Plasma Physics and Controlled Fusion

Particle-in-cell (PIC) methods have a long history in the study of laser-plasma interactions. Early electromagnetic codes used the Yee staggered grid for field variables combined with a leapfrog EM-field update and the Boris algorithm for particle pushing. The general properties of such schemes are well documented. Modern PIC codes tend to add to these high-order shape functions for particles, Poisson preserving field updates, collisions, ionisation, a hybrid scheme for solid density and high-field QED effects. In addition to these physics packages, the increase in computing power now allows simulations with real mass ratios, full 3D dynamics and multi-speckle interaction. This paper presents a review of the core algorithms used in current laser-plasma specific PIC codes. Also reported are estimates of self-heating rates, convergence of collisional routines and test of ionisation models which are not readily available elsewhere. Having reviewed the status of PIC algorithms we present a summary of recent applications of such codes in laser-plasma physics, concentrating on SRS, short-pulse laser-solid interactions, fast-electron transport, and QED effects.

The first stellarator design was a simple tube of plasma twisted and closed on itself in the form of a figure-8. The line of such devices, however, was quickly ended over concerns related to plasma stability. We revisit the figure-8 concept, re-imagined as a modern optimized stellarator, and find the potential for a high degree of stability, as well as exceptionally simple construction. In particular, the design that we find admits planar coils, and is the first quasi-isodynamic stellarator design to have this property. Our work is made possible by recent theoretical progress in the near-axis theory of quasi-isodynamic stellarators, combined with fundamental progress in the numerical solution of three-dimensional magnetohydrodynamic equilibria that cannot be well represented using traditional cylindrical coordinates.

During its 40 years of operations, the Joint European Torus (JET) tokamak has consistently pushed the physics and engineering boundaries of fusion research, providing the scientific community with a unique testing ground for theories and innovative ideas. This paper covers a selection of remarkable contributions of JET to various fields of tokamak science, from transport and plasma heating studies to plasma-wall interaction and D-T experiments, and their impact on the fusion research progress.

Disruptions present one of the leading concerns for reliable tokamak operation. The acceleration of electrons from the thermal bulk to relativistic energies, so-called runaway electron (RE) generation, is in particular a problem for future high current machines such as ITER. Accurately predicting the generation and impact of REs is therefore essential for making informed decisions concerning machine design and the use of disruption mitigation systems. This requires high-fidelity modeling also accounting for the large MHD activity observed throughout disruptions, which is made especially difficult by the mutual coupling between REs and the companion plasma. The non-linear 3D extended MHD code JOREK is a powerful tool for studying disruption and RE physics. This work details recent developments in JOREK, introducing a hybrid fluid-kinetic model where the REs are modeled kinetically and coupled to the non-linear MHD equations using a full-f particle-in-cell approach. The model goes beyond the state of the art and can accurately capture phase space distributions and dynamics of REs, drift orbits, and transport and losses caused by stochastic fields. Benchmarks are presented for both 2D and 3D configurations, concerning the impact of REs on the force balance and linear tearing mode growth rates, where a good agreement with analytically derived results is found. In addition, a demonstration of a particularly complicated non-linear application with high relevance to large machines is made, namely a RE benign termination linked to a violent burst of MHD activity.

Micro-cones so far mainly used for high energy density physics research have been proven to have an effective control on the fast electrons in the context of fast ignition research. In this paper we demonstrate by performing three-dimensional particle-in-cell simulations that an ultra-high intensity laser pulse can be intensified 28 times at the interaction with plastic micro-cones. The extreme intensities of the focused laser which are reached at the interaction with the plastic micro-cones are important in the plasma and nuclear physics investigations of dark matter, non-linear quantum electrodynamics, and fission–fusion experiments to study the N = 126 waiting point for better understanding of the Universe. Furthermore, we observe that micro-cones can shorten ultra-high intensity laser pulses both in time and space. The highest intensification of the incident laser pulse varies in time but not in position being localized very close to the rear side of the micro-cone tip. Therefore, the micro-cone can be a useful device in relativistic plasma optics.

Turbulent full-f simulations in a linear plasma device are presented. Extending the work of Frei et al (2024 Phys. Plasmas 31 012301), the simulations are based on a drift-kinetic (DK) model that includes corrections associated with higher-order drifts and finite Larmor radius (FLR) effects, while avoiding the Boussinesq approximation. To solve the DK equation, the ion distribution function is expanded on a Hermite-Laguerre basis and the expansion coefficients, denoted as the gyro-moments (GMs), are evolved. Convergence is demonstrated with a small number of GMs and the ion distribution function is shown to be, approximately, a bi-Maxwellian distribution. The simulations reveal significantly reduced cross-field transport with respect to standard DK simulations. Turbulent structures are observed, predominantly elongated in the parallel direction, and largely unaffected by the number of GMs. Linear investigations of the unstable turbulent modes reveal the presence of a long-wavelength Kelvin–Helmholtz mode and a short-wavelength mode driven unstable by finite FLR corrections. The role of these modes in the nonlinear simulations is discussed.

