The Hosking integral, which characterizes magnetic helicity fluctuations in subvolumes, is known to govern the decay of magnetically dominated turbulence. Here, we show that, when the evolution of the magnetic field is controlled by the motion of electrons only, as in neutron star crusts, the decay of the magnetic field is still controlled by the Hosking integral, but now it has effectively different dimensions than in ordinary magnetohydrodynamic (MHD) turbulence. This causes the correlation length to increase with time $t$ like $t^{4/13}$ instead of $t^{4/9}$ in MHD. The magnetic energy density decreases like $t^{-10/13}$, which is slower than in MHD, where it decays like $t^{-10/9}$. These new analytic results agree with earlier numerical simulations for the non-helical Hall cascade.

Some internal transport barriers in tokamaks have been related to the vicinity of extrema of the plasma equilibrium profiles. This effect is numerically investigated by considering the guiding-centre trajectories of plasma particles undergoing $\boldsymbol {E}\times \boldsymbol {B}$ drift motion, considering that the electric field has a stationary non-monotonic radial profile and an electrostatic fluctuation. In addition, the equilibrium configuration has a non-monotonic safety factor profile. The numerical integration of the equations of motion yields a symplectic map with shearless barriers. By changing the safety factor profile parameters, the appearance and breakup of these shearless curves are observed. The shearless curve's successive breakup and recovery are explained using concepts from bifurcation theory. We also present bifurcation sequences associated with the creation of multiple shearless curves. Physical consequences of scenarios with multiple shearless curves are discussed.

We present a general method for optimizing the configuration of an experimental diagnostic to minimize uncertainty and bias in inferred quantities from experimental data. The method relies on Bayesian inference to sample the posterior using a physical model of the experiment and instrument. The mean squared error (MSE) of posterior samples relative to true values obtained from a high fidelity model (HFM) across multiple configurations is used as the optimization metric. The method is demonstrated on a common problem in dense plasma research, the use of radiation detectors to estimate physical properties of the plasma. We optimize a set of filtered photoconducting diamond detectors to minimize the MSE in the inferred X-ray spectrum, from which we can derive quantities like the electron temperature. In the optimization we self-consistently account for uncertainties in the instrument response with appropriate prior probabilities. We also develop a penalty term, acting as a soft constraint on the optimization, to produce results that avoid negative instrumental effects. We show results of the optimization and compare with two other reference instrument configurations to demonstrate the improvement. The MSE with respect to the total inferred X-ray spectrum is reduced by more than an order of magnitude using our optimized configuration compared with the two reference cases. We also extract multiple other quantities from the inference and compare with the HFM, showing an overall improvement in multiple inferred quantities like the electron temperature, the peak in the X-ray spectrum and the total radiated energy.

A general infrastructure for tokamak controllers based on data-driven neural net models is presented. The paradigm allows for more flexible choices of both the underlying model and the desired controlled variables and targets. The system is implemented and tested on the DIII-D tokamak, enacting simultaneous pressure and temperature control via a finite-set model-predictive controller. Traditional control methods such as proportional–integral–derivative (PID) have proven effective for decoupled control tasks, but scale poorly when trying to achieve more complicated goals such as full state control. This is exactly where model-based controllers succeed.

Simulations of high-energy density physics often need non-local thermodynamic equilibrium opacity data. These data, however, are expensive to produce at relatively low fidelity. It is even more so at high fidelity such that the opacity calculations can contribute 95 % of the total computation time. This proportion can even reach large proportions. Neural networks can be used to replace the standard calculations of low-fidelity data, and the neural networks can be trained to reproduce artificial, high-fidelity opacity spectra. In this work, it is demonstrated that a novel neural network architecture trained to reproduce high-fidelity krypton spectra through transfer learning can be used in simulations. Further, it is demonstrated that this can be done while achieving a relative per cent error of the peak radiative temperature of the hohlraum of approximately 1 % to 4 % while achieving a 19.4$\times$ speed up.

Plasma vertical displacement control is essential for the stable operation of tokamak devices. The traditional plasma vertical displacement calculation method is not suitable for balancing speed and accuracy simultaneously, which is necessary for real-time feedback control. In this study, neural networks are used to rapidly detect vertical displacement recognition. Based on a fully connected neural network, the vertical displacement calculation model is trained and tested using magnetic data of approximately 2000 shots. To compare the effects of different inputs on vertical displacement calculation, different magnetic measurement diagnostic signals are used to train and test the model. Compared with a full magnetic measurement dataset, 39 magnetic measurement signals (38 magnetic probes and plasma current) show better accuracy with mean square error <0.0005. The model is tested using historical experimental data, and it demonstrates accurate vertical displacement calculation even in the case of a vertical displacement event. In general, neural network algorithm has great application potential in vertical displacement calculation.

