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The phenomenon of beam focusing of microwaves in a plasma near a turning-point caustic is discussed in the context of the analytical solution to the Gaussian beam-tracing equations in the 2D linear-layer problem. The location of maximum beam focusing and the beam width at that location are studied in terms of the beam initial conditions. The analytic solution is used to study the effect of this focusing on Doppler backscattering (DBS). We find that the filter function that characterises the scattering intensity contributions along the beam path through the plasma is inversely proportional to the beam width, predicting enhanced scattering contributions from the beam focusing region. We show that the DBS signal enhancement for small incident angles between the beam path and the density gradient is due to beam focusing and not due to forward scattering. The analytic beam model is used to predict the measurement of the $k_y$ density-fluctuation wavenumber power spectrum via DBS, showing that the spectral exponent of the turbulent, intermediate-to-high $k_y$ density-fluctuation spectrum might be quantitatively measurable via DBS, but not the spectral peak corresponding to the driving scale of the turbulent cascade.

Mechanisms of plasmoid drift following massive material injection are studied via 3D non-linear MHD modelling with the JOREK code, using a transient neutral source deposited at the low field side midplane of a JET H-mode plasma to clarify basic processes and compare with existing theories. The simulations confirm the important role of the propagation of shear Alfv\'en wave (SAW) packets from both ends of the plasmoid (``SAW braking'') and the development of external resistive currents along magnetic field lines (``P\'egouri\'e braking'') in limiting charge separation and thus the $\mathbf{E}\times \mathbf{B}$ plasmoid drift, where $\mathbf{E}$ and $\mathbf{B}$ are the electric and magnetic fields, respectively. The drift velocity is found to be limited by the SAW braking on the few microseconds timescale for cases with relatively small source amplitude while the P\'egouri\'e braking acting on a longer timescale is shown to set in earlier with larger toroidal extent of the source, both in good agreement with existing theories. The simulations also identify the key role of the size of the $\mathbf{E}\times \mathbf{B}$ flow region on plasmoid drift and show that the saturated velocity caused by dominant SAW braking agrees well with theory when considering an effective pressure within the $\mathbf{E}\times \mathbf{B}$ flow region. The existence of SAWs in the simulations is demonstrated and the 3D picture of plasmoid drift is discussed.

The capability of the global, electromagnetic gyrokinetic GENE code interfaced with the transport Tango solver is exploited to address the impact of fusion alpha particles (in their dual role of fast particles and heating source) on plasma profiles and performance at JET in the discharges with the highest quasi-stationary peak fusion power during the DTE2 experimental campaigns. Employing radially global nonlinear electromagnetic GENE-Tango simulations, we compare results with/without alpha particles and alpha heating. Our findings reveal that alpha particles have a negligible impact on turbulent transport, with GENE-Tango converging to similar plasma profiles regardless of their inclusion as a kinetic species in GENE. On the other hand, alpha heating is found to contribute to the peaking of the electron temperature profiles, leading to a 1keV drop on the on-axis electron temperature when alpha heating is neglected in Tango. The minimal impact of alpha particles on turbulent transport in this JET discharge - despite this being the shot with the highest fusion output - is attributed to the low content of fusion alpha in this discharge. To assess the potential impact of alpha particles on turbulent transport in regimes with higher alpha particle density, as expected in ITER and fusion reactors, we artificially increased the alpha particle concentration to levels expected for ITER. By performing global nonlinear GENE standalone simulations, we found that increasing the alpha particle density beyond five times the nominal value lead to significant overall turbulence destabilization.

While much about Alfven eigenmode (AE) stability has been explored in previous and current tokamaks, open questions remain for future burning plasma experiments, especially regarding exact stability threshold conditions and related isotope effects; the latter, of course, requiring good knowledge of the plasma ion composition. In the JET tokamak, eight in-vessel antennas actively excite stable AEs, from which their frequencies, toroidal mode numbers, and net damping rates are assessed. The effective ion mass can also be inferred using measurements of the plasma density and magnetic geometry. Thousands of AE stability measurements have been collected by the Alfven Eigenmode Active Diagnostic in hundreds of JET plasmas during the recent Hydrogen, Deuterium, Tritium, DT, and Helium-4 campaigns. In this novel AE stability database, spanning all four main ion species, damping is observed to decrease with increasing Hydrogenic mass, but increase for Helium, a trend consistent with radiative damping as the dominant damping mechanism. These data are important for confident predictions of AE stability in both non-nuclear (H/He) and nuclear (D/T) operations in future devices. In particular, if radiative damping plays a significant role in overall stability, some AEs could be more easily destabilized in D/T plasmas than their H/He reference pulses, even before considering fast ion and alpha particle drive. Active MHD spectroscopy is also employed on select HD, HT, and DT plasmas to infer the effective ion mass, thereby closing the loop on isotope analysis and demonstrating a complementary method to typical diagnosis of the isotope ratio.

Turbulent transport is a decisive factor in determining the pedestal structure of H-modes. Here, we present the first comprehensive characterization of gyrokinetic turbulent transport in a JET hybrid H-mode pedestal. Local, linear simulations are performed to identify instabilities and global, nonlinear electromagnetic simulations reveal the turbulent heat and particle flux structure of the pedestal. Our analysis focuses on the Deuterium reference discharge \#97781 performed in the scenario development for the Deuterium-Tritium campaign. We find the pedestal top transport to be dominated by ion temperature gradient (ITG) modes. In the pedestal center turbulent ion transport is suppressed and electron transport is driven by multi-faceted electron temperature gradient (ETG) modes, which extend down to ion-gyroradius scales. A strong impact of $E\times B$ shear on the absolute turbulence level is confirmed by the global, nonlinear simulations. Furthermore, impurities are shown to reduce the main ion transport. Dedicated density and ion temperature profile variations test the sensitivity of the results and do not find strong differences in the turbulent transport in more reactor-like conditions.