High-Z plasma facing components redeposit within the sheath through a combination of two distinct mechanisms: prompt (or geometric-driven) and local (or sheath-driven) redeposition. Experimental efforts are needed to determine the leading-order parameters influencing prompt-vs-local trade-off, which sets the fraction of material entering the scrape-off layer. In preparation for such experiments, leading-order parameters are isolated within the PYEAD-RustBCA-GITR coupled net erosion code using Sobol' sensitivity analysis. Then, experiments resolving prompt-vs-local trade-off under variation of these leading-order parameters are proposed using an isotopic coupon design with multifaceted diagnostic coverage. The measurability of these experiments is evaluated using synthetic diagnostics.

Resilient divertor features connected to open chaotic edge structures in the Helically Symmetric eXperiment are investigated. For the first time, an expanded vessel wall was considered that would give space for implementation of a physical divertor target structure. The analysis was done for four different magnetic configurations with very different chaotic plasma edges. A resilient plasma wall interaction pattern was identified across all configurations. This manifests as qualitatively very similar footprint behavior across the different plasma equilibria. Overall, the resilient field lines of interest with high connection length L_C lie within a helical band along the wall for all configurations. This resiliency can be used to identify the best location of a divertor. The details of the magnetic footprint's resilient helical band is subject to specific field line structures which are linked to the penetration depth of field lines into the plasma and directly influence the heat and particle flux patterns. The differences arising from these details are characterized by introducing a new metric, the minimum radial connection min$(\delta_N)$ of a field line from the last closed flux surface. The relationship, namely the deviation from a scaling law, between min$(\delta_N)$ and L_C of the field lines in the plasma edge field line behavior suggests that the field lines are associated with structures such as resonant islands, cantori, and turnstiles. This helps determine the relevant magnetic flux channels based on the radial location of these chaotic edge structures and the divertor target footprint. These details will need to be taken into account for resilient divertor design.

This article reviews applications of Bayesian inference and machine learning (ML) in nuclear fusion research. Current and next-generation nuclear fusion experiments require analysis and modelling efforts that integrate different models consistently and exploit information found across heterogeneous data sources in an efficient manner. Model-based Bayesian inference provides a framework well suited for the interpretation of observed data given physics and probabilistic assumptions, also for very complex systems, thanks to its rigorous and straightforward treatment of uncertainties and modelling hypothesis. On the other hand, ML, in particular neural networks and deep learning models, are based on black-box statistical models and allow the handling of large volumes of data and computation very efficiently. For this reason, approaches which make use of ML and Bayesian inference separately and also in conjunction are of particular interest for today's experiments and are the main topic of this review. This article also presents an approach where physics-based Bayesian inference and black-box ML play along, mitigating each other's drawbacks: the former is made more efficient, the latter more interpretable.

Being three-dimensional, stellarators have the advantage that plasma currents are not essential for creating rotational-transform; however, the external current-carrying coils in stellarators can have strong geometrical shaping, which can complicate the construction. Reducing the inter-coil electromagnetic forces acting on strongly shaped 3D coils and the stress on the support structure while preserving the favorable properties of the magnetic field is a design challenge. In this work, we recognize that the inter-coil forces are the gradient of the vacuum magnetic energy. We introduce an objective functional built on the usual quadratic flux on a prescribed target surface together with a weighed penalty on the vacuum energy. The Euler–Lagrange equation for stationary states is derived, and numerical illustrations are computed using a modern stellarator optimization framework. A study of the effect of the energy functional on the inter-coil forces is conducted and the energy is shown to be a promising quantity in producing coils with low forces.

