Transit-time damping (TTD) is a process in which the magnetic mirror force – induced by the parallel gradient of magnetic field strength – interacts with resonant plasma particles in a time-varying magnetic field, leading to the collisionless damping of electromagnetic waves and the resulting energization of those particles through the perpendicular component of the electric field, $E_\perp$. In this study, we utilize the recently developed field–particle correlation technique to analyse gyrokinetic simulation data. This method enables the identification of the velocity-space structure of the TTD energy transfer rate between waves and particles during the damping of plasma turbulence. Our analysis reveals a unique bipolar pattern of energy transfer in the velocity-space characteristic of TTD. By identifying this pattern, we provide clear evidence of TTD's significant role in the damping of strong plasma turbulence. Additionally, we compare the TTD signature with that of Landau damping (LD). Although they both produce a bipolar pattern of phase-space energy density loss and gain about the parallel resonant velocity of the Alfvénic waves, they are mediated by different forces and exhibit different behaviours as the perpendicular velocity $v_\perp \to 0$. We also explore how the dominant damping mechanism varies with ion plasma beta $\beta _i$, showing that TTD dominates over LD for $\beta _i > 1$. This work deepens our understanding of the role of TTD in the damping of weakly collisional plasma turbulence and paves the way to seek the signature of TTD using in situ spacecraft observations of turbulence in space plasmas.

We propose an algorithm for encoding linear kinetic plasma problems in quantum circuits. The focus is on modelling electrostatic linear waves in a one-dimensional Maxwellian electron plasma. The waves are described by the linearized Vlasov–Ampère system with a spatially localized external current that drives plasma oscillations. This system is formulated as a boundary-value problem and cast in the form of a linear vector equation $\boldsymbol {A}{\boldsymbol{\psi} } = \boldsymbol {b}$ to be solved by using the quantum signal processing algorithm. The latter requires encoding of matrix $\boldsymbol {A}$ in a quantum circuit as a sub-block of a unitary matrix. We propose how to encode $\boldsymbol {A}$ in a circuit in a compressed form and discuss how the resulting circuit scales with the problem size and the desired precision.

Understanding the partitioning of turbulent energy between ions and electrons in weakly collisional plasmas is crucial for the accurate interpretation of observations and modelling of various astrophysical phenomena. Many such plasmas are ‘imbalanced’, wherein the large-scale energy input is dominated by Alfvénic fluctuations propagating in a single direction. In this paper, we demonstrate that when strongly-magnetised plasma turbulence is imbalanced, nonlinear conservation laws imply the existence of a critical value of the electron plasma beta (the ratio of the thermal to magnetic pressures) that separates two dramatically different types of turbulence in parameter space. For betas below the critical value, the free energy injected on the largest scales is able to undergo a familiar Kolmogorov-type cascade to small scales where it is dissipated, heating electrons. For betas above the critical value, the system forms a ‘helicity barrier’ that prevents the cascade from proceeding past the ion Larmor radius, causing the majority of the injected free energy to be deposited into ion heating. Physically, the helicity barrier results from the inability of the system to adjust to the disparity between the perpendicular-wavenumber scalings of the free energy and generalised helicity below the ion Larmor radius; restoring finite electron inertia can annul, or even reverse, this disparity, giving rise to the aforementioned critical beta. We relate this physics to the ‘dynamic phase alignment’ mechanism (that operates under yet lower beta conditions and in pair plasmas), and characterise various other important features of the helicity barrier, including the nature of the nonlinear wavenumber-space fluxes, dissipation rates, and energy spectra. The existence of such a critical beta has important implications for heating, as it suggests that the dominant recipient of the turbulent energy, ions or electrons, can depend sensitively on the characteristics of the plasma at large scales.

The available energy of a plasma is defined as the maximum amount by which the plasma energy can be lowered by volume-preserving rearrangements in phase space, so-called Gardner restacking. A general expression is derived for the available energy of a nearly homogeneous plasma and is shown to be closely related to the Helmholtz free energy, which it can never exceed. A number of explicit examples are given.

