Motivated by explosive releases of energy in fusion, space and astrophysical plasmas, we consider the nonlinear stability of stratified magnetohydrodynamic equilibria against two-dimensional interchanges of straight magnetic-flux tubes. We demonstrate that, even within this restricted class of dynamics, the linear stability of an equilibrium does not guarantee its nonlinear stability: equilibria can be metastable. We show that the minimum-energy state accessible to a metastable equilibrium under non-diffusive two-dimensional dynamics can be found by solving a combinatorial optimisation problem. These minimum-energy states are, to good approximation, the final states reached by our simulations of destabilised metastable equilibria for which turbulent mixing is suppressed by viscosity. To predict the result of fully turbulent relaxation, we construct a statistical mechanical theory based on the maximisation of Boltzmann's mixing entropy. This theory is analogous to the Lynden-Bell statistical mechanics of collisionless stellar systems and plasma, and to the Robert–Sommeria–Miller theory of two-dimensional vortex turbulence. Our theory reproduces well the results of our numerical simulations for sufficiently large perturbations to the metastable equilibrium.

Electron cyclotron resonance ion thrusters (ECRITs) have the potential to be used for space gravitational wave detection due to their wide thrust range. However, an unclear understanding of dynamic processes of ECRITs with strongly coupled multi-operating parameters limits further improvements on thrust noise and response velocity by feedback control systems. An integrative mathematical model considering the non-Maxwell electron energy distribution function for ECRITs is validated by experiments and used to study the influence of operating parameters on the dynamic processes of thrusters, which provides a new simplified grid model. Simulation results show the response processes with microwave (MW) power can be divided into two stages. The characteristic times of the first and second stages are respectively several microseconds and 10 ms, which are respectively dominated by plasma motion and the volume effect. The overshoot of screen grid (SG) current decreases, while its response time remains unchanged when the response time of MW power is prolonged. The response time of SG current with a step increase of flow rate is approximately 10 ms, consistent with the volume effect. The SG current decreases with rise of flow rate for high flow rate operations due to the small increment of ion density limited by low electron temperature, the decrease of ion Bohm velocity and reduction of sheath extraction area. The influence of grid voltage on the dynamic process of the SG current depends on variation ranges of extraction capabilities. When variations of sheath extraction area are limited, the response time is 5 μs, consistent with plasma response time. It is prolonged to 0.5 ms if sheath extraction area variations are large because they cause obvious variations of plasma parameters in the discharge chamber. These dynamic results can not only facilitate designing feedback controllers of micro-propulsion systems for high-precision space missions, but also provide guidance for ion sources to generate highly stable or rapid-response ion beam.

The heat conductivity of a plasma is usually much higher along the magnetic field than across it, and, as a result, the presence of a magnetic island can significantly affect the temperature profile in its vicinity. Radiation energy losses, which depend sensitively on temperature, are thus strongly affected by magnetic islands. This phenomenon is explored in a simple mathematical setting, and it is shown that the presence of a magnetic island greatly enhances a plasma's capacity to radiate energy. In the limit of highly anisotropic heat conductivity, the steady-state heat conduction equation can be reduced to an ordinary differential equation. Although this equation operates in one dimension, the topology is not that of the real line, but corresponds to a rod with a cooling fin. As parameters such as the incoming heat flux or the radiation amplitude are varied, the radiation has a tendency to linger around the island, in particular in the region of the separatrix, and the total radiated energy is then significantly increased. The island acts as a ‘cooling fin’ to the plasma. Furthermore, the solutions exhibit bifurcations, where the location of the radiation zone suddenly changes.

The design of fusion devices is typically based on computationally expensive simulations. This can be alleviated using high aspect ratio models that employ a reduced number of free parameters, especially in the case of stellarator optimization where non-axisymmetric magnetic fields with a large parameter space are optimized to satisfy certain performance criteria. However, optimization is still required to find configurations with properties such as low elongation, high rotational transform, finite beta and good fast particle confinement. In this work, we train a machine learning model to construct configurations with favourable confinement properties by finding a solution to the inverse design problem, that is, obtaining a set of model input parameters for given desired properties. Since the solution of the inverse problem is non-unique, a probabilistic approach, based on mixture density networks, is used. It is shown that optimized configurations can be generated reliably using this method.

Quantum algorithms have been proposed to accelerate the simulation of the chaotic dynamical systems that are ubiquitous in the physics of plasmas. Quantum computers without error correction might even use noise to their advantage to calculate the Lyapunov exponent by measuring the Loschmidt echo fidelity decay rate. For the first time, digital Hamiltonian simulations of the quantum sawtooth map, performed on the IBM-Q quantum hardware platform, show that the fidelity decay rate of a digital quantum simulation increases during the transition from dynamical localization to chaotic diffusion in the map. The observed error per CNOT gate increases by $1.5{\times }$ as the dynamics varies from localized to diffusive, while only changing the phases of virtual RZ gates and keeping the overall gate count constant. A gate-based Lindblad noise model that captures the effective change in relaxation and dephasing errors during gate operation qualitatively explains the effect of dynamics on fidelity as being due to the localization and entanglement of the states created. Specifically, highly delocalized states that are entangled with random phases show an increased sensitivity to dephasing and, on average, a similar sensitivity to relaxation as localized states. In contrast, delocalized unentangled states show an increased sensitivity to dephasing but a lower sensitivity to relaxation. This gate-based Lindblad model is shown to be a useful benchmarking tool by estimating the effective Lindblad coherence times during CNOT gates and finding a consistent $2\unicode{x2013}3{\times }$ shorter $T_2$ time than reported for idle qubits. Thus, the interplay of the dynamics of a simulation with the noise processes that are active can strongly influence the overall fidelity decay rate.