The self-consistent simulation of the edge plasma is crucial for exploring the edge plasma solution compatible with high-performance plasma. While self-consistent edge plasma simulation is subject to the large gap between the turbulence and transport time scales, the coupling simulation of the turbulence and transport code is considered a reasonable way with both solid physics foundations and tolerable computational consumption. In this work, for the purpose of implementing the self-consistent turbulence-transport coupling simulation of the edge plasma automatically and efficiently, a simulation framework called edge plasma coupling simulation (EPCS) is developed based on Python. EPCS consists of various components to provide the interfaces for the specified turbulence and transport codes (BOUT++ and SOLPS-ITER at the present stage), the data transfer interfaces between the turbulence and transport code, the code running drivers and the function for configuration of the specified coupling simulation workflow. The inverse bilinear interpolation/bivariate spline interpolation under the flux-surface-aligned coordinate system is used to realize the accurate data transfer between different codes, and the breadth-first search algorithm is adopted to accelerate the interpolation process. A quasi-steady state identification method based on the coefficient of variation is developed to speed up the coupling simulation by terminating the turbulence simulation in time. Based on the components in EPCS, a steady-state coupling simulation workflow is developed, where the edge plasma is simulated by iterations of turbulence and transport codes. The steady-state coupling simulation workflow is validated by comparing the converged plasma profiles with EAST experiments (edge-localized-mode-free stage) at both upstream and divertor target, which implies the capability and flexibility of EPCS for the self-consistent simulation of the edge plasma under steady state.

State-selective electron capture in collisions of bare noble gas ions with ground-state hydrogen atoms serves as a crucial diagnostic tool in charge exchange recombination spectroscopy. In this work, we critically compare three classical trajectory Monte Carlo (CTMC) methodologies and present total, n-resolved, and ($n,l$)-resolved electron capture cross sections for Ne¹⁰⁺ and Ar¹⁸⁺ projectiles at impact energies in the range 0.1 keV u⁻¹–300 keV u⁻¹, which includes those relevant to tokamaks. The obtained cross sections are compared to reported experimental data as well as theoretical quantum mechanical data obtained with the two-center atomic orbital close-coupling method and the two-center wave-packet convergent close-coupling method where available. Present results lend credibility to one of these CTMC methods, thereby increasing confidence in its implementation for more highly charged projectiles.

JET returned to deuterium-tritium operations in 2023 (DTE3 campaign), approximately two years after DTE2. DTE3 was designed as an extension of JET's 2022-2023 deuterium campaigns, which focused on developing scenarios for ITER and DEMO, integrating in-depth physics understanding and control schemes. These scenarios were evaluated with mixed D-T fuel, using the only remaining tritium-capable tokamak until its closure in 2023. A core-edge-SOL integrated H-mode scenario was developed and tested in D-T, showing good confinement and partial divertor detachment with Ne-seeding. Stationary pulses with good performance, no tungsten accumulation, and even without ELMs were achieved in D-T. Plasmas with pedestals limited by peeling modes were studied with D, T-rich, and D-T fuel, revealing a positive correlation between pedestal electron pressure and pedestal electron density. The Quasi-Continuous Exhaust regime was successfully achieved with D-T fuel, with access criteria similar to those in D plasmas. A scenario with full detachment, the X-point radiator regime, was established in D-T, aided by the real-time control of the radiator's position. The crucial characterisation of tritium retention continued in DTE3, using gas balance measurements and the new LID-QMS diagnostic. Nuclear technology studies were advanced during the DTE3 campaign, addressing issues such as the activation of water in cooling loops and single event effects on electronics. Building on the previous D, T and DTE2 campaigns and the lessons learned from them, DTE3 extended our understanding of D-T plasmas, particularly in scenarios relevant to next-generation devices such as ITER and DEMO.

We investigate the behavior of heavy impurities in edge plasma turbulence by analyzing their trajectories using the Hasegawa–Wakatani model. Through direct numerical simulations, we track ensembles of charged impurity particles over hundreds of eddy turnover times within statistically steady turbulent flows. Assuming that heavy impurities lag behind the flow, a novel derivation of relaxation time of heavy impurities is proposed. Our results reveal that heavy impurities can cluster within turbulence. We provide multiscale geometrical Lagrangian statistics of heavy impurities trajectories. To quantify directional changes, we analyze the scale-dependent curvature angle, along with the influence of the Stokes number on the mean curvature angles and the probability distribution function of curvature angles.

Microwave reflectometry will serve as the primary diagnostic tool for measuring plasma density in ITER. The real-time inversion of high spatiotemporal resolution density profiles is a critical research focus for plasma fueling and control in both current and future fusion devices. A fast density profile inversion algorithm based on a deep neural network model has been proposed for the microwave reflectometry profile inversion database under various discharge parameters on EAST. Firstly, the model directly takes the high-sampling-rate raw time-domain $I/Q$ data from the multi-bands (Q-, V- and W-bands) microwave reflectometer as input and demonstrates rapid and effective feature extraction capabilities. Secondly, the model outputs a two-dimensional vector containing both the positions of the microwave cut-off layers and the density information. Notably, the model exhibits excellent adaptability across different discharge parameters on EAST, including variations in magnetic field strength ($B_\mathrm{t0}$ = 1.57–2.30 T), different plasma confinement such as L-mode and H-mode, and during phases such as current ramp-up and steady-state discharge. The next step involves integrating this data-driven real-time density profile algorithm directly into the deployed profile reflectometer data acquisition system on EAST to enable parallel computation of data acquisition and processing. This integration aims to provide real-time density profile distribution, particularly during density feedback control experiments, such as gas or pellet injection experiments.