This work successfully generates an uncertainty-aware surrogate model of the EuroPED plasma pedestal model using the Bayesian neural network with noise contrastive prior (BNN-NCP) technique. This model is trained using data from the JET-ILW pedestal database and subsequent model evaluations, conforming to EuroPED-NN. The BNN-NCP technique has been proven to be a suitable method for generating uncertainty-aware surrogate models. It matches the output results of a regular neural network while providing confidence estimates for predictions as uncertainties. Additionally, it highlights out-of-distribution (OOD) regions using surrogate model uncertainties. This provides critical insights into model robustness and reliability. EuroPED-NN has been physically validated, first, analyzing electron density $n_e\!\left(\psi_{\text{pol}}=0.94\right)$ with respect to increasing plasma current, $I_p$, and second, validating the $\Delta-\beta_{p,ped}$ relation associated with the EuroPED model. This affirms the robustness of the underlying physics learned by the surrogate model. On top of that, the method was used to develop a EuroPED-like model fed with experimental data, i.e. an uncertainty aware experimental model, which is functional in JET database. Both models have been also tested in $\sim 50$ AUG shots.

Model-based plasma scenario development lies at the heart of the design and operation of future fusion powerplants. Including turbulent transport in integrated models is essential for delivering a successful roadmap towards operation of ITER and the design of DEMO-class devices. Given the highly iterative nature of integrated models, fast machine-learning-based surrogates of turbulent transport are fundamental to fulfil the pressing need for faster simulations opening up pulse design, optimization, and flight simulator applications. A significant bottleneck is the generation of suitably large training datasets covering a large volume in parameter space, which can be prohibitively expensive to obtain for higher fidelity codes. In this work, we propose ADEPT (Active Deep Ensembles for Plasma Turbulence), a physics-informed, two-stage Active Learning strategy to ease this challenge. Active Learning queries a given model by means of an acquisition function that identifies regions where additional data would improve the surrogate model. We provide a benchmark study using available data from the literature for the QuaLiKiz quasilinear transport model. We demonstrate quantitatively that the physics-informed nature of the proposed workflow reduces the need to perform simulations in stable regions of the parameter space, resulting in significantly improved data efficiency. We show an up to a factor of 20 reduction in training dataset size needed to achieve the same performance as random sampling. We then validate the surrogates on multichannel integrated modelling of ITG-dominated JET scenarios and demonstrate that they recover the performance of QuaLiKiz to better than 10\%. This matches the performance obtained in previous work, but with two orders of magnitude fewer training data points., Comment: Submitted to Nuclear Fusion. Comments welcome

Providing stable and clean energy sources is a necessity for the increasing demands of humanity. Energy produced by fusion reactions, in particular in tokamaks, is a promising path towards that goal. However, there is little experience with plasmas under conditions close to those expected in future fusion reactors, because it requires the fusion of Deuterium (D) and Tritium (T), while most of the experiments are currently performed in pure D. After more than 20 years, the Joint European Torus (JET) has carried out new D-T experiments with the aim of exploring the unique characteristics of burning D-T plasmas, such as the presence of highly energetic ions. A new stable, high confinement and impurity-free D-T regime, with strong reduction of energy losses with respect to D, has been found. Multiscale physics mechanisms critically determine the thermal confinement and the fusion power yield. These crucial achievements importantly contribute to the establishment of fusion energy generation as an alternative to fossil fuels.

Previous studies with first-principle-based integrated modelling suggested that ETG turbulence may lead to an anti-GyroBohm isotope scaling in JET high-performance hybrid H-mode scenarios. A dedicated comparison study against higher-fidelity turbulence modelling invalidates this claim. Ion-scale turbulence with magnetic field perturbations included, can match the power balance fluxes within temperature gradient error margins. Multiscale gyrokinetic simulations from two distinct codes produce no significant ETG heat flux, demonstrating that simple rules-of-thumb are insufficient criteria for its onset.

Pedestal is the key to conventional high performance plasma scenarios in tokamaks. However, high fidelity simulations of pedestal plasmas are extremely challenging due to the multiple physical processes and scales that are encompassed by tokamak pedestals. The leading paradigm for predicting the pedestal top pressure is encompassed by EPED-like models. However, EPED does not predict the pedestal top density, $n_\text{e,ped}$, but requires it as an input. EUROPED employs simplified models, such as log-linear regression, to constrain $n_\text{e,ped}$ with tokamak machine control parameters in an EPED-like model. However, these simplified models for $n_\text{e,ped}$ often show disagreements with experimental observations and do not use all of the available numerical and categorical machine control information. In this work it is observed that using the same input parameters, decision tree ensembles and deep learning models improve the predictive quality of $n_\text{e,ped}$ by about 23% relative to that obtained with log-linear scaling laws, measured by root mean square error. Including all of the available tokamak machine control parameters, both numerical and categorical, leads to further improvement of about 13%. Finally, predictive quality was tested when including global normalized plasma pressure and effective charge state as inputs, as these parameters are known to impact pedestals. Surprisingly, these parameters lead to only a few percent further improvement of the predictive quality., Comment: 11 pages, 2 figures, 2 tables

A recent model coupling the shear-Alfv\'{e}n and acoustic continua, which depends strongly on the equilibrium shaping and on elongation in particular, is employed to explain the properties of Alfv\'{e}nic activity observed on JET plasmas below but close to the typical frequency of toroidicity-induced Alfv\'{e}n eigenmodes (TAEs). The frequency gaps predicted by the model result from high-order harmonics of the geodesic field-line curvature caused by plasma shaping (as opposed to lower-order toroidicity) and give rise to high-order geodesic acoustic eigenmodes (HOGAEs), their frequency value being close to one-half of the TAEs one. The theoretical predictions of HOGAE frequency and radial location are found to be in fair agreement with measurements in JET experiments, including magnetic, reflectometry and soft x-ray data. The stability of the observed HOGAEs is evaluated with the linear hybrid MHD/drift-kinetic code CASTOR-K, taking into account the energetic-ion populations produced by the NBI and ICRH heating systems. Wave-particle resonances, along with drive/damping mechanisms, are also discussed in order to understand the conditions leading to HOGAEs destabilization in JET plasmas., Comment: 10 pages, 11 figures, accepted for publication

In this paper, we report the novel experimental observation of both unstable and stable Toroidicity-induced Alfv\'en Eigenmodes (TAEs) measured simultaneously in a JET tokamak plasma. The three-ion-heating scheme (D-DNBI-3He) is employed to accelerate deuterons to MeV energies, thereby destabilizing TAEs with toroidal mode numbers n = 3-5, each decreasing in mode amplitude. At the same time, the Alfv\'en Eigenmode Active Diagnostic resonantly excites a stable n = 6 TAE with total normalized damping rate $-\gamma/\omega_0 \approx$ 1%-4%. Hybrid kinetic-MHD modeling with codes NOVA-K and MEGA both find eigenmodes with similar frequencies, mode structures, and radial locations as in experiment. NOVA-K demonstrates good agreement with the n = 3, 4, and 6 TAEs, matching the damping rate of the n = 6 mode within uncertainties and identifying radiative damping as the dominant contribution. Improved agreement is found with MEGA for all modes: the unstable n = 3-5 and stable n = 2, 6 modes, with the latter two stabilized by higher intrinsic damping and lower fast ion drive, respectively. While some discrepancies remain to be resolved, this unique validation effort gives us confidence in TAE stability predictions for future fusion devices.