Thanks to advances in plasma science and enabling technology, mirror machines are being reconsidered for fusion power plants and as possible fusion volumetric neutron sources. However, cross-field transport and turbulence in mirrors remains relatively understudied compared with toroidal devices. Turbulence and transport in mirror configurations were studied utilizing the flexible magnetic geometry of the Large Plasma Device (LAPD). Multiple mirror ratios from $M=1$ to $M=2.68$ and three mirror-cell lengths from $L=3.51$ to $L=10.86$ m were examined. Langmuir and magnetic probes were used to measure profiles of density, temperature, potential and magnetic field. The electric field-fluctuation-driven ${\tilde {\boldsymbol{E}}} \times {\boldsymbol{B}}$ particle flux, where $\boldsymbol{B}$ is the background field, was calculated from these quantities. Two probe correlation techniques were used to infer wavenumbers and two-dimensional structure. Cross-field particle flux and density fluctuation power decreased with increased mirror ratio. Core density and temperatures remain similar with mirror ratio, but radial line-integrated density increased. The physical expansion of the plasma in the mirror cell by using a higher field in the source region may have led to reduced density fluctuation power through the increased gradient scale length. This increased scale length reduced the growth rate and saturation level of rotational interchange and drift-like instabilities. Despite the introduction of magnetic curvature, no evidence of mirror-driven instabilities – interchange, velocity space or otherwise – were observed. For curvature-induced interchange, many possible stabilization mechanisms were present, suppressing the visibility of the instability.

The Cloudy photoionization codes have been employed to study a spherically distributed cloud, around an arbitrary planetary nebula, with core temperature 105 K. The ionization factor ${\chi (H)}$ is close to unity, in the inner face of the dusty plasma (DP) cloud, which follows a monotonic declining trend, afterwards. For hydrogen density ${n_H} = 10\;\textrm{c}{\textrm{m}^{ - 3}}$, an exponentially falling trend of temperature could be noticed. A grain charging$\setminus$discharging process is also witnessed, which is very common in a DP environment. For ${n_H} = 10\;\textrm{c}{\textrm{m}^{ - 3}}$, photoionization of grains is more common due to higher photon density; compared with ${n_H} > 10\;\textrm{c}{\textrm{m}^{ - 3}}$, where the grain–electron acquiring probability is maximum, because of significant electron density. Owing to the electrostatic interactions between the charged grain and the electrons, an unusual trend in temperature has been observed.

Two-dimensional particle-in-cell (PIC) simulations explore the collisionless tearing instability developing in a Harris equilibrium configuration in a pair (electron–positron) plasma, with no guide field, for a range of parameters from non-relativistic to relativistic temperatures and drift velocities. Growth rates match the predictions of Zelenyi & Krasnosel'skikh (Astron. Zh., vol. 56, 1979, pp. 819–832) modified for relativistic drifts by Hoshino (Astrophys. J., vol. 900, issue 1, 2020, p. 66) as long as the assumption holds that the thickness $a$ of the current sheet is larger than the Larmor radius $\rho _L$, with the fastest growing mode at $ka \approx 1/\sqrt {3}$. Aside from confirming these predictions, we explore the transitions from thick to thin current sheets and from classical to relativistic temperatures. We show that for thinner current sheets ($a< \rho _L$), the growth rate matches the prediction for the case $a=\rho _L$. We also explore the nonlinear evolution of the modes. While the wavenumber with the fastest growth rate initially matches the prediction of Zelenyi & Krasnosel'skikh (1979), these modes saturate moving the dominant mode to lower wavenumbers (especially for thick current sheets with low growth rates). Furthermore, at a late, nonlinear stage, the growth rate (initially following the growth rate prediction proportional to $(\rho _L/a)^{3/2} < 1$) increases faster than exponentially, reaching a maximum growth rate equivalent to the linear growth rate prediction at $\rho _L/a = 1$, before eventually saturating.

This paper explores structure formation in two-dimensional magnetohydrodynamic (MHD) turbulence as a modulational instability (MI) of turbulent fluctuations. We focus on the early stages of structure formation and consider simple backgrounds that allow for a tractable model of the MI while retaining the full chain of modulational harmonics. This approach allows us to systematically examine the validity of popular closures such as the quasilinear approximation and other low-order truncations. We find that, although such simple closures can provide quantitatively accurate approximations of the MI growth rates in some regimes, they can fail to capture the modulational dynamics in adjacent regimes even qualitatively, falsely predicting MI when the system is actually stable. We find that this discrepancy is due to the excitation of propagating spectral waves (PSWs) which can ballistically transport energy along the modulational spectrum, unimpeded until dissipative scales, thereby breaking the feedback loops that would otherwise sustain MIs. The PSWs can be self-maintained as global modes with real frequencies and drain energy from the primary structure at a constant rate until the primary structure is depleted. To describe these waves within a reduced model, we propose an approximate spectral closure that captures them and MIs on the same footing. We also find that introducing corrections to ideal MHD, conservative or dissipative, can suppress PSWs and reinstate the accuracy of the quasilinear approximation. In this sense, ideal MHD is a ‘singular’ system that is particularly sensitive to the accuracy of the closure within mean-field models.