In tokamak plasmas, non-linear interplay between transport and sources/sinks takes place for all transported quantities (current, heat, particles and momentum). Thanks to integrated modelling frameworks, we can iterate physics-based quasilinear turbulent transport models over multiple confinement times. Such modelling allows us to predict current, temperature, density and rotation profiles, and to disentangle the causality at play behind the modelled time evolution. An intense validation effort of such modelling against experimental measurements has been ongoing and has progressed our understanding. In dynamical phases, the so-called 'cold pulse' physics have been explained in the AUG tokamak, the isotope impact in plasma current ramp-up is understood in the JET tokamak, and the impact of the particle source (from neutral beam injection) on tungsten core accumulation has been clarified in JET and AUG. In stationary phases, the saturation of the ion temperature in electron-heated WEST plasmas has been clarified, and the energy content has been predicted with higher accuracy than empirical scaling laws with respect to the plasma current, magnetic field, plasma size and gas fueling, both in L and H modes on AUG. The validation of physics-based integrated modelling allows control optimisation in preparation for ITER operation as well as risk reduction for the design of future reactors. However, despite the reported progress, physics gaps remain on this path. For example, unlike today's devices, ITER-class devices will be opaque to neutrals and fuelled by pellets. In the absence of a physical understanding of the transport in the pedestal, extrapolation is uncertain. Moreover, in burning plasmas, the non-linear coupling between the central core profiles and the fusion power is very strong. The uncertainties in profile predictions due to unverified and unvalidated reduced transport models in such high-pressure plasmas lead to uncertain fusion power predictions. Solutions on how to address these challenges within integrated modelling will be proposed.

During its 40 years of operations, the Joint European Torus (JET) tokamak has consistently pushed the physics and engineering boundaries of fusion research, providing the scientific community with a unique testing ground for theories and innovative ideas. This paper covers a selection of remarkable contributions of JET to various fields of tokamak science, from transport and plasma heating studies to plasma-wall interaction and D-T experiments, and their impact on the fusion research progress.

Turbulence, a fascinating and intricate phenomenon, has captivated scientists over different domains, mainly for its complex cross-scale nature spanning a wide range of temporal and spatial scales. Despite significant advances in theories and observations in the last decades, some aspects of turbulence still remain unsolved, motivating new efforts to understand its underlying physical mechanisms and refine mathematical theories along with numerical models. This topical review explores recent findings from the Parker Solar Probe mission, providing a distinctive opportunity to characterize solar wind features at varying heliocentric distances. Analyzing the radial evolution of magnetic and velocity field fluctuations across the inertial range, a transition has been evidenced from local to global self-similarity as proximity to the Sun increases. This behavior has been reconciled with magnetohydrodynamic theory revising an old concept by emphasizing the evolving nature of the coupling between fields. This offers inspiration for novel modeling approaches to understand open challenges in interplanetary plasma physics as the heating and acceleration of the solar wind, as well as, its evolution within the inner Heliosphere.

This paper reviews current understanding of key physics elements that control the H-mode pedestal structure, which exists at the boundary of magnetically confined plasmas. The structure of interest is the width, height and gradient of temperature, density and pressure profiles in the pedestal. Emphasis is placed on understanding obtained from combined experimental, theoretical and simulation work and on results observed on multiple machines. Pedestal profiles are determined by the self-consistent interaction of sources, transport and magnetohydrodynamic limits. The heat source is primarily from heat deposited in the core and flowing to the pedestal. This source is computed from modeling of experimental data and is generally well understood. Neutrals at the periphery of the plasma provide the dominant particle source in current machines. This source has a complex spatial structure, is very difficult to measure and is poorly understood. For typical H-mode operation, the achievable pedestal pressure is limited by repetitive, transient magnetohydrodynamic instabilities. First principles models of peeling–ballooning modes are generally able to explain the observed limits. In some regimes, instability occurs below the predicted limits and these remain unexplained. Several mechanisms have been identified as plausible sources of heat transport. These include neoclassical processes for ion heat transport and several turbulent processes, driven by the steep pedestal gradients, as sources of electron and ion heat transport. Reduced models have successfully predicted the pedestal or density at the pedestal top. Firming up understanding of heat and particle transport remains a primary challenge for developing more complete predictive pedestal models.

