A Bayesian optimization framework is used to investigate scenarios for disruptions mitigated with combined deuterium and neon injection in ITER. The optimization cost function takes into account limits on the maximum runaway current, the transported fraction of the heat loss and the current quench time. The aim is to explore the dependence of the cost function on injected densities, and provide insights into the behaviour of the disruption dynamics for representative scenarios. The simulations are conducted using the numerical framework Dream (Disruption Runaway Electron Analysis Model). We show that, irrespective of the quantities of the material deposition, multi-megaampere runaway currents will be produced in the deuterium–tritium phase of operations, even in the optimal scenarios. However, the severity of the outcome can be influenced by tailoring the radial profile of the injected material; in particular, if the injected neon is deposited at the edge region it leads to a significant reduction of both the final runaway current and the transported heat losses. The Bayesian approach allows us to map the parameter space efficiently, with more accuracy in favourable parameter regions, thereby providing us with information about the robustness of the optima.

The problem of the electron dynamics on a closed magnetic field line passing through a high-$Z$ plasmoid is considered. The electron kinetic equation is integrated over bounce motion and pitch angle, reducing the independent variables to a single adiabatic invariant plus time. Integration of the full Landau self-collision operator is carried out exactly, resulting in a nonlinear integro-differential operator in the new invariant. Conservation laws and the $H$ theorem of the integrated self-collision operator are proven. Numerical solutions of the integrated kinetic equation are obtained with a self-consistent quasineutral electric potential, given the initial condition of a cold plasmoid immersed in a hot ambient plasma. The fact that cold electrons are deeply trapped in a potential with a parabolic peak leads to exactly 3/4 the usual rate of collisional heating by the ambient plasma, independent of any other parameters.

A collisionless shock is a self-organized structure where fields and particle distributions are mutually adjusted to ensure a stable mass, momentum and energy transfer from the upstream to the downstream region. This adjustment may involve rippling, reformation or whatever else is needed to maintain the shock. The fields inside the shock front are produced due to the motion of charged particles, which is in turn governed by the fields. The overshoot arises due to the deceleration of the ion flow by the increasing magnetic field, so that the drop of the dynamic pressure should be compensated by the increase of the magnetic pressure. The role of the overshoot is to regulate ion reflection, thus properly adjusting the downstream ion temperature and kinetic pressure and also speeding up the collisionless relaxation and reducing the anisotropy of the eventually gyrotropized distributions.

Laser-plasma instabilities (LPI) play a detrimental role in energy coupling to the target in inertial confinement fusion (ICF). The recent development of applied strong magnetic fields for use in ICF and laboratory astrophysics experiments has opened opportunities to investigate the role of external magnetic fields on LPIs. Recent numerical studies have shown that stimulated Raman scattering (SRS) can be mitigated by external magnetic fields in the kinetic regime of the instability and warrant systematic experimental studies to validate modelling. To this end, we design experiments at the OMEGA-EP laser facility to investigate the effect of an external perpendicular $B$-field of 5–30 T on the backscattered light spectrum from a gas-jet target. We present measurements from a proof-of-principle experiment, where the backward-SRS (BSRS) is in the kinetic regime, for which the magnetization is expected to produce the greatest effects on instability growth. New simulations motivated by this experiment are used to inform the proposal of an upgraded experimental design. Our simulation predictions show that the new design is suited to experimentally demonstrating BSRS mitigation by an external magnetic field, despite the magnetization effects on the hydrodynamics, as well as the inherent temporal and spatial variations in plasma conditions.

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.

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.