The reconstruction of the distribution function of runaway electrons (RE) in magnetically confined fusion plasmas gives insights on the runaway electron beam dynamics during plasma disruptions. In view of enabling a two-dimensional, energy-pitch reconstruction of the RE velocity space, in this work we present a calculation of the weight functions for the bremsstrahlung emission by the REs. The weight functions allow bridging the bremsstrahlung spectrum with the RE velocity space, as they tell the region of the velocity space that contributes to a particular spectral measurement. The results are applied to investigate the RE velocity-space sensitivity of the hard X-ray diagnostic installed at the Joint European Torus.

A linear response, local model for the DBS amplitude applied to gyrokinetic simulations shows that radial correlation Doppler reflectometry measurements (RCDR, Schirmer et al., Plasma Phys. Control. Fusion 49 1019 (2007)) are not sensitive to the average turbulence radial correlation length, but to a correlation length that depends on the binormal wavenumber $k_\perp$ selected by the Doppler backscattering (DBS) signal. Nonlinear gyrokinetic simulations show that the turbulence naturally exhibits a non-separable power law spectrum in wavenumber space, leading to a power law dependence of the radial correlation length with binormal wavenumber $l_r \sim C k_\perp^{-\alpha} (\alpha \approx 1)$ which agrees with the inverse proportionality relationship between the measured $l_r$ and $k_\perp $ in experiments (Fernandez-Marina et al., Nucl. Fusion 54 072001 (2014)). This offers the possibility of characterizing the eddy aspect ratio in the perpendicular plane to the magnetic field and motivates future use of a non-separable turbulent spectrum to quantitatively interpret RCDR and potentially other turbulence diagnostics. The radial correlation length is only measurable when the radial resolution at the cutoff location $W_n$ satisfies $W_n \ll l_r$, while the measurement becomes dominated by $W_n$ for $W_n \gg l_r$. This suggests that $l_r$ is likely inaccessible for electron-scale DBS measurements ($k_\perp\rho_s > 1$). The effect of $W_n$ on ion-scale radial correlation lengths could be non-negligible., Comment: Total of 13 figures, 36 pages. TEX commands are included in the abstract for mathematical expressions. Submitted to Plasma Physics and Controlled Fusion

The interaction of Alfv\'{e}n Eigenmodes (AEs) and energetic particles is one of many important factors determining the success of future tokamaks. In JET, eight in-vessel antennas were installed to actively probe stable AEs with frequencies ranging 25-250 kHz and toroidal mode numbers $\vert n \vert < 20$. During the 2019-2020 deuterium campaign, almost 7500 resonances and their frequencies $f_0$, net damping rates $\gamma < 0$, and toroidal mode numbers were measured in almost 800 plasma discharges. From a statistical analysis of this database, continuum and radiative damping are inferred to increase with edge safety factor, edge magnetic shear, and when including non-ideal effects. Both stable AE observations and their associated damping rates are found to decrease with $\vert n \vert$. Active antenna excitation is also found to be ineffective in H-mode as opposed to L-mode; this is likely due to the increased edge density gradient's effect on accessibility and ELM-related noise's impact on mode identification. A novel measurement is reported of a marginally stable, edge-localized Ellipticity-induced AE probed by the antennas during high-power auxiliary heating (ICRH and NBI) up to 25 MW. NOVA-K kinetic-MHD simulations show good agreement with experimental measurements of $f_0$, $\gamma$, and $n$, indicating the dominance of continuum and electron Landau damping in this case. Similar experimental and computational studies are planned for the recent hydrogen and ongoing tritium campaigns, in preparation for the upcoming DT campaign.

Long-pulse operation of a self-sustained fusion reactor using toroidal magnetic containment requires control over the content of alpha particles produced by D-T fusion reactions. On the one hand, MeV-class alpha particles must stay confined to heat the plasma. On the other hand, decelerated helium ash must be expelled before diluting the fusion fuel. Our kinetic-magnetohydrodynamic hybrid simulations of a large tokamak plasma confirm the existence of a parameter window where such energy-selective confinement can be accomplished by exploiting internal relaxation events known as `sawtooth crashes'. The physical picture -- consisting of a synergy between magnetic geometry, optimal crash duration and rapid particle motion -- is completed by clarifying the role played by magnetic drifts. Besides causing asymmetry between co- and counter-going particle populations, magnetic drifts determine the size of the confinement window by dictating where and how much `reconnection' occurs in particle orbit topology., Comment: Main article: 9 pages, 7 figures. Supplementary material: 9 pages, 15 figures. References: 3 pages. 2021 IAEA TCM EPPI Conference

This paper outlines an approach towards improved rigour in tokamak turbulence transport model validation within integrated modelling. Gaussian process regression (GPR) techniques were applied for profile fitting during the preparation of integrated modelling simulations allowing for rigourous sensitivity tests of prescribed initial and boundary conditions as both fit and derivative uncertainties are provided. This was demonstrated by a JETTO integrated modelling simulation of the JET ITER-like-wall H-mode baseline discharge #92436 with the QuaLiKiz quasilinear turbulent transport model, which is the subject of extrapolation towards a deuterium-tritium plasma. The simulation simultaneously evaluates the time evolution of heat, particle, and momentum fluxes over $\sim10$ confinement times, with a simulation boundary condition at $\rho_{tor} = 0.85$. Routine inclusion of momentum transport prediction in multi-channel flux-driven transport modelling is not standard and is facilitated here by recent developments within the QuaLiKiz model. Excellent agreement was achieved between the fitted and simulated profiles for $n_e$, $T_e$, $T_i$, and $\Omega_{tor}$ within $2\sigma$, but the simulation underpredicts the mid-radius $T_i$ and overpredicts the core $n_e$ and $T_e$ profiles for this discharge. Despite this, it was shown that this approach is capable of deriving reasonable inputs, including derivative quantities, to tokamak models from experimental data. Furthermore, multiple figures-of-merit were defined to quantitatively assess the agreement of integrated modelling predictions to experimental data within the GPR profile fitting framework., Comment: 26 pages, 16 figures, Nuclear Fusion