This article reviews applications of Bayesian inference and machine learning (ML) in nuclear fusion research. Current and next-generation nuclear fusion experiments require analysis and modelling efforts that integrate different models consistently and exploit information found across heterogeneous data sources in an efficient manner. Model-based Bayesian inference provides a framework well suited for the interpretation of observed data given physics and probabilistic assumptions, also for very complex systems, thanks to its rigorous and straightforward treatment of uncertainties and modelling hypothesis. On the other hand, ML, in particular neural networks and deep learning models, are based on black-box statistical models and allow the handling of large volumes of data and computation very efficiently. For this reason, approaches which make use of ML and Bayesian inference separately and also in conjunction are of particular interest for today's experiments and are the main topic of this review. This article also presents an approach where physics-based Bayesian inference and black-box ML play along, mitigating each other's drawbacks: the former is made more efficient, the latter more interpretable.

With the increased urgency to design fusion pilot plants, fast optimization of electron cyclotron current drive (ECCD) launchers is paramount. Traditionally, this is done by coarsely sampling the 4-D parameter space of possible launch conditions consisting of (1) the launch location (constrained to lie along the reactor vessel), (2) the launch frequency, (3) the toroidal launch angle, and (4) the poloidal launch angle. For each initial condition, a ray-tracing simulation is performed to evaluate the ECCD efficiency. Unfortunately, this approach often requires a large number of simulations (sometimes millions in extreme cases) to build up a dataset that adequately covers the plasma volume, which must then be repeated every time the design point changes. Here we adopt a different approach. Rather than launching rays from the plasma periphery and hoping for the best, we instead directly reconstruct the optimal ray for driving current at a given flux surface using a reduced physics model coupled with a commercial ray-tracing code. Repeating this throughout the plasma volume requires only hundreds of simulations, constituting a significant speedup. The new method is validated on two separate example tokamak profiles, and is shown to reliably drive localized current at the specified flux surface with the same optimal efficiency as obtained from the traditional approach.

Dedicated experiments were performed on MAST Upgrade to study beam-ion losses caused by charge exchange (CX) with edge neutrals. The fuelling was switched from the high-field side to the low-field side mid-discharge. Direct measurements suggest a strong increase in the neutral density around the plasma and a decrease in the beam-ion density, which is qualitatively explained by CX losses. Measurements by a resistive bolometer have suggested particle bombardment during neutral beam injection, providing a unique opportunity to separate CX from other loss mechanisms. To verify and quantify CX losses, the orbit-following code ASCOT, which accounts both for CX neutralization and reionization, was used to simulate beam-particle power loads on the bolometer. Simulations reproduce measured bolometer power loads during high-field-side fuelling, verifying CX losses of approximately 10% of the off-axis beam power. Toroidally symmetric simulations overestimate power loads on the bolometer during low-field-side fuelling, which is explained by toroidal asymmetry in the neutral density distribution, as is demonstrated by toroidally asymmetric simulations. Results suggest significantly higher CX losses during low-field-side fuelling, up to about 50% of off-axis beam power.

Observations show that dispersive Alfven waves have significant role in heating and generation of turbulence in reconnection sites. The present study examines dispersive Alfven wave and turbulence in the presence of magnetic islands (at the reconnection sites) in solar wind. A nonlinear model for dispersive Alfven wave has been developed by taking into account the ponderomotive force to be responsible for nonlinear phenomena. Using computer modeling and numerical techniques, the resulting dynamical equation is solved. The pseudo-spectral approach has been employed for spatial integration, whereas temporal evolution has been utilised by finite difference technique. The simulation findings validate the presence of turbulence and demonstrate the spatiotemporal evolution of the dispersive Alfven wave's localized structures and current sheets. The scale sizes of localized structures have been calculated using a semi-analytic model, and it has been demonstrated that these scale sizes are dependent on magnetic islands and ponderomotive nonlinearity. By using the power law scaling of turbulence generation thermal tail formation of energetic ions has been studied.