Gyrokinetic theories, even ‘global’ models, typically rely on a separation in scale (in perpendicular wavelength) between the fluctuations and the system scale. In such models direct simulation of system-scale dynamics like magnetohydrodynamic (MHD) motion is formally not consistent. Drift-kinetic theory, on the other hand, may be directly applied to model system-scale MHD-ordered behaviour. I review the long-wavelength limit of standard gyrokinetics and drift kinetics to present the relationships between these theories in an elementary fashion. This provides a pathway to global gyrokinetic modelling, resulting in an approach that is structurally similar to kinetic MHD, and I present dynamical equations for solving global field evolution in this framework. Departures from certain earlier global gyrokinetic theories include the appearance of magnetosonic (fast) modes, and the cross-coupling of the parallel and perpendicular currents with perpendicular and parallel magnetic field components. A periodic two-dimensional testcase is outlined as a benchmarking and implementation target, to help clarify practical aspects of these theories, with minimal complexity in terms of boundary conditions, and a proof-of-principle implementation of a field-solver is exhibited. To motivate this work, I first illustrate certain limitations of existing global gyrokinetic frameworks and directly identify how scale separation approximations lead to certain ‘missing’ system-scale field terms in global gyrokinetics, largely as a result of simplifications associated with the field representation in terms of $A_{\|}$ and $B_{\|}$. As a result, the currents in the gyrokinetic Ampère's law resulting from a gyrokinetic equilibrium distribution do not match the currents implied by Ampère's law in a force-balance MHD equilibrium. I present a simple choice of equilibrium distribution function whose drift-kinetic currents are consistent with MHD currents; a specific Grad–Shafranov equilibrium is used to illustrate the size of the components of the parallel currents.

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.

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.

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.

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.

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.

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.

A method is demonstrated to rapidly calculate the shapes and properties of quasi-axisymmetric and quasi-helically symmetric stellarators. In this approach, optimization is applied to the equations of magnetohydrodynamic equilibrium and quasisymmetry, expanded in the small distance from the magnetic axis, as formulated by Garren & Boozer [Phys. Fluids B, vol. 3, 1991, p. 2805]. Due to the reduction of the equations by the expansion, the computational cost is significantly reduced, to times of the order of 1 cpu second, enabling wide and high-resolution scans over parameter space. In contrast to traditional stellarator optimization, here, the cost function serves to maximize the volume in which the expansion is accurate. A key term in the cost function is $\| \boldsymbol {\nabla }\boldsymbol B \|$, the norm of the magnetic field gradient, to maximize scale lengths in the field. Using this method, a database of $5\times 10^5$ optimized configurations is calculated and presented. Quasisymmetric configurations are observed to exist in continuous bands, varying in the ratio of the magnetic axis length to average major radius. Several qualitatively new types of configuration are found, including quasi-helically symmetric fields in which the number of field periods is two or more than six.

Plasma jets are widely investigated both in the laboratory and in nature. Astrophysical objects such as black holes, active galactic nuclei and young stellar objects commonly emit plasma jets in various forms. With the availability of data from plasma jet experiments resembling astrophysical plasma jets, classification of such data would potentially aid in not only investigating the underlying physics of the experiments but also the study of astrophysical jets. In this work we use deep learning to process all of the laboratory plasma images from the Caltech Spheromak Experiment spanning two decades. We found that cosine similarity can aid in feature selection, classify images through comparison of feature vector direction and be used as a loss function for the training of AlexNet for plasma image classification. We also develop a simple vector direction comparison algorithm for binary and multi-class classification. Using our algorithm we demonstrate 93 % accurate binary classification to distinguish unstable columns from stable columns and 92 % accurate five-way classification of a small, labelled data set which includes three classes corresponding to varying levels of kink instability.

An important problem in nuclear fusion plasmas is the prediction and control of turbulence which drives the cross-field transport, thus leading to energy loss from the system and deteriorating confinement. Turbulence, being a highly nonlinear and multiscale process, is challenging to theoretically describe and computationally model. Most advanced computational models fall into one of the two categories: fluid or gyro-kinetic. They both come at a high computational cost and cannot be applied for routine simulation of plasma discharge evolution and control. Development of reduced models based on (physics informed) artificial neural networks could potentially fulfil the need for affordable simulations of plasma turbulence. However, the training requires an extensive data base and the obtained models lack extrapolation capability to scenarios not originally encountered during training. This leads to reduced models of limited validity which may not prove adequate for predicting scenarios in future machines. In contrast, we explore a data-driven model discovery approach based on sparse regression to infer governing nonlinear partial differential equations directly from the data. Our input data are generated by simulations of drift-wave turbulence according to the Hasegawa–Wakatani and modified Hasegawa–Wakatani models. Balancing model accuracy and complexity enables the reconstruction of the systems of partial differential equations accurately describing the dynamics simulated in the input data sets. Sparse regression is not data hungry and can be extrapolated to unexplored parameter ranges. We explore and demonstrate the potential of this approach for fusion plasma turbulence modelling. The findings show that the methodology is promising for the development of reduced and computationally efficient turbulence models as well as for existing model cross-validation.