Within integrated tokamak plasma modelling, turbulent transport codes are typically the computational bottleneck limiting their routine use outside of post-discharge analysis. Neural network (NN) surrogates have been used to accelerate these calculations while retaining the desired accuracy of the physics-based models. This paper extends a previous NN model, known as QLKNN-hyper-10D, by incorporating the impact of impurities, plasma rotation and magnetic equilibrium effects. This is achieved by adding a light impurity fractional density ($n_{imp,light} / n_e$) and its normalized gradient, the normalized pressure gradient ($\alpha$), the toroidal Mach number ($M_{tor}$) and the normalized toroidal flow velocity gradient. The input space was sampled based on experimental data from the JET tokamak to avoid the curse of dimensionality. The resulting networks, named QLKNN-jetexp-15D, show good agreement with the original QuaLiKiz model, both by comparing individual transport quantity predictions as well as comparing its impact within the integrated model, JINTRAC. The profile-averaged RMS of the integrated modelling simulations is <10% for each of the 5 scenarios tested. This is non-trivial given the potential numerical instabilities present within the highly nonlinear system of equations governing plasma transport, especially considering the novel addition of momentum flux predictions to the model proposed here. An evaluation of all 25 NN output quantities at one radial location takes $\sim$0.1 ms, $10^4$ times faster than the original QuaLiKiz model. Within the JINTRAC integrated modelling tests performed in this study, using QLKNN-jetexp-15D resulted in a speed increase of only 60 - 100 as other physics modules outside of turbulent transport become the bottleneck., Comment: 34 pages, 24 figures, Physics of Plasmas

Core turbulent particle transport with multiple isotopes can display observable differences in behaviour between the electron and ion particle channels. Experimental observations at JET with mixed H-D plasmas and varying NBI and gas-puff sources [M. Maslov et al., Nucl. Fusion 7 076022 (2018)] inferred source dominated electron peaking, but transport dominated isotope peaking. In this work, we apply the QuaLiKiz quasilinear gyrokinetic transport model within JINTRAC flux-driven integrated modelling, for core transport validation in this multiple-isotope regime. The experiments are successfully reproduced, predicting self consistently $ j $, $ n_{e} $, $ n_{Be} $, $ T_{e} $, $ T_{i} $, $\omega_{tor}$ and the isotope composition. As seen in the experiments, both H and D profiles are predicted to be peaked regardless of the core isotope source. An extensive sensitivity study confirmed that this result does not depend on the specific choices made for the boundary conditions and physics settings. While kinetic profiles and electron density peaking did vary depending on the simulation parameters, the isotope ratio remained nearly invariant, and tied to the electron density profile. These findings have positive ramifications for multiple-isotope fuelling, burn control, and helium ash removal., Comment: 14 pages, 7 figures, 4 tables

For the first time the pellet cycle of a multiple-isotope plasma is successfully reproduced with reduced turbulent transport modelling, within an integrated simulation framework. Future nuclear fusion reactors are likely to be fuelled by cryogenic pellet injection, due to higher penetration and faster response times. Accurate pellet cycle modelling is crucial to assess fuelling efficiency and burn control. In recent JET tokamak experiments, deuterium pellets with reactor-relevant deposition characteristics were injected into a pure hydrogen plasma. Measurements of the isotope ratio profile inferred a Deuterium penetration time comparable to the energy confinement time. The modelling successfully reproduces the plasma thermodynamic profiles and the fast deuterium penetration timescale. The predictions of the reduced turbulence model QuaLiKiz in the presence of a negative density gradient following pellet deposition are compared with GENE linear and nonlinear higher fidelity modelling. The results are encouraging with regard to reactor fuelling capability and burn control., Comment: 12 pages, 9 figures, 5 tables

We present a Bayesian method for inferring axisymmetric plasma equilibria from the magnetic field and plasma pressure measurements. The method calculates all possible solutions for plasma current and pressure distributions consistent with the measurements and magnetohydrodynamic (MHD) force balance. Toroidal plasma current and magnetic field coils are modelled as a set of axisymmetric current-carrying solid beams. The other parameters such as plasma pressure and poloidal current flux are given as a function of poloidal magnetic flux, which is determined given a 2D current distribution. Plasma pressure and poloidal current flux profiles are modelled as Gaussian processes whose smoothness is optimally chosen based on the principle of Occam's razor. To find equilibrium solutions, we introduce an MHD force balance constraint at every plasma current beam as a part of the prior knowledge. Given all these physical quantities, predictions calculated by the predictive (forward) models for diagnostics are compared to the observations. The high dimensional complex posterior probability distribution is explored by a new algorithm based on the Gibbs sampling scheme.

Disruptions in tokamak plasmas may lead to the generation of runaway electrons that have the potential to damage plasma-facing components. Improved understanding of the runaway generation process requires interpretative modelling of experiments. In this work we simulate eight discharges in the ASDEX Upgrade and JET tokamaks, where argon gas was injected to trigger the disruption. We use a fluid modelling framework with the capability to model the generation of runaway electrons through the hot-tail, Dreicer and avalanche mechanisms, as well as runaway electron losses. Using experimentally based initial values of plasma current and electron temperature and density, we can reproduce the plasma current evolution using realistic assumptions about temperature evolution and assimilation of the injected argon in the plasma. The assumptions and results are similar for the modelled discharges in ASDEX Upgrade and JET, indicating that the implemented models are applicable to machines of varying size, which is important for the modelling of future, larger machines. For the modelled discharges in ASDEX Upgrade, where the initial temperature was comparatively high, we had to assume that a large fraction of the hot-tail runaway electrons were lost in order to reproduce the measured current evolution., Comment: 17 pages, 7 figures