The study on scaling the scrape-off layer (SOL) power width (λq) is crucial for deepening the understanding of the SOL particle and heat transports. Due to the sparse distribution of the divertor Langmuir probes (Div-LPs) and the erosion of probe tips during the long-pulse high-performance operations on EAST, the estimation of SOL particle flux width (λjs, used to approximate λq) from the measured ion saturation current density profile (js) usually has relatively large uncertainty. This paper introduces a maximum a posteriori (MAP) estimation method based on the Bayes' theorem to reduce the fitting uncertainty for λjs (the fitting accuracy increases by 33% in terms of mean absolute error compared with the traditional ordinary least squares estimation). With the new estimation method and the FreeGS equilibrium code, the databases in [Liu X et al., Nucl. Fusion 64 (2024) 026002] are updated, which are further used to scale λjs. Compared with the old λjs scalings for the L-mode and H-mode databases in deuterium and helium plasmas, the updated λjs scalings show better regression quality with similar results. The deuterium and helium databases for L-mode and H-mode plasmas can be combined to get a unified scaling, λ_js [mm]= 1.35(L ̅_c [m])^1.07 f_GW^0.46 β_p^(-0.38) (P_SOL/S_LCFS [MWm^(-2) ])^0.27 Z^0.23, where L ̅_c is the averaged SOL connection length, f_GW is the fraction of Greenwald density, β_p is the poloidal beta, PSOL is the power crossing the last closed flux surface (LCFS), S_LCFS is the surface area of the LCFS, and Z is the charge number. The unified scaling reveals that: i) λjs has a strong scaling dependence on the SOL connection length suggesting the missing scaling dependence on the machine size for the Eich scaling; ii) the helium λjs is slightly larger than the deuterium λjs. Furthermore, the scalings for integrated particle flux width are also given in this paper.

The National Spherical Torus Experiment (NSTX) at the Princeton Plasma Physics Laboratory in the United States, and the Mega Ampere Spherical Tokamak (MAST) at the United Kingdom Atomic Energy Authority in the United Kingdom, and their respective upgrades (NSTX-U and MAST-U) are two mega-amp class spherical tokamak fusion devices that have operated roughly over the past two decades. Both devices have made significant contributions to understanding spherical tokamak plasma physics, and fusion plasmas in general, and both have contributed data to multi-machine database studies. Several diagnostics have been physically moved from one machine to the other by diagnostic teams working on both devices. Collaboration has benefited both research teams in the areas of operational expertise, scenario development, and equilibrium reconstruction techniques. More focused comparative studies between the two devices have been pursued over the years in many areas as well, including stability calculations, disruption characterization, pedestal and edge localized mode stability, confinement and transport, energetic particles, and heating and current drive modelling. Together NSTX/-U and MAST/-U set the stage for the future of spherical tokamaks, which is entering the phase of design of demonstration power plant devices.

JET returned to deuterium-tritium operations in 2023 (DTE3 campaign), approximately two years after DTE2. DTE3 was designed as an extension of JET's 2022-2023 deuterium campaigns, which focused on developing scenarios for ITER and DEMO, integrating in-depth physics understanding and control schemes. These scenarios were evaluated with mixed D-T fuel, using the only remaining tritium-capable tokamak until its closure in 2023. A core-edge-SOL integrated H-mode scenario was developed and tested in D-T, showing good confinement and partial divertor detachment with Ne-seeding. Stationary pulses with good performance, no tungsten accumulation, and even without ELMs were achieved in D-T. Plasmas with pedestals limited by peeling modes were studied with D, T-rich, and D-T fuel, revealing a positive correlation between pedestal electron pressure and pedestal electron density. The Quasi-Continuous Exhaust regime was successfully achieved with D-T fuel, with access criteria similar to those in D plasmas. A scenario with full detachment, the X-point radiator regime, was established in D-T, aided by the real-time control of the radiator's position. The crucial characterisation of tritium retention continued in DTE3, using gas balance measurements and the new LID-QMS diagnostic. Nuclear technology studies were advanced during the DTE3 campaign, addressing issues such as the activation of water in cooling loops and single event effects on electronics. Building on the previous D, T and DTE2 campaigns and the lessons learned from them, DTE3 extended our understanding of D-T plasmas, particularly in scenarios relevant to next-generation devices such as ITER and DEMO.

