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 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

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

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

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

Physics research on the TCV tokamak facility: from conventional to alternative scenarios and beyond

The research program of the TCV tokamak ranges from conventional to advanced-tokamak scenarios and alternative divertor configurations, to exploratory plasmas driven by theoretical insight, exploiting the device’s unique shaping capabilities. Disruption avoidance by real-time locked mode prevention or unlocking with electron-cyclotron resonance heating (ECRH) was thoroughly documented, using magnetic and radiation triggers. Runaway generation with high-Z noble-gas injection and runaway dissipation by subsequent Ne or Ar injection were studied for model validation. The new 1 MW neutral beam injector has expanded the parameter range, now encompassing ELMy H-modes in an ITER-like shape and nearly non-inductive H-mode discharges sustained by electron cyclotron and neutral beam current drive. In the H-mode, the pedestal pressure increases modestly with nitrogen seeding while fueling moves the density pedestal outwards, but the plasma stored energy is largely uncorrelated to either seeding or fueling. High fueling at high triangularity is key to accessing the attractive small edge-localized mode (type-II) regime. Turbulence is reduced in the core at negative triangularity, consistent with increased confinement and in accord with global gyrokinetic simulations. The geodesic acoustic mode, possibly coupled with avalanche events, has been linked with particle flow to the wall in diverted plasmas. Detachment, scrape-off layer transport, and turbulence were studied in L- and H-modes in both standard and alternative configurations (snowflake, super-X, and beyond). The detachment process is caused by power ‘starvation’ reducing the ionization source, with volume recombination playing only a minor role. Partial detachment in the H-mode is obtained with impurity seeding and has shown little dependence on flux expansion in standard single-null geometry. In the attached L-mode phase, increasing the outer connection length reduces the in–out heat-flow asymmetry. A doublet plasma, featuring an internal X-point, was achieved successfully, and a transport barrier was observed in the mantle just outside the internal separatrix. In the near future variable-configuration baffles and possibly divertor pumping will be introduced to investigate the effect of divertor closure on exhaust and performance, and 3.5 MW ECRH and 1 MW neutral beam injection heating will be added

Scattering poles near the real axis for two strictly convex obstacles

To study the location of poles for the acoustic scattering matrix for two strictly convex obstacles with smooth boundaries, one uses an approximation of the quantized billiard operator $M$ along the trapped ray between the two obstacles. Using this method Ikawa and G{\'e}rard established the existence of parallel rows of poles in a strip $Im z\leq c$ as $Re z$ tends to infinity. Assuming that the boundaries are analytic and the eigenvalues of Poincar{\'e} map are non-resonant we use the Birkhoff normal form for $M$ to improve this result and to get the complete asymptotic expansions for the poles in any logarithmic neighborhood of real axis