This paper presents a dedicated study of plasma-antenna (PA) coupling with the Alfven Eigenmode Active Diagnostic (AEAD) in JET. Stable AEs and their resonant frequencies f, damping rates $\gamma$ < 0, and toroidal mode numbers n are measured for various PA separations and limiter versus X-point magnetic configurations. Two stable AEs are observed to be resonantly excited at distinct low and high frequencies in limiter plasmas. The values of f and n do not vary with PA separation. However, $\vert\gamma\vert$ increases with PA separation for the low-f, but not high-f, mode, yet this may be due to slightly different edge conditions. The high-f AE is detected throughout the transition from limiter to X-point configuration, though its damping rate increases; the low-f mode, on the other hand, becomes unidentifiable. The linear resistive MHD code CASTOR is used to simulate the frequency scan of an AEAD-like external antenna. For the limiter pulses, the high-f mode is determined to be an n = 0 GAE, while the low-f mode is likely an n = 2 TAE. During the transition from limiter to X-point configuration, CASTOR indicates that n = 1 and 2 EAEs are excited in the edge gap. These results extend previous experimental studies in JET and Alcator C-Mod; validate the computational work performed by Dvornova et al 2020 Phys. Plasmas 27 012507; and provide guidance for the optimization of PA coupling in upcoming JET energetic particle experiments, for which the AEAD will aim to identify the contribution of alpha particles to AE drive during the DT campaign.

The JET baseline scenario is being developed to achieve high fusion performance and sustained fusion power. However, with higher plasma current and higher input power, an increase in pulse disruptivity is being observed. Although there is a wide range of possible disruption causes, the present disruptions seem to be closely related to radiative phenomena such as impurity accumulation, core radiation, and radiative collapse. In this work, we focus on bolometer tomography to reconstruct the plasma radiation profile and, on top of it, we apply anomaly detection to identify the radiation patterns that precede major disruptions. The approach makes extensive use of machine learning. First, we train a surrogate model for plasma tomography based on matrix multiplication, which provides a fast method to compute the plasma radiation profiles across the full extent of any given pulse. Then, we train a variational autoencoder to reproduce the radiation profiles by encoding them into a latent distribution and subsequently decoding them. As an anomaly detector, the variational autoencoder struggles to reproduce unusual behaviors, which includes not only the actual disruptions but their precursors as well. These precursors are identified based on an analysis of the anomaly score across all baseline pulses in two recent campaigns at JET., Comment: (to appear)

The radiation response and the MHD destabilization during the thermal quench after a mixed species Shattered Pellet Injection (SPI) with impurity species neon and argon are investigated via 3D non-linear MHD simulation using the JOREK code. Both the $n=0$ global current profile contraction and the local helical cooling at each rational surface caused by the pellet fragments are found to be responsible for MHD destabilization after the injection. Significant current driven mode growth is observed as the fragments cross low order rational surfaces, resulting in rapidly inward propagating stochastic magnetic field, ultimately causing the core temperature collapse. The Thermal Quench (TQ) is triggered as the fragments arrive on the $q=1$ or $q=2$ surface depending on the exact $q$ profile and thus mode structure. When injecting from a single toroidal location, strong radiation asymmetry is found before and during the TQ as a result of the unrelaxed impurity density profile along the field line and asymmetric outward heat flux. Such asymmetry gradually relaxes over the course of the TQ, and is entirely eliminated by the end of it. Simulation results indicate that the aforementioned asymmetric radiation behavior could be significantly mitigated by injection from toroidally opposite locations, provided that the time delay between the two injectors is shorter than $1ms$. It is also found that the MHD response are sensitive to the relative timing and injection configuration in these multiple injection cases., Comment: 35 pages, 21 figures

This paper presents results of extensive analysis of mode excitation observed during the operation of the Alfv\'{e}n Eigenmode Active Diagnostic (AEAD) in the JET tokamak during the 2019-2020 deuterium campaign. Six of eight toroidally spaced antennas, each with independent power and phasing, were successful in actively exciting stable MHD modes in 479 plasmas. In total, 4768 magnetic resonances were detected with up to fourteen fast magnetic probes. In this work, we present the calculations of resonant frequencies $f_0$, damping rates $\gamma < 0$, and toroidal mode numbers $n$, spanning the parameter range $f_0 \approx$ 30 - 250 kHz, $-\gamma \approx$ 0 - 13 kHz, and $\vert n \vert \leq 30$. In general, good agreement is seen between the resonant and the calculated toroidal Alfv\'{e}n Eigenmode frequencies, and between the toroidal mode numbers applied by the AEAD and estimated of the excited resonances. We note several trends in the database: the probability of resonance detection decreases with plasma current and external heating power; the normalized damping rate increases with edge safety factor but decreases with external heating. These results provide key information to prepare future experimental campaigns and to better understand the physics of excitation and damping of Alfv\'{e}n Eigenmodes in the presence of alpha particles during the upcoming DT campaign, thereby extrapolating with confidence to future tokamaks.

We report on a detailed study of magnetic fluctuations in the JET pedestal, employing basic theoretical considerations, gyrokinetic simulations, and experimental fluctuation data, to establish the physical basis for their origin, role, and distinctive characteristics. We demonstrate quantitative agreement between gyrokinetic simulations of microtearing modes (MTMs) and two magnetic frequency bands with corresponding toroidal mode numbers n=4 and 8. Such disparate fluctuation scales, with substantial gaps between toroidal mode numbers, are commonly observed in pedestal fluctuations. Here we provide a clear explanation, namely the alignment of the relevant rational surfaces (and not others) with the peak in the omega star profile, which is localized in the steep gradient region of the pedestal. We demonstrate that a global treatment is required to capture this effect. Nonlinear simulations suggest that the MTM fluctuations produce experimentally-relevant transport levels and saturate by relaxing the background electron temperature gradient, slightly downshifting the fluctuation frequencies from the linear predictions. Scans in collisionality are compared with simple MTM dispersion relations. At the experimental points considered, MTM growth rates can either increase or decrease with collision frequency depending on the parameters thus defying any simple characterization of collisionality dependence.