The inclusion of kinetic effects into fluid models has been a long standing problem in magnetic reconnection and plasma physics. Generally, the pressure tensor is reduced to a scalar which is an approximation used to aid in the modelling of large scale global systems such as the Earth's magnetosphere. This unfortunately omits important kinetic physics which have been shown to play a crucial role in collisionless regimes. The multi-fluid ten-moment model, however, retains the full symmetric pressure tensor. The ten-moment model is constructed by taking moments of the Vlasov equation up to second order, and includes the scalar density, the vector bulk-flow and the symmetric pressure tensor for a total of ten separate components. Use of the multi-fluid ten-moment model requires a closure which truncates the cascading system of equations. Here we look to leverage data-driven methodologies to seek a closure which may improve the physical fidelity of the ten-moment multi-fluid model in collisionless regimes. Specifically, we use the sparse identification of nonlinear dynamics (SINDy) method for symbolic equation discovery to seek the truncating closure from fully kinetic particle-in-cell simulation data, which inherently retains the relevant kinetic physics. We verify our method by reproducing the ten-moment model from the particle-in-cell (PIC) data and use the method to generate a closure truncating the ten-moment model which is analysed through the nonlinear phase of reconnection.

Electron resonant interactions with electromagnetic whistler-mode waves play an important role in electron flux dynamics in various space plasma systems: planetary radiation belts, bow shocks, solar wind and magnetic reconnection regions. Two key wave characteristics determining the regime of wave–particle interactions are the wave intensity and the wave coherency. The classical quasi-linear diffusion approach describes well electron diffusion by incoherent and low-amplitude waves, whereas the nonlinear resonant models describe electron phase bunching and trapping by highly coherent intense waves. This study is devoted to the investigation of the regime of electron resonant interactions with incoherent but intense waves. Although this regime is characterized by electron diffusion, we show that diffusion rates scale linearly with the wave amplitude, $D\propto B_w$, in contrast to the quasi-linear diffusion scaling $D_{QL}\propto B_w^2$. Using observed wave amplitude distributions, we demonstrate that the quasi-linear diffusion model significantly overestimates electron scattering by incoherent, but intense whistler-mode waves. We discuss the results obtained in the context of simulations of long-term electron flux dynamics in space plasma systems.

The formation time of the surrounding sheath of Langmuir probes in an ionospheric plasma has been studied to better understand the constraints this puts on the sampling frequency of a probe. A fully kinetic three-dimensional particle-in-cell model is used to simulate the temporal effects in the electron saturation region as the sheath forms. The stability of the probe current and the stability of the ion and electron density in the vicinity of the probe have been used to evaluate when the sheath was formed. Simulated results were compared with theoretical models and are in good agreement with the theoretical results. This shows that theoretical models can be used as guidance to estimate the formation time and to determine the sampling rate for a swept bias Langmuir system. Our results also show that the formation time is less affected by the plasma temperature and bias voltage as we move into the thick sheath regime, and will instead be determined by the plasma density. The presented results also show that applying a step function to the probe could be used to characterise ions species composition, or to estimate the ion density.

A systematic simulation study of the $n/m=1/1$ instability driven by energetic counter-passing particles in tokamak plasmas has been carried out using the kinetic-MHD (Magnetohydrodynamics) hybrid code M3D-K. The safety factor's radial profile is monotonically increasing with central value $q_0$ less than unity. The linear simulation results show that the instability is either a $m/n=1/1$ energetic particle mode or a $m/n=1/1$ global Alfvén eigenmode depending on the value of the central safety factor. The mode frequencies are close to the tip of Alfvén continuum spectrum at the magnetic axis. The excited modes are radially localized near the magnetic axis well within the safety factor $q=1$ surface. The main wave particle resonance is found to be $\omega _\phi +2\omega _\theta =\omega$, where ω is the mode frequency. The nonlinear simulation results show that there is a long period of quasi-steady-state saturation phase with frequency chirping up after initial saturation. Correspondingly, the energetic particle distribution with low energies is flattened in the core of the plasma. After this quasi-steady phase, the mode amplitude grows again and frequency jumps down to a low value corresponding to a new mode similar to the energetic co-passing particle-driven low-frequency fishbone while the energetic particle distribution is flattened for higher energies in the core of plasma.

