Periodic Jacobi operator with finitely supported perturbation on the half-lattice

We consider the periodic Jacobi operator $J$ with finitely supported perturbations on the half-lattice. We describe all eigenvalues and resonances of $J$ and give their properties. We solve the inverse resonance problem: we prove that the mapping from finitely supported perturbations to the Jost functions is one-to-one and onto, we show how the Jost functions can be reconstructed from the eigenvalues, resonances and the set of zeros of S(\l)-1, where S(\l) is the scattering matrix.Comment: 29 page

First principles of modelling the stabilization of microturbulence by fast ions

The observation that fast ions stabilize ion-temperature-gradient-driven microturbulence has profound implications for future fusion reactors. It is also important in optimizing the performance of present-day devices. In this work, we examine in detail the phenomenology of fast ion stabilization and present a reduced model which describes this effect. This model is derived from the high-energy limit of the gyrokinetic equation and extends the existing "dilution" model to account for nontrivial fast ion kinetics. Our model provides a physically-transparent explanation for the observed stabilization and makes several key qualitative predictions. Firstly, that different classes of fast ions, depending on their radial density or temperature variation, have different stabilizing properties. Secondly, that zonal flows are an important ingredient in this effect precisely because the fast ion zonal response is negligible. Finally, that in the limit of highly-energetic fast ions, their response approaches that of the "dilution" model; in particular, alpha particles are expected to have little, if any, stabilizing effect on plasma turbulence. We support these conclusions through detailed linear and nonlinear gyrokinetic simulations.Comment: 29 pages, 10 figures, 3 table

L^{2}-restriction bounds for eigenfunctions along curves in the quantum completely integrable case

We show that for a quantum completely integrable system in two dimensions,the $L^{2}$-normalized joint eigenfunctions of the commuting semiclassical pseudodifferential operators satisfy restriction bounds ofthe form $\int_{\gamma} |\phi_{j}^{\hbar}|^2 ds = {\mathcal O}(|\log \hbar|)$ for generic curves $\gamma$ on the surface. We also prove that the maximal restriction bounds of Burq-Gerard-Tzvetkov are always attained for certain exceptional subsequences of eigenfunctions.Comment: Correct some typos and added some more detail in section

First principles of modelling the stabilization of microturbulence by fast ions

The observation that fast ions stabilize ion-temperature-gradient-driven microturbulence has profound implications for future fusion reactors. It is also important in optimizing the performance of present-day devices. In this work, we examine in detail the phenomenology of fast ion stabilization and present a reduced model which describes this effect. This model is derived from the high-energy limit of the gyrokinetic equation and extends the existing ‘dilution’ model to account for nontrivial fast ion kinetics. Our model provides a physicallytransparent explanation for the observed stabilization and makes several key qualitative predictions. Firstly, that different classes of fast ions, depending on their radial density or temperature variation, have different stabilizing properties. Secondly, that zonal flows are an important ingredient in this effect precisely because the fast ion zonal response is negligible. Finally, that in the limit of highly-energetic fast ions, their response approaches that of the ‘dilution’ model; in particular, alpha particles are expected to have little, if any, stabilizing effect on plasma turbulence. We support these conclusions through detailed linear and nonlinear gyrokinetic simulations

Hearing shapes of drums - mathematical and physical aspects of isospectrality

In a celebrated paper '"Can one hear the shape of a drum?"' M. Kac [Amer. Math. Monthly 73, 1 (1966)] asked his famous question about the existence of nonisometric billiards having the same spectrum of the Laplacian. This question was eventually answered positively in 1992 by the construction of noncongruent planar isospectral pairs. This review highlights mathematical and physical aspects of isospectrality.Comment: 42 pages, 60 figure

Study of fast-ion-driven toroidal Alfvén eigenmodes impacting on the global confinement in TCV L-mode plasmas

Following recent observations of unstable Toroidal Alfvén Eigenmodes (TAEs) in a counter-current Neutral Beam Injection (NBI) scenario developed in TCV, an in-depth analysis of the impact of such modes on the global confinement and performance is carried out. The study shows experimental evidence of non-degradation of ion thermal confinement despite the increasing of auxiliary power. During such an improved confinement period, Toroidal Alfvén Eigenmodes (TAEs) driven by fast ions generated through Neutral Beam Injection (NBI) are found unstable. Together with the TAEs, various instabilities associated with the injection of the fast neutrals are observed by multiple diagnostics, and a first characterization is given. Nonlinear wave-wave couplings are also detected through multi-mode analysis, revealing a complex picture of the stability dynamics of the TCV scenario at hand. The measurements provided by a short-pulse reflectometer corroborate the identification and radial localization of the instabilities. A preliminary, but not conclusive, analysis of the impact of TAEs on the amplitude of the electron density fluctuations is carried out. Local flux-tube gyrokinetic simulations show that the dominant underlying instabilities in the absence of fast ions are Trapped Electron Modes (TEM), and that these modes are effectively suppressed by zonal flows. Attempts to simulate the simultaneous presence of fast-ion driven TAEs and TEM turbulence show that elongated streamers develop up to the full radial extent of the flux-tube domain, thereby invalidating the local assumption and indicating that a global approach is mandatory in these TCV plasmas

Plasma physics and control studies planned in JT-60SA for ITER and DEMO operations and risk mitigation

| openaire: EC/H2020/633053/EU//EUROfusionA large superconducting machine, JT-60SA has been constructed to provide major contributions to the ITER program and DEMO design. For the success of the ITER project and fusion reactor, understanding and development of plasma controllability in ITER and DEMO relevant higher beta regimes are essential. JT-60SA has focused the program on the plasma controllability for scenario development and risk mitigation in ITER as well as on investigating DEMO relevant regimes. This paper summarizes the high research priorities and strategy for the JT-60SA project. Recent works on simulation studies to prepare the plasma physics and control experiments are presented, such as plasma breakdown and equilibrium controls, hybrid and steady-state scenario development, and risk mitigation techniques. Contributions of JT-60SA to ITER and DEMO have been clarified through those studies.Peer reviewe

Experimental research on the TCV tokamak

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

Overview of the TCV tokamak experimental programme

The tokamak a configuration variable (TCV) continues to leverage its unique shaping capabilities, flexible heating systems and modern control system to address critical issues in preparation for ITER and a fusion power plant. For the 2019-20 campaign its configurational flexibility has been enhanced with the installation of removable divertor gas baffles, its diagnostic capabilities with an extensive set of upgrades and its heating systems with new dual frequency gyrotrons. The gas baffles reduce coupling between the divertor and the main chamber and allow for detailed investigations on the role of fuelling in general and, together with upgraded boundary diagnostics, test divertor and edge models in particular. The increased heating capabilities broaden the operational regime to include T (e)/T (i) similar to 1 and have stimulated refocussing studies from L-mode to H-mode across a range of research topics. ITER baseline parameters were reached in type-I ELMy H-modes and alternative regimes with \u27small\u27 (or no) ELMs explored. Most prominently, negative triangularity was investigated in detail and confirmed as an attractive scenario with H-mode level core confinement but an L-mode edge. Emphasis was also placed on control, where an increased number of observers, actuators and control solutions became available and are now integrated into a generic control framework as will be needed in future devices. The quantity and quality of results of the 2019-20 TCV campaign are a testament to its successful integration within the European research effort alongside a vibrant domestic programme and international collaborations