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In JET deuterium-tritium (D-T) plasmas, the fusion power is produced through thermonuclear reactions and reactions between thermal ions and fast particles generated by neutral beam injection (NBI) heating or accelerated by electromagnetic wave heating in the ion cyclotron range of frequencies (ICRFs). To complement the experiments with 50/50 D/T mixtures maximizing thermonuclear reactivity, a scenario with dominant non-thermal reactivity has been developed and successfully demonstrated during the second JET deuterium-tritium campaign DTE2, as it was predicted to generate the highest fusion power in JET with a Be/W wall. It was performed in a 15/85 D/T mixture with pure D-NBI heating combined with ICRF heating at the fundamental deuterium resonance. In steady plasma conditions, a record 59 MJ of fusion energy has been achieved in a single pulse, of which 50.5 MJ were produced in a 5 s time window ( P fus = 10.1 MW) with average Q = 0.33, confirming predictive modelling in preparation of the experiment. The highest fusion power in these experiments, P fus = 12.5 MW with average Q = 0.38, was achieved over a shorter 2 s time window, with the period of sustainment limited by high-Z impurity accumulation. This scenario provides unique data for the validation of physics-based models used to predict D-T fusion power.

We present a method to analytically compute gamma-ray spectra generated via two-step fusion reactions, where a gamma-ray is emitted from the excited nucleus generated in the first step of the reaction. If one reactant is energetic and the other is at rest, the first step of the reaction can be treated analytically. The second step, which is the gamma-ray emission from the excited nucleus, can always be treated analytically. The model we derive is tested against the established forward-model code GENESIS, obtaining very satisfactory results. Our fully analytic treatment is a far less expensive technique than standard Monte Carlo methods, achieving several times faster computations. Fast calculations of spectra are especially beneficial when working with finely-resolved 3D-4D phase spaces. Furthermore, tractable analytical expressions give insight that is not provided by Monte Carlo methods. The formalism used for the first step of the reaction additionally allows the computation of birth distributions of fusion products from any beam-target reaction with one reactant at rest, e.g. fusion-born alpha distributions.

We present a fully analytical model for calculating energy spectra of neutrons generated by fusion reactions involving a fast ion, or beam, and a stationary ion, or target, in magnetic fusion plasmas. For neutrons moving along the line-of-sight of a detector, the neutron spectrum is given by an analytical expression and the usual differential cross section. This makes the model several orders of magnitude faster than ordinary Monte Carlo simulations and free of any related statistical noise. Additionally, the analytical description of the reaction physics provides much more insight into the formation of the spectrum. An example of this is the bias of beam-target spectra towards high-energy neutron counts, which corresponds to forward-emission events. On the other hand, the fast-ion uniform gyro-angle distribution has an opposite effect, but is ultimately weaker than the preferential forward emission of neutrons. The model is validated against numerical calculations from the forward model code GENESIS to verify its validity and it is furthermore derived from a probabilistic viewpoint, adding further insight.

The fast-ion distribution function in fusion plasmas can only be measured indirectly by solving an ill-posed inverse problem. The inversion being ill-posed necessitates regularisation of the problem to ensure that the reconstruction of the fast-ion distribution function depends smoothly on the measurements obtained by fast-ion diagnostics. In turn, the resulting reconstruction depends on the choice of regularisation, and it is therefore beneficial to choose a physics-informed prior as regularisation scheme. In this work, we reconstruct the high-energy tail in the MeV-range of the fast-deuterium distribution in JET discharges heated by waves in the ion cyclotron range of frequencies (ICRF) using neutron and gamma-ray emission spectroscopy. We do this by applying a physics-informed prior based on collision physics and a newly formulated ICRF-physics prior, and we compare these results with numerical simulations and inversions based on a standard Tikhonov regularisation scheme. Our findings suggest that the physics-informed regularisation scheme including the ICRF prior improves the reconstructions compared with standard Tikhonov regularisation. Finally, it is shown that constraining the reconstruction to have negative gradients in the directions of phase space dictated by ICRF physics results in a reconstruction that well resembles expectations based on ICRF physics theory and numerical simulations.

We compute reconstructions of 4D and 5D fast-ion phase-space distribution functions in fusion plasmas from synthetic projections of these functions. The fast-ion phase-space distribution functions originating from neutral beam injection (NBI) at TCV and Wendelstein 7-X (W7-X) at full, half, and one-third injection energies can be distinguished and particle densities of each component inferred based on 20 synthetic spectra of projected velocities at TCV and 680 at W7-X. Further, we demonstrate that an expansion into a basis of slowing-down distribution functions is equivalent to regularization using slowing-down physics as prior information. Using this technique in a Tikhonov formulation, we infer the particle density fractions for each NBI energy for each NBI beam from synthetic measurements, resulting in six unknowns at TCV and 24 unknowns at W7-X. Additionally, we show that installing 40 LOS in each of 17 ports at W7-X, providing full beam coverage and almost full angle coverage, produces the highest quality reconstructions.