GX is a code designed to solve the nonlinear gyrokinetic system for low-frequency turbulence in magnetized plasmas, particularly tokamaks and stellarators. In GX, our primary motivation and target is a fast gyrokinetic solver that can be used for fusion reactor design and optimization along with wide-ranging physics exploration. This has led to several code and algorithm design decisions, specifically chosen to prioritize time to solution. First, we have used a discretization algorithm that is pseudospectral in the entire phase space, including a Laguerre–Hermite pseudospectral formulation of velocity space, which allows for smooth interpolation between coarse gyrofluid-like resolutions and finer conventional gyrokinetic resolutions and efficient evaluation of a model collision operator. Additionally, we have built GX to natively target graphics processors (GPUs), which are among the fastest computational platforms available today. Finally, we have taken advantage of the reactor-relevant limit of small $\rho _*$ by using the radially local flux-tube approach. In this paper we present details about the gyrokinetic system and the numerical algorithms used in GX to solve the system. We then present several numerical benchmarks against established gyrokinetic codes in both tokamak and stellarator magnetic geometries to verify that GX correctly simulates gyrokinetic turbulence in the small $\rho _*$ limit. Moreover, we show that the convergence properties of the Laguerre–Hermite spectral velocity formulation are quite favourable for nonlinear problems of interest. Coupled with GPU acceleration, which we also investigate with scaling studies, this enables GX to be able to produce useful turbulence simulations in minutes on one (or a few) GPUs and higher fidelity results in a few hours using several GPUs. GX is open-source software that is ready for fusion reactor design studies.

The femtosecond laser filament-induced air laser plays a significant role for the remote sensing of air pollutants. The spatial distributions of air laser intensity were investigated experimentally in previous studies. However, the mechanism of the air laser propagation properties inside the filament plasma has not been quite clear yet. Moreover, few studies have been dedicated to the reproduction of the air laser profile from nitrogen molecules propagating in the filament plasma based on the numerical simulation method. In this study, the lasing action of the air laser from the transition of the first negative (0,0) band of nitrogen ions at 391 nm was simulated during the femtosecond laser filamentation. The beam profile of the air laser changes from a Gaussian or super-Gaussian shape to an outer ring structure by increasing the filament length or nitrogen ion density, which is in accord with the previous experimental result. A multiple-diffraction effect has been proposed to clarify the mechanism of the outer rings beam pattern formation, which is induced by the dynamical interaction between the lasing effect and diffraction effect of the air laser propagating inside the filament plasma. In addition, the amplified air laser power as a function of both the filament length and nitrogen ion density was investigated. Our study would pave the way to improve the energy conversion efficiency and directivity of remote air lasers, which would be significant for remote sensing applications.

The paper presents experimental results from the SMOLA device, which was built in the Budker Institute of Nuclear Physics for the verification of the helical mirror confinement idea. This concept involves active control of axial losses from the confinement zone in an open magnetic trap through the use of multiple mirrors that move in the plasma frame of reference. The discussed experiments focused on determining the cumulative effect of a helical mirror system in combination with a short segment of a stronger magnetic field. Combination of these two methods of axial flow suppression results in higher efficiency compared with each method individually. Different combinations of the mirrors were tested. The most effective flow suppression was observed if the short mirror was placed between the confinement region and the helical mirror. In this configuration, an effective mirror ratio of $R_{{\rm eff}} = 32.6\pm 7.8$ was achieved, along with a more than three-fold increase in plasma density within the confinement region. The possibility of a cumulative effect of different types of magnetic mirrors offers a way to improve the confinement performance of the reactor-grade mirror confinement devices.

Microinstabilities drive turbulent fluctuations in inhomogeneous, magnetised plasmas. In the context of magnetic confinement fusion devices, this leads to an enhanced transport of particles, momentum and energy, thereby degrading confinement. In this work, we describe an application of the adjoint method to efficiently determine variations of gyrokinetic linear growth rates on a general set of external parameters in the local $\delta f$-gyrokinetic model. We then offer numerical verification of this approach. When coupled with gradient-based techniques, this methodology can facilitate the optimisation process for the microstability of the confined plasmas across a high-dimensional parameter space. We present a numerical demonstration wherein the ion-temperature-gradient instability growth rate in a tokamak plasma is minimised with respect to flux surface shaping parameters. The adjoint method approach demonstrates a significant computational speed-up compared with a finite-difference gradient calculation.