Experimental observations, as well as theoretical predictions, indicate that the transport of energetic electrons decreases with energy. This reduction in transport is attributed to finite orbit width (FOW) effects. Using orbit-following simulations in perturbed tokamak magnetic fields that have an ideal homogeneous stochastic layer at the edge, we quantify the energy dependence of energetic electrons transport and confirm previous theoretical estimates. However, using magnetic configurations characteristic of JET disruptions, we find no reduction in RE transport at higher energies, which we attribute to the mode widths being comparable to the minor radius, making the FOW effects negligible. Instead, the presence of islands and nonuniform magnetic perturbations are found to be more important. The diffusive-advective transport coefficients calculated in this work, based on simulations for electron energies 10 keV -- 100 MeV, can be used in reduced kinetic models to account for the transport due to the magnetic field perturbations.

A summary of recent results on filamentary transport, mostly obtained in the ASDEX-Upgrade tokamak (AUG), is presented and discussed in an attempt to produce a coherent picture of SOL filamentary transport: A clear correlation is found between L-mode density shoulder formation in the outer midplane and a transition between the sheath limited and the inertial filamentary regimes. Divertor collisionality is found to be the parameter triggering the transition. A clear reduction of the ion temperature takes place in the far SOL after the transition, both for the background and the filaments. This coincides with a strong variation of the ion temperature distribution, which deviates from Gaussianity and becomes dominated by a strong peak below $5$ eV. The filament transition mechanism triggered by a critical value of collisionality seems to be generally applicable to inter-ELM H-mode plasmas, although a secondary threshold related to deuterium fueling is observed. EMC3-EIRENE simulations of neutral dynamics show that an ionization front near the main chamber wall is formed after the shoulder formation. Finally, a clear increase of SOL opacity to neutrals is observed associated to the shoulder formation. A common SOL transport framework is proposed account for all these results, and their potential implications for future generation devices are discussed., Comment: Published in Nuclear Fusion

Local linear gyrokinetic simulations show that electron temperature gradient (ETG) instabilities are the fastest growing modes for $k_y \rho_i \gtrsim 0.1$ in the steep gradient region for a JET pedestal discharge (92174) where the electron temperature gradient is steeper than the ion temperature gradient. Here, $k_y$ is the wavenumber in the direction perpendicular to both the magnetic field and the radial direction, and $\rho_i$ is the ion gyroradius. At $k_y \rho_i \gtrsim 1$, the fastest growing mode is often a novel type of toroidal ETG instability. This toroidal ETG mode is driven at scales as large as $k_y \rho_i \sim (\rho_i/\rho_e) L_{Te} / R_0 \sim 1$ and at a sufficiently large radial wavenumber that electron finite Larmor radius effects become important; that is, $K_x \rho_e \sim 1$, where $K_x$ is the effective radial wavenumber. Here, $\rho_e$ is the electron gyroradius, $R_0$ is the major radius of the last closed flux surface, and $1/L_{Te}$ is an inverse length proportional to the logarithmic gradient of the equilibrium electron temperature. The fastest growing toroidal ETG modes are often driven far away from the outboard midplane. In this equilibrium, ion temperature gradient instability is subdominant at all scales and kinetic ballooning modes are shown to be suppressed by $\mathbf{ E} \times \mathbf{ B} $ shear. ETG modes are very resilient to $\mathbf{ E} \times \mathbf{ B}$ shear. Heuristic quasilinear arguments suggest that the novel toroidal ETG instability is important for transport., Comment: 67 pages, 29 figures, accepted in Nuclear Fusion 2020

We present an ultrafast neural network (NN) model, QLKNN, which predicts core tokamak transport heat and particle fluxes. QLKNN is a surrogate model based on a database of 300 million flux calculations of the quasilinear gyrokinetic transport model QuaLiKiz. The database covers a wide range of realistic tokamak core parameters. Physical features such as the existence of a critical gradient for the onset of turbulent transport were integrated into the neural network training methodology. We have coupled QLKNN to the tokamak modelling framework JINTRAC and rapid control-oriented tokamak transport solver RAPTOR. The coupled frameworks are demonstrated and validated through application to three JET shots covering a representative spread of H-mode operating space, predicting turbulent transport of energy and particles in the plasma core. JINTRAC-QLKNN and RAPTOR-QLKNN are able to accurately reproduce JINTRAC-QuaLiKiz T i,e and n e profiles, but 3 to 5 orders of magnitude faster. Simulations which take hours are reduced down to only a few tens of seconds. The discrepancy in the final source-driven predicted profiles between QLKNN and QuaLiKiz is on the order 1%-15%. Also the dynamic behaviour was well captured by QLKNN, with differences of only 4%-10% compared to JINTRAC-QuaLiKiz observed at mid-radius, for a study of density buildup following the L-H transition. Deployment of neural network surrogate models in multi-physics integrated tokamak modelling is a promising route towards enabling accurate and fast tokamak scenario optimization, Uncertainty Quantification, and control applications., Comment: 18 pages, 11 figures, Physics of Plasmas, ICDDPS 2019 conference paper

A global heat flux model based on a fractional derivative of plasma pressure is proposed for the heat transport in fusion plasmas. The degree of the fractional derivative of the heat flux, $\alpha$, is defined through the power balance analysis of the steady state. The model was used to obtain the experimental values of $\alpha$ for a large database of the JET Carbon-wall as well as ITER Like-wall plasmas. The findings show that the average fractional degree of the heat flux over the database for electrons is $\alpha \sim 0.8$, suggesting a global scaling between the net heating and the pressure profile in the JET plasmas. The model is expected to provide an accurate and a simple description of heat transport that can be used in transport studies of fusion plasmas., Comment: 6 pages submitted to Physical Review Research

Fusion performance in tokamaks hinges critically on the efficacy of the Edge Transport Barrier (ETB) at suppressing energy losses. The new concept of fingerprints is introduced to identify the instabilities that cause the transport losses in the ETB of many of today's experiments, from widely posited candidates. Analysis of the Gyrokinetic-Maxwell equations, and gyrokinetic simulations of experiments, find that each mode type produces characteristic ratios of transport in the various channels: density, heat and impurities. This, together with experimental observations of transport in some channel, or, of the relative size of the driving sources of channels, can identify or determine the dominant modes causing energy transport. In multiple ELMy H-mode cases that are examined, these fingerprints indicate that MHD-like modes are apparently not the dominant agent of energy transport; rather, this role is played by Micro-Tearing Modes (MTM) and Electron Temperature Gradient (ETG) modes, and in addition, possibly Ion Temperature Gradient (ITG)/Trapped Electron Modes (ITG/TEM) on JET. MHD-like modes may dominate the electron particle losses. Fluctuation frequency can also be an important means of identification, and is often closely related to the transport fingerprint. The analytical arguments unify and explain previously disparate experimental observations on multiple devices, including DIII-D, JET and ASDEX-U, and detailed simulations of two DIII-D ETBs also demonstrate and corroborate this.