Plasma-terminating disruptions in future fusion reactors may result in conversion of the initial current to a relativistic runaway electron beam. Validated predictive tools are required to optimise the scenarios and mitigation actuators to avoid the excessive damage that can be caused by such events. Many of the simulation tools applied in fusion energy research require the user to specify input parameters that are not constrained by the available experimental information. The conventional approach, where an expert modeller calibrates these input parameters based on domain knowledge, is prone to lead to an intractable validation challenge without systematic uncertainty quantification. Bayesian inference algorithms offer a promising alternative approach that naturally includes uncertainty quantification and is less subject to user bias in choosing the input parameters. The main challenge in using these methods is the computational cost of simulating enough samples to construct the posterior distributions for the uncertain input parameters. This challenge can be overcome by combining probabilistic surrogate modelling, such as Gaussian process regression, with Bayesian optimisation, which can reduce the number of required simulations by several orders of magnitude. Here, we implement this type of Bayesian optimisation framework for a model for analysis of disruption runaway electrons, and explore for simulations of current quench in a JET plasma discharge with an argon induced disruption. We use this proof-of-principle framework to explore the optimum input parameters with uncertainties in optimisation tasks ranging from one to seven dimensions. The relevant Python codes that are used in the analysis are available via https://github.com/aejarvin/BO_FOR_RE_SIMULATIONS/.

Understanding generation and mitigation of runaway electrons in disruptions is important for the safe operation of future tokamaks. In this paper we investigate the runaway dynamics in reactor-scale spherical tokamaks, focusing on a compact nominal design with a plasma current of 21 megaamperes (MA), 1.8 T magnetic field on axis and major radius of approximately 3 m. We study both the severity of runaway generation during unmitigated disruptions, and the effect that typical mitigation schemes based on massive material injection have on runaway production. The study is conducted using the numerical framework dream (Disruption Runaway Electron Analysis Model). We find that, in many cases, mitigation strategies are necessary to prevent the runaway current from reaching multi-MA levels. Our results indicate that, with a suitably chosen deuterium–neon mixture for mitigation, it is possible to achieve a tolerable runaway current and ohmic current evolution. However, this does not account for the runaway source due to wall activation, which has been found to severely limit successful mitigation at conventional aspect ratios, but whose definition requires a more complete wall specification. Furthermore, the majority of the thermal energy loss is found to happen through radial transport rather than radiation, which poses a risk of unacceptable localised heat loads.

We revise in detail and in a pedagogical way the analysis of the boundary layer theory of warm tearing modes in slab, reduced magnetohydrodynamics (MHD), when magnetic reconnection is driven by electron inertia and/or resistivity, and ion-sound Larmor radius effects are included. By comparison with the numerical solution of the corresponding eigenvalue problem, we interpret these results by means of a heuristic approach, which in the warm-electron regime, we show to be in general not feasible without knowledge of the scaling of the gradient of the magnetic flux function, differently from what happens in the cold-electron regimes. We put in evidence for a non-trivial relation between the first derivative of the magnetic flux function and of the velocity parallel to the neutral line, evaluated in its proximity, by thus providing insight to the multiple boundary layer analysis that Pegoraro & Schep (Plasma Phys. Control. Fusion, vol. 28, 1986, p. 647) first showed to be required in warm-tearing regimes. In this way, we also suggest and justify a general operational definition of the reconnecting layer width and we discuss the linear appearance of microscopic scales related to the gradients of the eigenfunctions of the tearing modes.