Microwave reflectometry will serve as the primary diagnostic tool for measuring plasma density in ITER. The real-time inversion of high spatiotemporal resolution density profiles is a critical research focus for plasma fueling and control in both current and future fusion devices. A fast density profile inversion algorithm based on a deep neural network model has been proposed for the microwave reflectometry profile inversion database under various discharge parameters on EAST. Firstly, the model directly takes the high-sampling-rate raw time-domain $I/Q$ data from the multi-bands (Q-, V- and W-bands) microwave reflectometer as input and demonstrates rapid and effective feature extraction capabilities. Secondly, the model outputs a two-dimensional vector containing both the positions of the microwave cut-off layers and the density information. Notably, the model exhibits excellent adaptability across different discharge parameters on EAST, including variations in magnetic field strength ($B_\mathrm{t0}$ = 1.57–2.30 T), different plasma confinement such as L-mode and H-mode, and during phases such as current ramp-up and steady-state discharge. The next step involves integrating this data-driven real-time density profile algorithm directly into the deployed profile reflectometer data acquisition system on EAST to enable parallel computation of data acquisition and processing. This integration aims to provide real-time density profile distribution, particularly during density feedback control experiments, such as gas or pellet injection experiments.

With the increased urgency to design fusion pilot plants, fast optimization of electron cyclotron current drive (ECCD) launchers is paramount. Traditionally, this is done by coarsely sampling the 4-D parameter space of possible launch conditions consisting of (1) the launch location (constrained to lie along the reactor vessel), (2) the launch frequency, (3) the toroidal launch angle, and (4) the poloidal launch angle. For each initial condition, a ray-tracing simulation is performed to evaluate the ECCD efficiency. Unfortunately, this approach often requires a large number of simulations (sometimes millions in extreme cases) to build up a dataset that adequately covers the plasma volume, which must then be repeated every time the design point changes. Here we adopt a different approach. Rather than launching rays from the plasma periphery and hoping for the best, we instead directly reconstruct the optimal ray for driving current at a given flux surface using a reduced physics model coupled with a commercial ray-tracing code. Repeating this throughout the plasma volume requires only hundreds of simulations, constituting a significant speedup. The new method is validated on two separate example tokamak profiles, and is shown to reliably drive localized current at the specified flux surface with the same optimal efficiency as obtained from the traditional approach.

Dedicated experiments were performed on MAST Upgrade to study beam-ion losses caused by charge exchange (CX) with edge neutrals. The fuelling was switched from the high-field side to the low-field side mid-discharge. Direct measurements suggest a strong increase in the neutral density around the plasma and a decrease in the beam-ion density, which is qualitatively explained by CX losses. Measurements by a resistive bolometer have suggested particle bombardment during neutral beam injection, providing a unique opportunity to separate CX from other loss mechanisms. To verify and quantify CX losses, the orbit-following code ASCOT, which accounts both for CX neutralization and reionization, was used to simulate beam-particle power loads on the bolometer. Simulations reproduce measured bolometer power loads during high-field-side fuelling, verifying CX losses of approximately 10% of the off-axis beam power. Toroidally symmetric simulations overestimate power loads on the bolometer during low-field-side fuelling, which is explained by toroidal asymmetry in the neutral density distribution, as is demonstrated by toroidally asymmetric simulations. Results suggest significantly higher CX losses during low-field-side fuelling, up to about 50% of off-axis beam power.

The National Spherical Torus Experiment (NSTX) at the Princeton Plasma Physics Laboratory in the United States, and the Mega Ampere Spherical Tokamak (MAST) at the United Kingdom Atomic Energy Authority in the United Kingdom, and their respective upgrades (NSTX-U and MAST-U) are two mega-amp class spherical tokamak fusion devices that have operated roughly over the past two decades. Both devices have made significant contributions to understanding spherical tokamak plasma physics, and fusion plasmas in general, and both have contributed data to multi-machine database studies. Several diagnostics have been physically moved from one machine to the other by diagnostic teams working on both devices. Collaboration has benefited both research teams in the areas of operational expertise, scenario development, and equilibrium reconstruction techniques. More focused comparative studies between the two devices have been pursued over the years in many areas as well, including stability calculations, disruption characterization, pedestal and edge localized mode stability, confinement and transport, energetic particles, and heating and current drive modelling. Together NSTX/-U and MAST/-U set the stage for the future of spherical tokamaks, which is entering the phase of design of demonstration power plant devices.

A simple model of coupling an electromagnetic wave in the Ion Cyclotron (IC) frequency domain with a plasma in tokamak configuration is presented and solved in a simplified Cartesian geometry. The electromagnetic field radiated by the antenna is accurately described by the CST Studio Suite ® that shows the electromagnetic field radiated by the antenna but does not consider the load due to the plasma just in front of the antenna itself. The Ion Cyclotron Resonance Heating (ICRH) antenna consists of several metallic straps (accommodated in a tokamak port), on which a current flows that varies sinusoidally with time. The spectrum of the electromagnetic field radiated by the antenna acts as boundary condition for the solution of the wave equation inside the plasma. A simplified equation for the IC mode inside the plasma is derived and solved in straight Cartesian geometry by considering a simplified model of the space variation of the plasma density, temperature and magnetic field profiles. In deriving the simplified wave equation, a complex dielectric tensor has been considered by separating the Hermitian (essentially given in the cold plasma approximation) from anti-Hermitian part (temperature effects and wave absorption). This model results are relevant for the Divertor Tokamak Test facility (DTT), a new tokamak device under construction at ENEA research center in Frascati (Italy). DTT will be equipped with an ICRH system, whose construction is ongoing.