Measurements are reported of electromagnetic emission close to the cyclotron frequency of energetic ions in JET plasmas heated by waves in the ion cyclotron range of frequencies (ICRF). Hydrogen was the majority ion species in all of these plasmas. The measurements were obtained using a sub-harmonic arc detection (SHAD) system in the transmission lines of one of the ICRF antennas. The measured ion cyclotron emission (ICE) spectra were strongly filtered by the antenna system, and typically contained sub-structure, consisting of sets of peaks with a separation of a few kHz, suggesting the excitation of compressional Alfven eigenmodes (CAEs) closely spaced in frequency. In most cases the energetic ions can be clearly identified as ICRF-accelerated He-3 minority ions, although in two pulses the emission may have been produced by energetic He-4 ions, originating from third harmonic ICRF wave acceleration. It is proposed that the emission close to the He-3 cyclotron frequency was produced by energetic ions of this species undergoing drift orbit excursions to the outer midplane plasma edge. Particle-in-cell and hybrid (kinetic ion, fluid electron) simulations using plasma parameters corresponding to edge plasma conditions in these JET pulses, and energetic particle parameters inferred from the cyclotron resonance location, indicate strong excitation of waves at He-3 cyclotron harmonics, including the fundamental, which is identified with the observed emission. These results underline the potential importance of ICE measurements as a method of studying confined fast particles that are strongly suprathermal but have insufficient energies or are not present in sufficient numbers to excite detectable levels of gamma-ray emission or other collective instabilities., Comment: 33 pages, 15 figures

Fast ions have recently been found to significantly impact and partially suppress plasma turbulence both in experimental and numerical studies in a number of scenarios. Understanding the underlying physics and identifying the range of their beneficial effect is an essential task for future fusion reactors, where highly energetic ions are generated through fusion reactions and external heating schemes. However, in many of the gyrokinetic codes fast ions are, for simplicity, treated as equivalent-Maxwellian-distributed particle species, although it is well known that to rigorously model highly non-thermalised particles, a non-Maxwellian background distribution function is needed. To study the impact of this assumption, the gyrokinetic code GENE has recently been extended to support arbitrary background distribution functions which might be either analytic, e.g. slowing down and bi-Maxwellian, or obtained from numerical fast ion models. A particular JET plasma with strong fast-ion related turbulence suppression is revised with these new code capabilities both with linear and nonlinear gyrokinetic simulations. It appears that the fast ion stabilization tends to be less strong but still substantial with more realistic distributions, and this improves the quantitative power balance agreement with experiments., Comment: Submitted to Physics of Plasmas

Quasilinear turbulent transport models are a successful tool for prediction of core tokamak plasma profiles in many regimes. Their success hinges on the reproduction of local nonlinear gyrokinetic fluxes. We focus on significant progress in the quasilinear gyrokinetic transport model QuaLiKiz [C. Bourdelle et al. 2016 Plasma Phys. Control. Fusion 58 014036], which employs an approximated solution of the mode structures to significantly speed up computation time compared to full linear gyrokinetic solvers. Optimization of the dispersion relation solution algorithm within integrated modelling applications leads to flux calculations $\times10^{6-7}$ faster than local nonlinear simulations. This allows tractable simulation of flux-driven dynamic profile evolution including all transport channels: ion and electron heat, main particles, impurities, and momentum. Furthermore, QuaLiKiz now includes the impact of rotation and temperature anisotropy induced poloidal asymmetry on heavy impurity transport, important for W-transport applications. Application within the JETTO integrated modelling code results in 1s of JET plasma simulation within 10 hours using 10 CPUs. Simultaneous predictions of core density, temperature, and toroidal rotation profiles for both JET hybrid and baseline experiments are presented, covering both ion and electron turbulence scales. The simulations are successfully compared to measured profiles, with agreement mostly in the 5-25% range according to standard figures of merit.

This paper presents the use of a novel modelling technique based around intermittent transport due to filament motion, to interpret experimental profile and fluctuation data in the scrape-off layer (SOL) of JET during the onset and evolution of a density profile shoulder. A baseline case is established, prior to shoulder formation, and the stochastic model is shown to be capable of simultaneously matching the time averaged profile measurement as well as the PDF shape and autocorrelation function from the ion-saturation current time series at the outer wall. Aspects of the stochastic model are then varied with the aim of producing a profile shoulder with statistical measurements consistent with experiment. This is achieved through a strong localised reduction in the density sink acting on the filaments within the model. The required reduction of the density sink occurs over a highly localised region with the timescale of the density sink increased by a factor of 25. This alone is found to be insufficient to model the expansion and flattening of the shoulder region as the density increases, which requires additional changes within the stochastic model. An example is found which includes both a reduction in the density sink and filament acceleration and provides a consistent match to the experimental data as the shoulder expands, though the uniqueness of this solution can not be guaranteed. Within the context of the stochastic model, this implies that the localised reduction in the density sink can trigger shoulder formation, but additional physics is required to explain the subsequent evolution of the profile.

Deep learning is having a profound impact in many fields, especially those that involve some form of image processing. Deep neural networks excel in turning an input image into a set of high-level features. On the other hand, tomography deals with the inverse problem of recreating an image from a number of projections. In plasma diagnostics, tomography aims at reconstructing the cross-section of the plasma from radiation measurements. This reconstruction can be computed with neural networks. However, previous attempts have focused on learning a parametric model of the plasma profile. In this work, we use a deep neural network to produce a full, pixel-by-pixel reconstruction of the plasma profile. For this purpose, we use the overview bolometer system at JET, and we introduce an up-convolutional network that has been trained and tested on a large set of sample tomograms. We show that this network is able to reproduce existing reconstructions with a high level of accuracy, as measured by several metrics.