Local gyrokinetic simulations, performed with the GENE code, are used to investigate the interaction between (negative) triangularity $\delta$ and magnetic shear $s$, in both ion temperature gradient and trapped electron mode dominated plasmas. Magnetic shear turns out to influence in a non-trivial way the effect of negative triangularity. Also, $\delta <0$ is found to lead to a reduction of fluxes when $s>1$ but not anymore when shear is reduced. In certain parameter regimes, this effect can be inverted, up to obtaining higher fluxes when $\delta <0$ with respect to its $\delta >0$ counterpart.

We present Vlasov–Poisson three-dimensional linear stability analysis of an initially planar electron hole structure, solving for the distribution function by integration along unperturbed orbits. The non-sinusoidal potential perturbation shape (parallel to $B$) is expanded in eigenfunctions of the adiabatic Poisson operator, generalizing the prior assumption of a rigid shift of the equilibrium. We show that the shiftmode is then modified by a second discrete mode plus an integral over a continuum of wave-like modes. A rigorous treatment shows that the continuum can be approximated effectively by a single mode that satisfies the external wave dispersion relation, thus making the perturbation a weighted sum of three modes. We find numerically the solution for the complex instability frequency, and the corresponding three mode amplitudes determining the perturbation eigenmode. This multimode analysis refines the accuracy of the prior single-mode results, giving slightly higher growth rates at most parameters, as expected from the extra mode shape freedom. Oscillating modes near stability boundaries have larger mode distortions which help explain particle-in-cell simulations that observe instability up to ${\sim }20$ % beyond the prior shiftmode thresholds, and narrowing of the perturbation. At high magnetic field, the multimode analysis predicts a reduction of the already small growth rate.

Alpha particle confinement is one of the most demanding issues for stellarators. It now seems clear that it is possible to design optimized stellarators that confine the background plasma at near tokamak radial transport levels. Moreover, adequate collisionless alpha particle confinement is possible in the core of a highly optimized stellarator. Here, the collisional confinement of barely trapped alphas in an optimized stellarator is considered by accounting for the resonance due to the reversal in direction of the drift within a flux surface and investigating the sensitive role of magnetic shear in keeping this resonance close to the passing boundary in some nearly quasisymmetric stellarator configurations. The treatment relies on a narrow collisional boundary layer formulation that combines the responses of both these resonant pitch angle alphas and the remaining barely trapped alphas. A novel merged regime treatment leads to explicit expressions for the energy diffusivity for both superbanana plateau (or resonant plateau) and $\sqrt \nu$ transport in the large aspect ratio limit for a slowing down tail alpha distribution function, where $\nu$ is the effective pitch angle scattering collision frequency of the trapped alphas off the background ions. Depending on the details of the optimization scheme and the sign of the magnetic shear, modest magnetic shear can be used to reduce superbanana (or resonant) plateau transport to below the $\sqrt \nu$ transport level. In addition, a quasilinear equation retaining spatial diffusion is derived for a general alpha distribution function that allows the radial alpha transport to modify the distribution so it is no longer isotropic in velocity space.

The theory of terahertz (THz) wave emission at the oblique incidence of a focused s-polarized laser pulse on the boundary of a rarefied plasma is developed. The angular, spectral and energy characteristics of the THz signal as a function of the focal spot size and the incidence angle of laser radiation, as well as the plasma density, are investigated. It is shown that the THz radiation energy increases with a decrease in the laser pulse focal spot and has the maximum value when the tightly focused laser pulse is incident at the angle of total reflection on the plasma boundary.

In this work, we revisit the linear gyro-kinetic theory of geodesic acoustic modes (GAMs) and derive a general dispersion relation for an arbitrary equilibrium distribution function of ions. A bi-Maxwellian distribution of ions is then used to study the effects of ion temperature anisotropy on GAM frequency and growth rate. We find that ion temperature anisotropy yields sensible modifications to both the GAM frequency and growth rate as both tend to increase with anisotropy and these results are strongly affected by the electron to ion temperature ratio.

A full-F isothermal gyro-fluid model and code (which is based on the full distribution function F compared to only small fluctuations) is extended to handle self-consistent coupling of multiple quasi-neutral ion species via the polarisation equation in the long wavelength approximation. The numerical model is used to determine two-dimensional interchange driven ‘blob’ transport in a plasma with intrinsic impurity content for a range of impurity parameters. With the same model, the self-consistent advective interaction of a main plasma species blob with a non-trace impurity cloud is studied. For homogeneous impurity distributions an increased effective mass reduces blob transport, whereas it is found that localised impurity clouds can lead either to acceleration or slowing down of blob propagation depending on the alignment of the impurity density gradient during the acceleration phase of the main ion species blob.

