A collisionless shock structure results from the nonlinear interaction between charged particles and electromagnetic fields. Yet, a collisionless shock is globally governed by the mass, momentum and energy conservation requirements. A stable shock structure must ensure that the fluxes of the conserved quantities are constant on average, and, therefore, is determined by this necessity. Here, we study an observed high upstream temperature high Mach number shock and show that the conservation laws cannot be fulfilled unless the shock is spatially inhomogeneous along the shock front and time-dependent.

The pellet ablation mechanism is an interesting subject for plasma fuelling in fusion plasmas. In GAMMA 10/PDX, pellet injection experiments for higher density plasma production are planned to conduct detached plasma experiments in the higher density plasma condition. We measured the pellet ablation cloud by using the two-directional simultaneous photography system in GAMMA 10/PDX. The tomography reconstruction technique was used for considering the pellet trajectory in the plasma and pellet ablation. The three-dimensional pellet trajectory and pellet ablation images in the plasma were clearly obtained for the first time, to the best of our knowledge.

A unique field-reversed configuration (FRC) experiment is presently being assembled at the Plasma Technology Research Institute, KFE. It is a compact small-scale FRC device, which uses a set of radio frequency (RF) antennas to produce an internal E × B that drives the electrons for current-drive, in which E is the electric field and B is the magnetic field. This is very similar to the rotating magnetic field (RMF) current-drive, where the horizontal and vertical antennas are driven 90° out of phase. For this device, the RF antennas are arranged differently than the RMF. The RF antennas, being two separate sets, are positioned inside the vacuum chamber. Each set consists of 8 coils, for a total of 16 coils, where 80~100 kHz sine and cosine waveform currents are applied. One set of coils generates a radial B-field, while the other set provides an E-field in the z-direction. As the phase changes, the E and B fields are switched by these two sets. Nevertheless, E × B propagates in the same θ-direction so that this allows the electrons to rotate around the circumference of the device. The FRC device will test wave heating by launching 2.45 GHz microwaves. Also, passive stabilizers are positioned at each end to provide extra stability while preventing tilt instability. The experiment is expected to produce its first plasma in 2025.

The extended guiding-centre Lagrangian equations of motion are derived by the Lie-transform perturbation method under the assumption of time-dependent and inhomogeneous electric and magnetic fields that satisfy the standard guiding-centre space–time orderings. Polarization effects are introduced into the Lagrangian dynamics by the inclusion of the polarization drift velocity in the guiding-centre velocity and the appearance of finite-Larmor-radius corrections in the guiding-centre Hamiltonian and guiding-centre Poisson bracket.

We derive an advanced surrogate model for predicting turbulent transport at the edge of tokamaks driven by electron temperature gradient (ETG) modes. Our derivation is based on a recently developed sensitivity-driven sparse grid interpolation approach for uncertainty quantification and sensitivity analysis at scale, which informs the set of parameters that define the surrogate model as a scaling law. Our model reveals that ETG-driven electron heat flux is influenced by the safety factor $q$, electron beta $\beta _e$ and normalized electron Debye length $\lambda _D$, in addition to well-established parameters such as the electron temperature and density gradients. To assess the trustworthiness of our model's predictions beyond training, we compute prediction intervals using bootstrapping. The surrogate model's predictive power is tested across a wide range of parameter values, including within-distribution testing parameters (to verify our model) as well as out-of-bounds and out-of-distribution testing (to validate the proposed model). Overall, validation efforts show that our model competes well with, or can even outperform, existing scaling laws in predicting ETG-driven transport.

Quasisymmetry (QS), a hidden symmetry of the magnetic field strength, is known to support nested flux surfaces and provide superior particle confinement in stellarators. In this work, we study the ideal magnetohydrodynamic (MHD) equilibrium and stability of high-beta plasma in a large-aspect-ratio stellarator. In particular, we show that the lowest-order description of a near-axisymmetric equilibrium vastly simplifies the problem of three-dimensional quasisymmetric MHD equilibria, which can be reduced to a standard elliptic Grad–Shafranov equation for the flux function. We show that any large-aspect-ratio tokamak, deformed periodically in the vertical direction, is a stellarator with approximate volumetric QS. We discuss exact analytical solutions and numerical benchmarks. Finally, we discuss the ideal ballooning and interchange stability of some of our equilibrium configurations.