The next generation of Petawatt-class lasers presents the opportunity to study positron production and acceleration experimentally, in an all-optical setting. Several configurations were proposed to produce and accelerate positrons in a single laser stage. However, these configurations have yielded limited positron beam quality and low particle count. This paper presents methods for improving the injection and retention of positrons obtained via Bethe-Heitler pair production and accelerated using direct laser acceleration (DLA) in a plasma channel. The work first introduces a semi-analytical model which predicts laser energy depletion in this highly nonlinear regime. We demonstrate through PIC simulations that accelerated electrons can induce charge inversion within the channel, leading to positron trapping and acceleration. We investigate how laser focusing position, channel wall density, target foil position and target thickness influence positron creation and retention. Our configuration can achieve an 8-fold increase in positron retention compared to previous studies and a higher number of positrons produced overall. This work establishes a robust, single-stage approach for obtaining positron beams, opening new avenues for experiments with Petawatt-class lasers and potential applications in electron-positron collisions and QED cascades.

This study presents analysis of gyrokinetic simulations on the National Spherical Torus
Experiment (NSTX) to investigate the effects of electromagnetic fields on plasma turbulence and
transport. The simulations, performed with varying levels of fidelity using the gyrokinetic CGYRO
code, include electrostatic (ES), single-field electromagnetic (EM1), and two-field electromagnetic
(EM2) models. A detailed comparison across the simulation database reveals that electromagnetic
effects increase both predicted growth rates and quasilinear fluxes, with EM2 simulations producing
stronger turbulence than ES and EM1 cases. Quasilinear modeling using QLGYRO demonstrates
that while the perturbed parallel magnetic field (δB∥) does not drastically affect the total flux at
experimental gradients, it leads to a shift in the dominant instability, altering mode structures from
microtearing to kinetic ballooning modes (KBMs). The proximity of the plasma profiles to the
KBM threshold is explored, with the experimental conditions being near the onset of KBM-driven
transport. The KBM, with its large growth rates, is identified as a potential driver of electron
temperature flattening, as it can rapidly transport heat across flux surfaces. Performing stability
analysis shows core-localized unstable a low-ntor mode that could contribute to the flattening at
the early times of the discharge. TGYRO predictive modeling, incorporating both TGLF and
QLGYRO, indicates that the inclusion of δB∥ significantly improves the accuracy of temperature
profile predictions in NSTX high-beta plasmas, although challenges remain in modeling the sharp
flux discontinuities caused by KBM-driven instabilities.

Advances in edge and scrape-off layer diagnostics have shown that often the ion temperature is higher than the electron temperature in scrape-off layer filaments. We have therefore extended the STORM model beyond the cold ion limit commonly used, to allow for the inclusion of hot ion effects in the slab geometry used to investigate filament dynamics. We find that filaments are both faster and more coherent than in a cold ion model, resulting in increased particle transport. We trace the differences back to the effect of individual hot ion terms, compared using an isothermal ion model. Evolving ion temperature has a modest additional effect on net particle transport, but an ion temperature perturbation in a filament can counteract the instability caused by an electron temperature perturbation.

A general method for solving the drift kinetic equations is developed to derive the closure and transport relations for electron–ion plasmas in an axisymmetric magnetic field with nested flux surfaces. By expanding the electron and ion distribution functions into Fourier series of general moments, the drift kinetic equations are converted to a coupled system of algebraic equations. By eliminating the fluid equations, the electron and ion systems are decoupled, allowing each system of equations to be solved separately for closures. The closure relations connect parallel heat flux density, friction force density, and viscosity to the radial and parallel gradients of density and temperature, the parallel gradient of flow velocity, and the parallel relative flow velocity of electrons and ions. When these closure relations are combined with the fluid equations, the fluid quantities are expressed in terms of the radial gradients of density and temperature, as well as the radial and parallel components of the electric field. This framework offers a robust approach to studying transport phenomena in electron–ion plasmas. The transport relations are expected to provide a foundation for investigating plasma rotation, including intrinsic rotation, in various tokamak systems and under different plasma conditions.