Machine learning techniques are used to construct models capable of inferring plasma state variables from non-emissive (LP) and emissive (EP) cylindrical Langmuir probes under conditions in which standard analytic theories are not applicable. Synthetic data sets, consisting of plasma parameters and probe characteristics computed kinetically in the orbital motion theory framework, are used to train and test regression models to infer electron densities, temperatures, and plasma potentials. Model skill metrics are introduced to determine uncertainty margins on inferred parameters, when models are applied to test sets not involved in the model optimization process. The different scalings and transformations required to obtain optimal accuracy are described in each case considered for both LPs and EPs. Excellent inferences are made for all three parameters considered from LP characteristics, but owing to the strong dependence on the plasma potential, and weak dependences on electron temperature and density with EPs, only plasma potential inferences are reported with acceptable accuracy for this type of probe. Our findings demonstrate that the combination of kinetic simulations and machine learning techniques is a promising and practical way to infer plasma parameters efficiently from cylindrical probes, under conditions beyond, and more general than those under which commonly used analytic approximations are valid.

High-power-density tokamaks offer a potential solution to design cost-effective fusion devices. One way to achieve high power density is to operate at a high $\beta$ value (the ratio of thermal to magnetic pressure), i.e. $\beta \sim 1$. However, a $\beta \sim 1$ state may be unstable to various pressure- and current-driven instabilities or have unfavourable microstability properties. To explore these possibilities, we generate $\beta \sim 1$ equilibria and investigate their stability. First, we demonstrate the generation of high-$\beta$ equilibria with the computer code VMEC. We then analyse these equilibria to determine their stability against the infinite-$n$ ideal-ballooning mode. We follow that by engaging in a detailed microstability study using the GS2 code, beginning with assessments of electrostatic ion-temperature-gradient and trapped election mode instabilities. We observe interesting behaviour for the high-$\beta$ equilibria – stabilization of these modes through two distinct mechanisms – large negative local shear and reversal of electron precession drift. Finally, we perform electromagnetic gyrokinetic simulations and observe enhanced stability in the outer core of high-$\beta$ equilibria and absence of kinetic ballooning modes in the negative-triangularity, high-$\beta$ equilibria. The enhanced outer-core stability of high-$\beta$ equilibria is different from their lower-$\beta$ counterparts and offers an alternative, potentially favourable regime of tokamak operation.

A novel curved surface nanowire target is proposed to improve the cutoff energy of accelerated protons via target normal sheath acceleration. The interaction of a laser of intensity $1.37\times 10^{20}\ {\rm W}\ {\rm cm}^{-2}$ with a curved surface nanowire target is studied by two-dimensional particle-in-cell simulations. The numerical results indicate that the sheath electric field at the target rear side is significantly enhanced by this simple target design, compared with using the planar nanowire target. The transverse motion of hot electrons is effectively confined and the energy density of electrons is naturally increased. A series of simulations with various target parameters is carried out to investigate the performance of this novel target. This tailored target may provide implications for generating high-quality proton beams in experiments.

In this research, the process of electron acceleration and wakefield generation by Gaussian-like (GL), super-Gaussian (SG) and Bessel–Gaussian (BG) laser pulses through cold collisionless plasma in the presence of a planar magnetostatic wiggler are studied. Three different types of laser spatial profiles, GL, SG and BG, are considered. Additionally, using the hydrodynamics fluid equations, Maxwell's equations as well as the perturbation technique for GL, SG and BG laser pulses in the weakly nonlinear regime and in the presence of a planar magnetostatic wiggler, governing equations for analysing the laser wakefield and electron acceleration have been derived and compared correspondingly. In addition, the effect of some important factors, including the wiggler field strengths, laser intensity, pulse length, plasma electron density and laser frequency on the wakefield and the electron energy gain, have been investigated. Numerical results show that enhancing the wiggler magnetic field results in an increase in the amplitude of the wakefield. Furthermore, it is observed that in comparison with the wakefield amplitude excited by SG and GL laser pulses, the amplitude of the wakefield excited by BG laser pulse is larger when the wiggler field is enhanced. Moreover, it is realized that the type of the laser profile, selected laser parameters and wiggler magnetic field are the most decisive and effective factors in the wakefield amplitude and shape of wakefield generation through cold collisionless plasma. Also, it is seen that as the pulse length declines, the amplitude of the wakefield increases, and correspondingly the resonance positions shift to higher ${({\varOmega _w}/{\varOmega _p})_{max}}$ values.