The maser instability associated with the loss-cone distribution has been widely invoked to explain the radio bursts observed in the astrophysical plasma environment, such as aurora and corona. In the laboratory plasma of a tokamak, events reminiscent of these radio bursts have also been frequently observed as an electron cyclotron emission (ECE) burst in the microwave range ($\mathrm{\sim }2{f_{\textrm{ce}}}$ near the last closed flux surface) during transient magnetohydrodynamic events. These bursts have a short duration of ~10 μs and display a radiation spectrum corresponding to a radiation temperature ${T_{e,\textrm{rad}}}$ of over $30\ \textrm{keV}$ while the edge thermal electron temperature ${T_e}$ is only in the range of $1\ \textrm{keV}$. Suprathermal electrons can be generated through magnetic reconnection, and a loss-cone distribution can be generated through open stochastic field lines in the magnetic mirror of the near-edge region of a tokamak plasma. Radiation modelling shows that a sharp distribution gradient $\partial f/\partial {v_ \bot } > 0$ at the loss-cone boundary can cause a negative absorption of ECE radiation through the maser instability. The negative absorption then amplifies the radiation so that the microwave intensity is significantly stronger than the thermal value. The significant ${T_{e,\textrm{rad}}}$ from the simulations suggests the potential role of the loss-cone maser instability in generating the ECE burst in a tokamak.

The formation and evolution of unconfined counter-helicity spheromaks merging have been experimentally investigated by using a magnetized coaxial plasma gun. By comparing the time-dependent photodiode signals and plasma radiation images of counter-helicity spheromaks merging and plasma jets merging, it is found that the field-reversed configuration (FRC) plasma formed by counter-helicity spheromaks merging has a distinct contour and a long maintenance time. For plasma jets merging, the resulting plasma has no discernible contours and a shorter lifetime. In addition, it is inferred from these data that stagnation heating and magnetic reconnection events occur during the counter-helicity spheromaks merging, causing a rapid rise in plasma pressure at the merging midplane and sharp kinks in the field lines near the merger region. By changing different operating parameters and observing the impact on the merger characteristics, it is suggested that the qualitative dynamics of the FRC plasma depends on the balance between the plasma pressure and the magnetic pressure. The high discharge voltage breaks the equilibrium in the merged body, while the large gas-puffed mass just weakens the compression effect of the merged body. These results give us an intuitive understanding of the counter-helicity spheromak merger process and its dependence on discharge parameters, and also provide a distinct perspective for the optimal design of FRC.

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.

Prompted by the relevant problem of temperature inversion (i.e. gradient of density anti-correlated to the gradient of temperature) in astrophysics, we introduce a novel method to model a gravitationally confined multi-component collisionless plasma in contact with a fluctuating thermal boundary. We focus on systems with anti-correlated (inverted) density and temperature profiles, with applications to solar physics. The dynamics of the plasma is analytically described via the coupling of an appropriated coarse-grained distribution function and a temporally coarse-grained Vlasov dynamics. We derive a stationary solution of the system and predict the inverted density and temperature profiles of the two species for scenarios relevant for the corona. We validate our method by comparing the analytical results with kinetic numerical simulations of the plasma dynamics in the context of the two-species Hamiltonian mean-field model. Finally, we apply our theoretical framework to the problem of the temperature inversion in the solar corona, obtaining density and temperature profiles in remarkably good agreement with the observations.

An open problem of the derivation of the relativistic Vlasov equation for systems of charged particles moving with velocities up to the speed of light and creating the electromagnetic field in accordance with the full set of the Maxwell equations is considered. Moreover, the method of derivation is illustrated on the non-relativistic kinetic model. Independent derivation of the relativistic hydrodynamics is also demonstrated. The key role of these derivations of the hydrodynamic and kinetic equations includes the explicit operator of averaging on the physically infinitesimal volume suggested by L.S. Kuzmenkov.

