Non-linear MHD modelling of Edge Localized Modes suppression by Resonant Magnetic Perturbations in ITER

Edge Localized Modes (ELMs) suppression by Resonant Magnetic Perturbations (RMPs) was studied with the non-linear MHD code JOREK for the ITER H-mode scenarios at 15MA,12.5MA,10MA/5.3T. The main aim of this work was to demonstrate that ELMs can be suppressed by RMPs while the divertor 3D footprints of heat and particle fluxes remain within divertor material limits. The unstable peeling-ballooning modes responsible for ELMs without RMPs were modelled first for each scenario using numerically accessible parameters for ITER. Then the stabilization of ELMs by RMPs was modelled with the same parameters. RMP spectra, optimized by the linear MHD MARS-F code, with main toroidal harmonics N=2, N=3, N=4 have been used as boundary conditions of the computational domain of JOREK, including realistic RMP coils, main plasma, Scrape Off Layer (SOL) divertor and realistic first wall. The model includes all relevant plasma flows: toroidal rotation, two fluid diamagnetic effects and neoclassical poloidal friction. With RMPs, the main toroidal harmonic and the non-linearly coupled harmonics remain dominant at the plasma edge, producing saturated modes and a continuous MHD turbulent transport thereby avoiding ELM crashes in all scenarios considered here. The threshold for ELM suppression was found at a maximum RMP coils current of 45kAt-60kAt compared to the coils maximum capability of 90kAt. In the high beta poloidal steady-state 10MA/5.3T scenario, a rotating QH-mode without ELMs was observed even without RMPs. In this scenario with RMPs N=3, N=4 at 20kAt maximum current in RMP coils, similar QH-mode behavior was observed however with dominant edge harmonic corresponding to the main toroidal number of RMPs. The 3D footprints with RMPs show the characteristic splitting with the main RMP toroidal symmetry. The maximum radial extension of the footprints typically was ~20 cm in inner divertor and ~40 cm in outer divertor with stationary heat fluxes decreasing further out from the initial strike point from ~5MW/m2 to ~1MW/m2 assuming a total power in the divertor and walls is 50MW.

Temperature oscillation in one-dimensional superlattice induced by phonon localization

Thermal transport properties and thermodynamic quantities often present anomalous behaviors in low-dimensional systems. In this paper, we find that temperature oscillates spatially in one dimensional harmonic and weakly anharmonic superlattice. With the increase of anharmonicity, the temperature oscillation gradually disappears and a normal temperature gradient forms. Further analysis reveals that the formation of temperature oscillation is due to the localization of high frequency phonons which cannot be thermalized. Moreover, the localized modes interact weakly with heat reservoirs, thus, their contributions to local temperature remain negligible while varying the temperatures of heat reservoirs. The oscillated temperature profile is in a good agreement with Visscher's formula. These discoveries of temperature oscillation phenomenon have great potential in applications of phononic devices for heat manipulation.

Pellet triggering of edge localized modes in low collisionality pedestals at DIII-D

Edge localized modes (ELMs) are triggered using deuterium pellets injected into plasmas with ITER-relevant low collisionality pedestals, and the resulting peak ELM energy fluence is reduced by approximately 25-50% relative to natural ELMs destabilized at similar pedestal pressures. Cryogenically frozen deuterium pellets are injected from the low-field side of the DIII-D tokamak at frequencies lower than the natural ELM frequency, and heat flux is measured by infrared cameras. Ideal MHD pedestal stability calculations show that without pellet injection, these low collisionality pedestals were limited by their current density (peeling-limited) rather than their pressure gradient (ballooning-limited). ELM triggering success correlates strongly with pellet mass, consistent with the theory that a large pressure perturbation is required to trigger an ELM in low collisionality discharges that are far from the ballooning stability boundary. For sufficiently large pellets, both instantaneous and time-integrated ELM energy deposition measured by infrared cameras is reduced with respect to naturally occurring ELMs at the inner strike point, which is the position where it is largest for natural ELMs. Energy fluence at the outer strike point is less effected. Cameras observing both heat flux and D-alpha emission often find significant toroidally asymmetric striations in the outboard far scrape-off layer resulting from ELMs that are triggered by pellets. Toroidal asymmetries at the inner strike point are similar between natural and pellet-triggered ELMs, suggesting that the reduction in peak heat flux and total fluence at that location is robust for the conditions reported here.