The fast-ion phase-space distribution function in axisymmetric tokamak plasmas is completely described by the three constants of motion: energy, magnetic moment and toroidal canonical angular momentum. In this work, the observable regions of constants-of-motion phase-space, given a diagnostic setup, are identified and explained using projected velocities of the fast ions along the diagnostic lines-of-sight as a proxy for several fast-ion diagnostics, such as fast-ion Dα spectroscopy, collective Thomson scattering, neutron emission spectroscopy and gamma-ray spectroscopy. The observable region in constants-of-motion space is given by a position condition and a velocity condition, and the diagnostic sensitivity is given by a gyro-orbit and a drift-orbit weighting. As a practical example, 3D orbit weight functions quantifying the diagnostic sensitivity to each point in phase-space are computed and investigated for the future COMPASS-Upgrade and MAST-Upgrade tokamaks.

Tomographic reconstructions of a 3D fast-ion constants-of-motion phase-space distribution function are computed by inverting synthetic signals based on projected velocities of the fast ions along the diagnostic lines of sight. A spectrum of projected velocities is a key element of the spectrum formation in fast-ion D-alpha spectroscopy, collective Thomson scattering, and gamma-ray and neutron emission spectroscopy, and it can hence serve as a proxy for any of these. The fast-ion distribution functions are parameterised by three constants of motion, the kinetic energy, the magnetic moment and the toroidal canonical angular momentum. The reconstructions are computed using both zeroth-order and first-order Tikhonov regularisation expressed in terms of Bayesian inference to allow uncertainty quantification. In addition to this, a discontinuity appears to be present in the solution across the trapped-passing boundary surface in the three-dimensional phase space due to a singularity in the Jacobian of the transformation from position and velocity space to phase space. A method to allow for this apparent discontinuity while simultaneously penalising large gradients in the solution is demonstrated. Finally, we use our new methods to optimise the diagnostic performance of a set of six fans of sightlines by finding where the detectors contribute most complementary diagnostic information for the future COMPASS-Upgrade tokamak.

This study introduces the use of a deep convolutional neural network for reconstructing fast-ion velocity distributions from fast-ion loss detectors and imaging neutral particle analyzers (INPAs), automatically integrating uncertainty quantification through Monte Carlo dropout. The network-based reconstructions reveal pitch-angle splitting in high-energy features of lost fast-ion velocity distributions at ASDEX Upgrade during active neutral beam injection, a previously observed phenomenon now confirmed through neural networks. Moreover, contrary to common theories attributing these high-energy features to edge localized mode (ELM)-driven acceleration, we provide experimental evidence that they also occur in type-I ELM-quiescent phases. Additionally, we demonstrate improved reconstructions from INPA measurements, both synthetic and from an ASDEX Upgrade commissioning discharge, with the reconstructions closely matching TRANSP simulations. These findings suggest that neural networks can provide robust reconstructions with well-defined uncertainties, improving the reliability of interpretations of fast-ion behavior in magnetically confined plasmas.

We calculate the orbit-space sensitivity of two-step reaction gamma-ray spectroscopy diagnostics in toroidally symmetric magnetic equilibria, using the reaction between alpha particles and beryllium-9 as an example. To reduce the computational cost, we use analytical solutions obtained by neglecting the velocity of the thermal beryllium. The sensitivity is quantified by weight functions, which we calculate in the alpha-particle orbit space of energy, maximum major radius and pitch at that maximum major radius. Each alpha-particle guiding-center orbit leads to a characteristic gamma-ray spectrum depending on the line-of-sight geometry. We highlight the geometry dependence by repeating the calculation for three different cases, observing significant changes in the sensitivity patterns. Weight functions also allow one to quickly compute forward model problems if spectra from many distribution functions are to be calculated and compared with experimental measurements.

The Doppler-shifted resonance condition for high frequency Alfvénic eigenmodes has been extensively studied on ASDEX Upgrade in the presence of one or a combination of two neutral beam injected (NBI) fast ion populations. In general, only centrally deposited NBI sources drive these modes, while off-axis sources globally stabilize the mode activity. For the case of a single central NBI source, the observed trend is: the highest frequency modes are driven by the lowest energy and lowest pitch angle NBI sources, in line with the expectation from the Doppler-shifted resonance condition. The expected mode frequencies are determined analytically from the two-fluid cold plasma dispersion relation and the most unstable frequency relation, while the mode growth rates are estimated using the fast ion slowing down distribution functions from the ASCOT code. The overall mode frequency trend in a source-to-source variation is tracked, although a systematic overestimate of ∼1 MHz is observed. Possible causes of this overestimate include the finite size of the resonant fast ion drift orbit and non-linear effects such as mode sideband formation. Alternatively, the expected mode frequencies are determined by tracking the growth rate maxima trajectories, this method improves the agreement with the experimentally measured values. A combination of two central mode-driving NBI sources results in the suppression of the mode driven by the lowest energy and the lowest pitch angle NBI source. Computing the analytically expected mode frequency following the method outlined above, again, generally tracks the experimentally observed trend. The mode’s Alfvénic nature allows for a practical application to track the core hydrogen fraction by following the mode frequency changes in response to a varying ion mass density. Such application is demonstrated in a discharge where the average ion mass is varied from ∼2mp to ∼1.5mp (where mp is the proton mass) via a hydrogen puff in a deuterium plasma, in the presence of a strong mode activity. The expected mode frequency changes are computed from the existence of the resonance condition, and the values track the measured results with an offset of ∼0.5 MHz. Overall, the results suggest an intriguing possibility to monitor and control the D-T ion fraction in the core of a fusion reactor in real time using a non-invasive diagnostic.