The two-time energy spectrum of weak magnetohydrodynamic turbulence is found by applying a wave-turbulence closure to the cumulant hierarchy constructed from the dynamical equations. Solutions are facilitated via asymptotic expansions in terms of the small parameter $\varepsilon$, describing the ratio of time scales corresponding to Alfvénic propagation and nonlinear interactions between counter-propagating Alfvén waves. The strength of nonlinearity at a given spatial scale is further quantified by an integration over all possible delta-correlated modes compliant in a given set of three-wave interactions that are associated with energy flux through the said scale. The wave-turbulence closure for the two-time spectrum uncovers a secularity occurring on a time scale of order $\varepsilon ^{-2}$, and the asymptotic expansion for the spectrum is reordered in a manner comparable to the one-time case. It is shown that for the regime of stationary turbulence, the two-time energy spectrum exponentially decays on a lagged time scale $(\varepsilon ^2 \gamma _k^s)^{-1}$ in proportion to the strength of the associated three-wave interactions, characterized by nonlinear decorrelation frequency $\gamma _k^s$. The scaling of the form $k_{\perp } v_0 \chi _0$ exhibited by this frequency is reminiscent of random sweeping by the outer scale with characteristic fluctuation velocity $v_0$ that is modified due to competition with Alfvénic propagation (characterized by $\chi _0$) at the said scale. A brief calculation of frequency broadening of the power spectrum due to nonlinear interactions is also presented.

We present new stellarator equilibria that have been optimized for reduced turbulent transport using nonlinear gyrokinetic simulations within the optimization loop. The optimization routine involves coupling the pseudo-spectral GPU-native gyrokinetic code GX with the stellarator equilibrium and optimization code DESC. Since using GX allows for fast nonlinear simulations, we directly optimize for reduced nonlinear heat fluxes. To handle the noisy heat flux traces returned by these simulations, we employ the simultaneous perturbation stochastic approximation (SPSA) method that only uses two objective function evaluations for a simple estimate of the gradient. We show several examples that optimize for both reduced heat fluxes and good quasi-symmetry as a proxy for low neoclassical transport. Finally, we run full transport simulations using the T3D stellarator transport code to evaluate the changes in the macroscopic profiles.

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.

We present the results of numerical simulation by two-dimensional hybrid particle-in-cell code of high-beta plasma with hot ions in an axisymmetric mirror machine. Two particular effects are discussed: the self-rotating of plasma with Maxwellian ions in regime of diamagnetic confinement and the excitation of axisymmetric magnetosonic waves in a high-beta plasma with sloshing ions.

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.

The impact of an edge radial electric field on the particle orbits and the orbital spectrum in an axisymmetric toroidal magnetic equilibrium is investigated using a guiding centre canonical formalism. Poloidal and bounce/transit-averaged toroidal precession frequencies are calculated, highlighting the role of the radial electric field. The radial electric field is shown to drastically modify the resonance conditions between particles with certain kinetic characteristics and specific perturbative non-axisymmetric modes, and to enable the formation of transport barriers. The locations of the resonances and the transport barriers that determine the particle, energy and momentum transport are shown to be accurately pinpointed in the phase space by employing the calculated orbital frequencies.

The self-consistent propagation of electrical impulses and of the accompanying distortions of the electron surface in the framework of a cold plasma model with a sharp boundary has been described with help of a derived system of two equations. The method of ‘shallow water theory’ has been applied for the case of bounded plasma and deriving an equation with which to link the spatial and temporal structures and evolution of the boundary curvature and the surface charge. Under certain conditions, such perturbations can propagate along the boundary without changing their shape for a long distance. An approximate analytical solution has been found, and numerical calculations have been performed. Mutual connections between basic parameters of the considered perturbations (velocity components, electrostatic field, etc.) have been presented.

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.

Some stellarators tend to benefit from favourable average magnetic curvature for trapped particles when the plasma pressure is sufficiently high. This so-called maximum-$J$ property has several positive implications, such as good fast-particle confinement, magnetohydrodynamic stability and suppression of certain trapped-particle instabilities. This property cannot be attained in quasisymmetric stellarators, in which deeply trapped particles experience average bad curvature and therefore precess in the diamagnetic direction close to the magnetic axis. However, quasi-isodynamic stellarators offer greater flexibility and allow the average curvature to be favourable and the precession to be reversed. We find that it is possible to design such stellarators so that the maximum-$J$ condition is satisfied for the great majority of all particles, even when the plasma pressure vanishes. The qualitative properties of such a stellarator field can be derived analytically by examining the most deeply and the most shallowly trapped particles, although some small fraction of the latter will inevitably not behave as desired. However, through numerical optimisation, we construct a vacuum field in which 99.6 % of all trapped particles satisfy the maximum-$J$ condition.