The model of synchronization between internal reconnections and edge-localized modes

A new model for interaction between the internal reconnections caused by sawtooth and the edge-localized modes (ELM) was presented. The experimental evidence of the coupling between sawtooth crash and ELM events were observed in the Globus-M and Globus-M2 tokamaks. The numerical analysis of magnetic equilibrium showed that internal reconnections can induce the excess current density near the separatrix during the several hundreds of μs. The excess current destabilizes the peeling-ballooning instability. The peeling-ballooning stability analysis showed that the penetration depth of the induced current should be in the range of ψnorm = 0.8 - 0.95 to trigger the instability.

Spectral and correlation analysis of microturbulences in the spherical Globus-M/M2 tokamaks

Results of the studies on turbulences carried out on the Globus-M2 and Globus-M tokamaks are presented. The main focus was on the analysis of the data obtained using Doppler backscattering method (DBS). The developed codes for the analysis of DBS signals allowed to study the effects of turbulences on the operational mode of the tokamak. A description of the data processing codes is also included. The analysis performed indicates the suppression of turbulence and the formation of a velocity shear during the L-H transition. It was also successfully used to study density fluctuations during and between edge localized modes (ELMs). Spectral and correlation analysis also led to the discovery of limit-cycle oscillations (LCO) and quasi coherent fluctuations (QCFs) during the I-phase.

Normal Mode Analysis of The Thermal conductivity in Amorphous Polymers: The Importance of Localized Modes

Polymers are a unique class of materials from the perspective of normal mode analysis. Polymers consist of individual chains with repeating units and strong intra-chain covalent bonds, and amorphous arrangements among chains with weak inter-chain van der Waals and for some polymers also electrostatic interactions. Intuitively, this strong heterogeneity in bond strength can give rise to interesting features in the constituent phonons, but such effects have not been studied deeply before. Here, we use lattice dynamics and molecular dynamics to perform modal analysis of the thermal conductivity in amorphous polymers for the first time. We find an abnormally large population of localized modes in amorphous polymers, which is dramatically different from amorphous inorganic materials. Contrary to the common picture of thermal transport, localized modes in amorphous polymers are found to be the dominant contributors to thermal conductivity. We find that a significant portion of the localization happens within individual chains, but heat is dominantly conducted when localized modes involve two chains. These results suggest that even though each polymer is different, localized modes play a key role. The results provide new perspective on why polymer thermal conductivity is generally quite low and gives insight into how to potentially change it.

Singular Nonlinear Equation Class : Theoretical and Experimental Concept

This work generalizes and extends our work in refs [10,29,37], dealing a theoretical model of a monoatomic chain immersed in a potential of periodic and deformable substrate, the third and fourth non-linearities being taken into account. Looking at the analytical localized modes provides an extended interpretation of system dynamics based upon modes existence and yields an extended form of the nonlinear Schrodinger equation to describe the eikonal wave's complex amplitude. In this equation, the coeffcients depend on the wavenumber, whereas the parallel with the nonlinear transmission electrical line introduced in references results in [1,2] not fully resolved dynamic equations. So far, only specific solutions have been presented. Our dynamic study thus presents a theoretical prediction for their experimental set up. In contrast to previous works done for particular values of the wavenumber, namely on the behavior of gap (k = 0 and k = π) solutions of the model [10], or for k (k = ±2π=3) in the central bandpass area [37], we consider here rather behaviors of the system when the angular frequency is arbitrary. By using bifurcation theory of planar dynamical systems and investigating the dynamical behavior, we derive a variety of solutions corresponding to the phase trajectories under different parameter conditions.