Universality in the ion flux to the JET outer-wall is observed in outerwall limiter mounted Langmuir probe (OLP) time-series across a large range of plasma current and line-averaged density during Ohmically heated horizontal target L-mode plasmas. The mean, M, and the standard deviation, sigma, of the ion-saturation current measured by the OLP show systematic variation with plasma current and density. Both increase as either plasma current decreases and/or density increases. Upon renormalization, achieved by subtraction of M and rescaling by sigma, the probability distribution functions (PDFs) of each signal collapse approximately onto a single curve. The shape of the curve deviates from a distribution in the tail of the PDF and is better described by a log-normal distribution. The collapse occurs over 4 decades of the ordinate which, given the wide parameter space over which the data spans, is a strong indication of universality., Comment: 10 pages, 6 figures. This is an author-created, un-copyedited version of an article submitted for publication in Nuclear Fusion Letter. IoP Publishing Ltd is not responsible for any errors or omissions in this version of the manuscript or any version derived from it

In Hybrid plasma operation in JET with its ITER-like wall (JET-ILW) it is found that n>1 tearing activity can significantly enhance the rate of on-axis peaking of tungsten impurities, which in turn significantly degrades discharge performance. Core n=1 instabilities can be beneficial in removing tungsten impurities from the plasma core (e.g. sawteeth or fishbones), but can conversely also degrade core confinement (particularly in combination with simultaneous n=3 activity). The nature of MHD instabilities in JET Hybrid discharges, with both its previous Carbon wall and subsequent JET-ILW, is surveyed statistically and the character of the instabilities is examined. Possible qualitative models for how the n>1 islands can enhance on-axis tungsten transport accumulation processes are presented., Comment: 19 pages, 17 figures. This is an author-created, un-copyedited version of an article submitted for publication in Nuclear Fusion. IoP Publishing Ltd is not responsible for any errors or omissions in this version of the manuscript or any version derived from it

A Bayesian model of the emission spectrum of the JET lithium beam has been developed to infer the intensity of the Li I (2p-2s) line radiation and associated uncertainties. The detected spectrum for each channel of the lithium beam emission spectroscopy (Li-BES) system is here modelled by a single Li line modified by an instrumental function, Bremsstrahlung background, instrumental offset, and interference filter curve. Both the instrumental function and the interference filter curve are modelled with non-parametric Gaussian processes. All free parameters of the model, the intensities of the Li line, Bremsstrahlung background, and instrumental offset, are inferred using Bayesian probability theory with a Gaussian likelihood for photon statistics and electronic background noise. The prior distributions of the free parameters are chosen as Gaussians. Given these assumptions, the intensity of the Li line and corresponding uncertainties are analytically available using a Bayesian linear inversion technique. The proposed approach makes it possible to extract the intensity of Li line without doing a separate background subtraction through modulation of the Li beam., Comment: 6 pages, 6 figures, submitted to Review of Scientific Instruments

In a wide variety of natural and laboratory magnetized plasmas, filaments appear as a result of interchange instability. These convective structures substantially enhance transport in the direction perpendicular to the magnetic field. According to filament models, their propagation may follow different regimes depending on the parallel closure of charge conservation. This is of paramount importance in magnetic fusion plasmas, as high collisionality in the scrape-off layer may trigger a regime transition leading to strongly enhanced perpendicular particle fluxes. This work reports for the first time on an experimental verification of this process, linking enhanced transport with a regime transition as predicted by models. Based on these results, a novel scaling for global perpendicular particle transport in reactor relevant tokamaks such as ASDEX-Upgrade and JET is found, leading to important implications for next generation fusion devices., Comment: Regarding JET-EFDA Contributors, see the Appendix of F. Romanelli et al., Proceedings of the 25th IAEA Conference 2014, St Petersburg, Russia. Submitted to Physical Review Letters

A global signature of the build-up to an intrinsic ELM is found in the phase of signals measured in full flux azimuthal loops in the divertor region of JET. Full flux loop signals provide a global measurement proportional to the voltage induced by changes in poloidal magnetic flux; they are electromagnetically induced by the dynamics of spatially integrated current density. We perform direct time-domain analysis of the high time-resolution full flux loop signals VLD2 and VLD3. We analyze plasmas where a steady H-mode is sustained over several seconds, during which all the observed ELMs are intrinsic; there is no deliberate intent to pace the ELMing process by external means. ELM occurrence times are determined from the Be II emission at the divertor. We previously found that the occurrence times of intrinsic ELMs correlate with specific phases of the VLD2 and VLD3 signals. Here, we investigate how the VLD2 and VLD3 phases vary with time in advance of the ELM occurrence time. We identify a build-up to the ELM in which the VLD2 and VLD3 signals progressively align to the phase at which ELMs preferentially occur, on a ~ 2 -5ms timescale. At the same time, the VLD2 and VLD3 signals become phase synchronized with each other, consistent with the emergence of coherent global dynamics in the integrated current density. In a plasma that remains close to a global magnetic equilibrium, this can reflect bulk displacement or motion of the plasma. This build-up signature to an intrinsic ELM can be extracted from a time interval of data that does not extend beyond the ELM occurrence time, so that these full flux loop signals could assist in ELM prediction or mitigation., Comment: 31 pages, 13 figures. The following article has been submitted to Physics of Plasmas. After it is published it will be found at http://scitation.aip.org/content/aip/journal/pop/browse

A unique experiment in the Joint European Torus (JET) consecutively produced 120 almost identical plasma pulses, providing two orders of magnitude more data than is usually available. This allows the statistical detection of previously unobservable phenomena such as a sequence of resonant-like waiting times between edge-localised instabilities (ELMs). Here we investigate the causes of this phenomenon. By synchronising data to the 1000s of ELM times and averaging the results, random errors are reduced by a factor of 50, allowing unprecedentedly detailed behaviour to be described. A clear link can then be observed between plasma confinement, ELM occurrence, vertical plasma oscillations, and an otherwise unobservable oscillation in a control coil current that is not usually associated with ELM occurrence. The results suggest a strong and unanticipated edge-plasma dependence on control system behaviour., Comment: 4 pages, 5 figures created from 7 figure files