetic well, Mercier's criterion, and resistive interchange stability near a magnetic axis of arbitrary shape. In contrast to previous work on interchange stability near the magnetic axis, which used an expansion of the flux coordinates, here we use the ‘inverse expansion’ in which the flux coordinates are the independent variables. Reduced expressions are presented for the magnetic well and stability criterion in the case of quasisymmetry. The analytic results are shown to agree with calculations from the VMEC equilibrium code. Finally, we show that near the axis, Glasser, Greene and Johnson's stability criterion for resistive modes approximately coincides with Mercier's ideal condition.

The turbulence-induced quasi-linear particle flux of a highly charged, collisional impurity species is calculated from the electrostatic gyrokinetic equation including collisions with the bulk ions and the impurities themselves. The equation is solved by an expansion in powers of the impurity charge number $Z$. In this formalism, the collision operator only affects the impurity flux through the dynamics of the impurities in the direction parallel to the magnetic field. At reactor-relevant collisionality, the parallel dynamics is dominated by the parallel electric field, and collisions have a minor effect on the turbulent particle flux of highly charged, collisional impurities.

The fundamental difference between incompressible ideal magnetohydrodynamics and the dynamics of a non-conducting fluid is that magnetic fields exert a tension force that opposes their bending; magnetic fields behave like elastic strings threading the fluid. It is natural, therefore, to expect that a magnetic field tangled at small length scales should resist a large-scale shear in an elastic way, much as a ball of tangled elastic strings responds elastically to an impulse. Furthermore, a tangled field should support the propagation of ‘magnetoelastic waves’, the isotropic analogue of Alfvén waves on a straight magnetic field. Here, we study magnetoelasticity in the idealised context of an equilibrium tangled field configuration. In contrast to previous treatments, we explicitly account for intermittency of the Maxwell stress, and show that this intermittency necessarily decreases the frequency of magnetoelastic waves in a stable field configuration. We develop a mean-field formalism to describe magnetoelastic behaviour, retaining leading-order corrections due to the coupling of large- and small-scale motions, and solve the initial-value problem for viscous fluids subjected to a large-scale shear, showing that the development of small-scale motions results in anomalous viscous damping of large-scale waves. Finally, we test these analytic predictions using numerical simulations of standing waves on tangled, linear force-free magnetic-field equilibria.

The island divertor topology of the Wendelstein 7-X (W7-X) scrape-off-layer exhibits regions of highly varying connection length. Here, we present drift-plane simulations of seeded filaments in regions of sharp transitions in parallel connection length – a parameter which dictates the propagation regime for plasma blobs. It is determined that a transition in parallel connection length alters the trajectory of filaments; filaments which enter regions of lower connection length are decelerated, and vice versa. It is also determined that if the lobes of a potential dipole created by diamagnetic drifts within the filament exist in two regions of distinct parallel connection length, the filament is then steered towards the region of higher connection length. The extreme case of a narrow region of varying connection length can also alter the trajectory of a filament, depending on the extent of this region. Finally, simulations mimicking the view from the W7-X gas puff imaging (GPI) diagnostic view plane are presented. It is determined that filaments in the view of the W7-X GPI diagnostic exhibit a predominantly poloidal propagation due to the radial electric field, since the radial velocity is relatively small.

Two-dimensional spatial measurements of magnetic field and plasma parameters have been performed in conventional magnetron DC discharges during the formation of metallic nanoparticles. Correlations between the electron density and temperature distributions, and the magnetic field geometry and strength have been established. A sharp increase of the plasma potential is found on the edge of the last magnetic arch followed by a decrease towards the anode plate and edges. It is shown that the spatial variation of the plasma potential is at the origin of a potential well that can trap negatively charged nanoparticles.

The edge region of quasi-adiabatic plasma is pedagogically simulated by the dynamics between the electric potential $\unicode[STIX]{x1D711}$ and the electron density $n$ whose equilibrium density gradient is negative and held fixed. The zonal flow (ZF) $V$ is either enforced sinusoidally or generated self-consistently from the turbulence. Cross-phase $\unicode[STIX]{x1D6FF}$ between $\unicode[STIX]{x1D711}$ and $n$, which is important in the determination of the turbulence level and the transport, is strongly influenced by the ZF. In the region near $V=0$, $\unicode[STIX]{x1D6FF}$ becomes negative due to the large gradient of the ZF. It is found that the instabilities are quenched there, and the fluctuations decay. The ZF thus works as a transport barrier in the region where the ZF changes direction with large gradient.

In the present analysis, we study effects of the radiation reaction (RR) on the dynamics of charged particles submitted to the action of localized longitudinal high-frequency carriers travelling at the speed of light. As the wave's crests and troughs keep overtaking particles, dissipative RR forces tend to drag particles alongside the wave in an effort to reduce the relative wave–particle speed. Particles of course never reach the phase velocity of the wave, but are instead driven to an ever-growing velocity, towards the speed of light, while in the wave localization region. We developed a modified average Hamiltonian formalism capable of describing the intricacies of the corresponding dynamics. The modified formalism agrees with simulations and is of particular usefulness in the study of optimum values for the localization length and maximum wave amplitude.

The present work considers the stability of a high-$\beta$, large aspect ratio, circular plasma with diffuse profiles for the safety factor and the angular toroidal frequency (López & Guazzotto, Phys. Plasmas, vol. 24, 032501). An application of the Frieman–Rotenberg formalism results in a system of scalar eigenmode equations whose coupling is retained at the plasma–vacuum transition but is disregarded across the plasma column, which is a standard practice. The solution technique consists of a multidimensional shooting method for the poloidal harmonics; robust initial guesses are constructed by solving the dispersion relation in the static scenario with vanishing magnetic shear. Flow shear appears as a high-$\beta$ toroidal contribution, and we illustrate its destabilizing influence on $n=1$ external kink modes in the presence of ideal and resistive walls. Internal resonances are avoided by means of the selection of appropriate equilibrium parameters. The stabilizing influence of a finite positive average magnetic shear is also exemplified.

An error in Klimas & Viñas (J. Plasma Phys., vol. 85 (6), 2019, 905850610) is noted and explained. It is shown that the results in Klimas and Viñas were unaffected by the error. Further ramifications for future non-periodic spectral simulations are discussed.