A numerical study of the homo-interactions between two falling droplets and between two rising bubbles in a strongly coupled dusty plasma medium is presented in this article. The strongly coupled dusty plasma is considered as a viscoelastic fluid using the generalized hydrodynamic fluid model formalism. Two factors that affect homo-interactions are taken into account: the initial spacing and the coupling strength of the medium. Three different spacings between two droplets are simulated: widely, medium and closely. In each case, the coupling strength has been given as mild–strong and strong. It is shown that the overall dynamic is governed by the competition between the acceleration of two droplets/bubbles due to gravity and the interaction due to the closeness of the droplets/bubbles. Particularly in viscoelastic fluids, apart from the initial separation, shear waves originating from rotating vortices are responsible for the closeness of two droplets or bubbles. Several two-dimensional simulations have been carried out. This work is a continuation of the work done in Parts 1 (Dharodi & Das, J. Plasma Phys., vol. 87, issue 2, 2021, 905870216) and 2 (Dharodi, J. Plasma Phys., vol. 87, issue 4, 2021, 905870402).

A systematic theory of the asymptotic expansion of the magnetohydrostatics (MHS) equilibrium in the distance from the magnetic axis is developed to include arbitrary smooth currents near the magnetic axis. Compared with the vacuum and the force-free system, an additional magnetic differential equation must be solved to obtain the pressure-driven currents. It is shown that there exist variables in which the rest of the MHS system closely mimics the vacuum system. Thus, a unified treatment of MHS fields is possible. The mathematical structure of the near-axis expansions to arbitrary order is examined carefully to show that the double-periodicity of physical quantities in a toroidal domain can be satisfied order by order. The essential role played by the leading-order Birkhoff–Gustavson normal form in solving the magnetic differential equations is highlighted. Several explicit examples of vacuum, force-free and MHS equilibrium in different geometries are presented.

New plasma applications in advanced fields, such as fundamental nuclear fusion research, require high-density, large-diameter plasma with a strong and non-uniform magnetic field. A helicon plasma (HP) source using a flat-type antenna is expected to be one of the promising methods for such applications. In this study, we developed an HP source with a two-turn flat-loop antenna connected to a 30 kW radio frequency power supply in the Compact Test Plasma device. In the argon plasma generation experiment with various magnetic fields, HP generation was observed for the first time in this device. The electron density was calculated from the dispersion relation with the magnetic field strength at 45 cm from the antenna surface, assuming a fundamental radial mode and an azimuthal mode of $m=0$. The electron density expected from the experimental result was approximately in the same range as the calculation result by a factor of 2.3 to 3.5. In addition, the magnetic field strength and shape around the antenna are important factors in the plasma properties. This plasma source has been installed in the pilot GAMMA PDX-SC, which is under development for nuclear plasma research, and it contributes to the study of the HP generation process.

A surrogate model of the runaway electron avalanche growth rate in a magnetic fusion plasma is developed. This is accomplished by employing a physics-informed neural network (PINN) to learn the parametric solution of the adjoint to the relativistic Fokker–Planck equation. The resulting PINN is able to evaluate the runaway probability function across a broad range of parameters in the absence of any synthetic or experimental data. This surrogate of the adjoint relativistic Fokker–Planck equation is then used to infer the avalanche growth rate as a function of the electric field, synchrotron radiation and effective charge. Predictions of the avalanche PINN are compared against first principle calculations of the avalanche growth rate with excellent agreement observed across a broad range of parameters.

