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Local gyrokinetic simulations are used to model turbulent transport for the first time in a representative high-performance plasma discharge projected for the new JT-60SA tokamak. The discharge features a double-null separatrix, 41 MW of combined neutral beam heating and electron cyclotron heating, and a high predicted ratio of the normalized plasma kinetic to magnetic pressure β. When considering input parameters computed from reduced transport models, gyrokinetic simulations predict a turbulent heat flux well below the injected 41 MW. Increasing the background gradients, on the other hand, can trigger a non-zonal transition (NZT), causing heat fluxes to no longer saturate. Furthermore, when considering fast ions in the simulations, a high-frequency mode is destabilized that substantially impacts the turbulence. The NZT is avoided by reducing the electron pressure by 10% below its nominal value, and the fast-ion resonance is removed by reducing the fast-ion temperature. The thus-obtained simulation features broadband frequency spectra and density and temperature fluctuation levels δn/n≈1% –2%, δT/T≈1% –6% that should be measurable with fluctuation diagnostics planned for JT-60SA. The temperature profile is fixed by the critical main-ion temperature gradient as a consequence of the high stiffness; heat fluxes increase by a factor of ten when increasing the main ion temperature gradient by 17%. Despite large gradients, it is demonstrated that, due to the large β, retaining compressional magnetic field fluctuations and in particular, the contribution of the pressure gradient in the ∇B drifts, is crucial to achieving non-zero heat fluxes.

The effects of different working gases on the transition from linear ohmic confinement (LOC) regime to saturated ohmic confinement (SOC) regime and its relation to the intrinsic toroidal rotation reversal phenomenon were explored in the TCV tokamak. The energy confinement saturation was studied across D, H and He density ramps, and a range of ECRH injection power and through variations of ohmic plasma current. The occurrence of rotation reversal, concomitantly with the LOC–SOC transition, was observed only for certain cases, making us formally exclude a causal relation between the two phenomena. A strong correlation between the evolution of toroidal rotation profiles and electron density gradients was, however, observed, in agreement with previous works (Lebschy et al 2017 Nucl. Fusion 58 026013; Hornsby et al 2018 Nucl. Fusion 58 056008). Linear gyrokinetic simulations were performed to probe the turbulent regime of these discharges, showing a dominance of trapped electron mode (TEM) during the LOC phase and a mixture of TEM and ion temperature gradient (ITG) following the transition to SOC regime in D. Such a TEM/ITG bifurcation was less pronounced in H and He. MHD activity was monitored throughout the discharges and possible correlations between sawteeth instability activity, energy confinement time saturation and rotation reversal are highlighted.

Tokamak à configuration variable (TCV), recently celebrating 30 years of near-continual operation, continues in its missions to advance outstanding key physics and operational scenario issues for ITER and the design of future power plants such as DEMO. The main machine heating systems and operational changes are first described. Then follow five sections: plasma scenarios. ITER Base-Line (IBL) discharges, triangularity studies together with X3 heating and N2 seeding. Edge localised mode suppression, with a high radiation region near the X-point is reported with N2 injection with and without divertor baffles in a snowflake configuration. Negative triangularity (NT) discharges attained record, albeit transient, βN ∼ 3 with lower turbulence, higher low-Z impurity transport, vertical stability and density limits and core transport better than the IBL. Positive triangularity L-Mode linear and saturated ohmic confinement confinement saturation, often-correlated with intrinsic toroidal rotation reversals, was probed for D, H and He working gases. H-mode confinement and pedestal studies were extended to low collisionality with electron cyclotron heating obtaining steady state electron iternal transport barrier with neutral beam heating (NBH), and NBH driven H-mode configurations with off-axis co-electron cyclotron current drive. Fast particle physics. The physics of disruptions, runaway electrons and fast ions (FIs) was developed using near-full current conversion at disruption with recombination thresholds characterised for impurity species (Ne, Ar, Kr). Different flushing gases (D2, H2) and pathways to trigger a benign disruption were explored. The 55 kV NBH II generated a rich Alfvénic spectrum modulating the FI fas ion loss detector signal. NT configurations showed less toroidal Alfvén excitation activity preferentially affecting higher FI pitch angles. Scrape-off layer and edge physics. gas puff imaging systems characterised turbulent plasma ejection for several advanced divertor configurations, including NT. Combined diagnostic array divertor state analysis in detachment conditions was compared to modelling revealing an importance for molecular processes. Divertor physics. Internal gas baffles diversified to include shorter/longer structures on the high and/or low field side to probe compressive efficiency. Divertor studies concentrated upon mitigating target power, facilitating detachment and increasing the radiated power fraction employing alternative divertor geometries, optimised X-point radiator regimes and long-legged configurations. Smaller-than-expected improvements with total flux expansion were better modelled when including parallel flows. Peak outer target heat flux reduction was achieved (>50%) for high flux-expansion geometries, maintaining core performance (H98 > 1). A reduction in target heat loads and facilitated detachment access at lower core densities is reported. Real-time control. TCV’s real-time control upgrades employed MIMO gas injector control of stable, robust, partial detachment and plasma β feedback control avoiding neoclassical tearing modes with plasma confinement changes. Machine-learning enhancements include trajectory tracking disruption proximity and avoidance as well as a first-of-its-kind reinforcement learning-based controller for the plasma equilibrium trained entirely on a free-boundary simulator. Finally, a short description of TCV’s immediate future plans will be given.

In this work we construct logarithms and Birkhoff normal forms for elliptic Fourier integral operators in the semi-classical limit, under more general assumptions than in a previous work by the first author. The methods are similar but slightly different.

The electron density of the neutral atoms at the distances , from the nucleus in the limit when the charge of the nucleus Z tends to infinity is well approximated by the function , which is a common limiting value for both the Thomas-Fermi density at the origin and the hydrogen density at infinity. This conjecture by Lieb is proved in some weak sense by using the Ivrii and Sigal method.

We prove that the suitably rescaled density matrix of ground states of atomic Schrödinger operators with nuclear chargeZ converges on the scale 1/Z to the projection of the negative spectral subspace of the Schrödinger operator of the hydrogen atom (Z=1).

In this work we construct logarithms and Birkhoff normal forms for elliptic Fourier integral operators in the semi-classical limit under more general assumptions than in aprevious work by the first author. The methods are similar but slightly different.

We apply recent results on semi-classical trace formulae and on Birkhoff normal forms for semi-classical Fourier integral operators to a wide range of semi-classical and high energy spectral inverse problems.

A large amplitude oscillatory shear (LAOS) is considered in the strain-controlled regime, and the interrelation between the Fourier transform and the stress decomposition approaches is established. Several definitions of the generalized storage and loss moduli are examined in a unified conceptual scheme based on the Lissajous–Bowditch plots. An illustrative example of evaluating the generalized moduli from a LAOS flow is given.

A large amplitude oscillatory shear (LAOS) is considered in the strain-controlled regime, and the interrelation between the Fourier transform and the stress decomposition approaches is established. Several definitions of the generalized storage and loss moduli are examined in a unified conceptual scheme based on the Lissajous–Bowditch plots. An illustrative example of evaluating the generalized moduli from a LAOS flow is given.