To expand on recent work, we introduce collisional terms in the analysis of the warm ion–electron, two-fluid equations for a homogeneous plasma at rest. Consequently, the plasma is now described by six variables: the magnetisation, the ratio of masses over charges, the electron and ion sound speeds, the angle between the wave vector and the magnetic field and a new parameter describing the electron–ion collision frequency. This additional parameter does not introduce new wave modes compared with the collisionless case, but does result in complex mode frequencies. Both for the backward and forward propagating modes the imaginary components are negative and thus quantify collisional damping. We provide convenient (polynomial) expressions to quantify frequencies and damping rates in all short- and long-wavelength limits, including the cutoff and resonance limits, whilst the one-fluid magnetohydrodynamic limit is retained with the familiar undamped slow, Alfvén and fast waves. As collisions only introduce a damping, the previously introduced labelling of the wave modes S, A, F, M, O and X can be kept and assigned based on their long- and short-wavelength behaviour. The obtained damping at cutoff and resonance limits is parametrised with the collision frequency, and can be tailored to match known kinetic damping expressions. It is demonstrated that varying the angle can introduce crossings between the wave modes, as was already present in the ideal ion–electron case, but also a collision frequency exceeding a critical collision frequency can lead to crossings at angles where previously only avoided crossings were found.

During a space mission, switching to an electric propulsion system from chemical propulsion, once the spacecraft is out of the Earth's gravity, significantly reduces the mission's overall cost. In electric propulsion, the Hall thruster and gridded ion thruster are established technologies. These thrusters compromise mission longevity due to continuous erosion of the device electrode material. To overcome this issue, an electrode less expanding magnetic field plasma thruster or helicon plasma thruster (HPT), was proposed and research is on going worldwide. The HPT shows scaling of thrust with input power while Hall thrusters and ion thrusters do not. Typically, an inert xenon gas is used as a fuel in HPT devices due to a low ionization potential and non-hazardous nature. Xenon is not easily available in nature and during a space mission it needs to be stored in high pressure tanks. Recently, iodine has been proposed as an alternate to xenon as it is easily available and does not have any storage issues. In most of the numerical simulations, argon is used as a fuel gas to reduce the simulation cost. Using a 1D3V particle-in-cell Monte Carlo collision code, we present here a net thrust generation for different fuel gases such as argon, xenon and iodine. We compare plasma flow rates and directed ion beam velocity for different fuel gases having identical inputs. Thrust and plasma flow are investigated for different magnetic field gradients in the plasma expansion region for unidirectional and bidirectional HPT and is reported here. Using iodine fuel, a significant increase in net thrust is obtained for higher magnetic field divergence for identical simulation input parameters while comparing with xenon fueled cases.

This paper investigates the influence of compressibility on the internal wave modes and the density gradient-driven Rayleigh–Taylor (R–T) instability in magnetized strongly coupled dusty plasmas. The dusty magnetohydrodynamic model is formulated for compressible fluids, accounting for the effects of weakly coupled electrons/ions and strongly coupled dust particles under the influence of the gravitational field. The effect of the magnetic field on the dust dynamics has been incorporated through the magnetic force on the electrons and ions in quasineutral dusty plasmas. A dispersion relation of the R–T instability has been derived which has been modified because of the compressibility effect, dust acoustic wave speed and viscoelastic coefficients. The shear Alfvén and compressional viscoelastic wave modes become coupled in the dispersion characteristics. The modified R–T instability criterion is derived in terms of the Alfvén speed, viscoelastic effects and dust grain parameters. The graphical illustrations show that the growth rate of R–T instability has been suppressed due to compressibility, viscoelastic coefficients and dust acoustic speed. The results are useful to discuss the development of R–T instability in magnetized astrophysical dusty plasmas.

In the present work, we extend the results of a previous investigation on the dynamics of electrons under the action of an inverse free-electron-laser scheme (Almansa et al., Phys. Plasmas, vol. 26, 2019, 033105). While the former work examined electrons as single test particles subject to the combined action of a modulated wiggler plus a laser field, we now look at electrons as composing a particle beam, where collective space-charge effects are relevant and included in the analysis. Our previous work showed that effective acceleration is achieved when the initial velocities of the particles are close enough to the phase velocity of the beat-wave mode formed by the laser and the wiggler fields. Electrons are then initially accelerated by a ponderomotive uphill effect generated by the beat mode and, once reaching the phase velocity of the beat, undergo a final strong resonant acceleration step resembling a catapult effect. The present work shows that, under proper conditions, space-charge effects play a similar role as the initial (or injected) velocity of the beam. Even if acceleration is absent when space charge is neglected, it may be present and effective when charge effects are taken into account. We also discuss how far the space charge can grow without affecting the sustainability of the acceleration process.

We present a detailed characterization of the structure and evolution of differentially rotating plasmas driven on the MAGPIE pulsed-power generator (1.4 MA peak current, 240 ns rise time). The experiments were designed to simulate physics relevant to accretion discs and jets on laboratory scales. A cylindrical aluminium wire array Z pinch enclosed by return posts with an overall azimuthal off-set angle was driven to produce ablation plasma flows that propagate inwards in a slightly off-radial trajectory, injecting mass, angular momentum and confining ram pressure to a rotating plasma column on the axis. However, the plasma is free to expand axially, forming a collimated, differentially rotating axial jet that propagates at ${\approx }100\,{\rm km}\,{\rm s}^{-1}$. The density profile of the jet corresponds to a dense shell surrounding a low-density core, which is consistent with the centrifugal barrier effect being sustained along the jet's propagation. We show analytically that, as the rotating plasma accretes mass, conservation of mass and momentum implies plasma radial growth scaling as $r \propto t^{1/3}$. As the characteristic moment of inertia increases, the rotation velocity is predicted to decrease and settle on a characteristic value ${\approx }20\,{\rm km}\,{\rm s}^{-1}$. We find that both predictions are in agreement with Thomson scattering and optical self-emission imaging measurements.

This study documents several correlations observed during the first run of the plasma wakefield acceleration experiment E300 conducted at FACET-II, using a single drive electron bunch. The established correlations include those between the measured maximum energy loss of the drive electron beam and the integrated betatron X-ray signal, the calculated total beam energy deposited in the plasma and the integrated X-ray signal, among three visible light emission measuring cameras and between the visible plasma light and X-ray signal. The integrated X-ray signal correlates almost linearly with both the maximum energy loss of the drive beam and the energy deposited into the plasma, demonstrating its usability as a measure of energy transfer from the drive beam to the plasma. Visible plasma light is found to be a useful indicator of the presence of a wake at three locations that overall are two metres apart. Despite the complex dynamics and vastly different time scales, the X-ray radiation from the drive bunch and visible light emission from the plasma may prove to be effective non-invasive diagnostics for monitoring the energy transfer from the beam to the plasma in future high-repetition-rate experiments.

Electrostatic gyrokinetic instabilities and turbulence in the Wendelstein 7-X stellarator are studied. Particular attention is paid to the ion-temperature-gradient (ITG) instability and its character close to marginal stability [Floquet-type turbulence (Zocco et al., Phys. Rev. E, vol. 106, 2022, p. L013202) with no electron temperature gradient]. The flux tube version of the $\delta f$ code stella (Barnes et al., J. Comput. Phys., vol. 391, 2019, pp. 365–380) is used to run linear and nonlinear gyrokinetic simulations with kinetic electrons. The nature of the dominant instability depends on the wavelength perpendicular to the magnetic field, and the results are conveniently displayed in stability diagrams that take this dependence into account. This approach highlights the presence of universal instabilities, which are less unstable but have longer wavelengths than other modes. A quasi-linear estimate of the heat flux suggests they are relevant for transport. Close to the stability threshold, the linear eigenmodes and turbulence form highly extended structures along the computational domain if the magnetic shear is small. Numerical experiments and diagnostics are undertaken to assess the resulting radial localisation of the turbulence, which affects the interaction of the latter with zonal flows. Increasing the amplitude of the magnetic shear (e.g.through current drive) has a stabilising effect on the turbulence and, thus, reduces the nonlinear energy transport.

We introduce an extension of the particle-in-cell method that captures the Landau collisional effects in the Vlasov–Maxwell–Landau equations. The method arises from a regularisation of the variational formulation of the Landau equation, leading to a discretisation of the collision operator that conserves mass, charge, momentum and energy, while increasing the (regularised) entropy. The collisional effects appear as a fully deterministic effective force, thus the method does not require any transport–collision splitting. The scheme can be used in arbitrary dimension, and for a general interaction, including the Coulomb case. We validate the scheme on scenarios such as the Landau damping, the two-stream instability and the Weibel instability, demonstrating its effectiveness in the numerical simulation of plasma.