Analysis of Alfven eigenmodes destabilization by energetic particles in TJ-II using a Landau-closure model

Alfven Eigenmodes (AE) can be destabilized by energetic particles in neutral beam injection (NBI) heated plasmas through inverse Landau damping and couplings with gap modes in the shear Alfven continua. We describe the linear evolution of the poloidal flux and the toroidal component of the vorticity in a full 3D system using the reduced MHD equations, density and parallel velocity moments for the energetic particles as well as the geodesic acoustic wave dynamics. A closure relation adds the Landau damping and resonant destabilization effects in the model. We apply the model to study the Alfven modes stability in TJ-II, performing a parametric analysis in a range of realistic values of energetic particle beta (beta(f)), ratios of thermal/Alfven velocities (V-th/V-A0), energetic particle density profiles and toroidal modes (n) including toroidal and helical couplings. The study predicts a large helical coupling between different toroidal modes and the destabilization of helical Alfven eigenmodes (HAE) with frequencies similar to the AE activity measured in TJ-II, between 50-400 kHz. The analysis has also revealed the destabilization of GAE (global Alfven eigenmodes), TAE (toroidal Alfven eigenmodes) and EPM (energetic particle modes). For the modes considered here, optimized TJ-II operations require a t profile in the range of [0.845, 0.979] to stabilize AEs in the inner and middle plasma. AEs in the plasma periphery cannot be fully stabilized, although for a configuration with t = [0.945, 1.079], only n = 7, 11, 15 AE are unstable with a growth rate 4 times smaller compared to the standard t = [1.54, 1.68] case and a frequency of 100 kHz. We reproduce the frequency sweeping evolution of the AE frequency observed in TJ-II as the t profile is varied. The AE frequency sweeping is caused by consecutive changes of the instability dominant modes between different helical families.This material based on work is supported both by the U.S. Department of Energy, Office of Science, under Contract DE-AC05-00OR22725 with UT-Battelle, LLC. This research was sponsored in part by the Ministerio of Economia y Competitividad of Spain under project no. ENE2015-68265-P. We also want to acknowledge Alexander Melnikov and the TJ-II group at CIEMAT for providing us the initial VMEC equilibria and useful discussions regarding the experimental phenomena

Tomonaga-Luttinger model with an impurity for a weak two-body interaction

The Tomonaga-Luttinger model with impurity is studied by means of flow equations for Hamiltonians. The system is formulated within collective density fluctuations but no use of the bosonization formula is made. The truncation scheme includes operators consisting of up to four fermion operators and is valid for small electron-electron interactions. In this regime, the exact expression for the anomalous dimension is recovered. Furthermore, we verify the phase diagram of Kane and Fisher also for intermediate impurity strength. The approach can be extended to more general one-body potentials.Comment: 10 pages, 1 figur

High-definition velocity-space tomography of fast-ion dynamics

Velocity-space tomography of the fast-ion distribution function in a fusion plasma is usually a photon-starved tomography method due to limited optical access and signal-to-noise ratio of fast-ion Dα (FIDA) spectroscopy as well as the strive for high-resolution images. In high-definition tomography, prior information makes up for this lack of data. We restrict the target velocity space through the measured absence of FIDA light, impose phase-space densities to be non-negative, and encode the known geometry of neutral beam injection (NBI) sources. We further use a numerical simulation as prior information to reconstruct where in velocity space the measurements and the simulation disagree. This alternative approach is demonstrated for four-view as well as for two-view FIDA measurements. The high-definition tomography tools allow us to study fast ions in sawtoothing plasmas and the formation of NBI peaks at full, half and one-third energy by time-resolved tomographic movies

Cross-calibration of neutron detectors for deuterium-tritium operation in TFTR

During the initial deuterium-tritium experiments on TFTR, neutron emission was measured with {sup 235}U and {sup 238}U fission chambers, silicon surface barrier diodes, spatially collimated {sup 4}He proportional counters and ZnS scintillators, and a variety of elemental activation foils. The activation foils, {sup 4}He counters and silicon diodes can discriminate between 14 MeV and 2.5 MeV neutrons. The other detectors respond to both DD and DT neutrons but are more sensitive to the latter. The proportional counters, scintillators, and some of the fission chambers were calibrated absolutely, using a 14-MeV neutron generator positioned at numerous locations inside the TFTR vacuum vessel. Although the directly calibrated systems were saturated during the highest power deuterium-tritium operation, they allowed cross-calibration of less sensitive fission chambers and silicon diodes. The estimated absolute accuracy of the uncertainty-weighted mean of these cross-calibrations, combined with an independent calibration derived from activation foil determinations of total neutron yield, is {plus_minus}7%

Cross calibration of neutron detectors for deuterium‐tritium operation in TFTR

During the initial deuterium-tritium experiments on TFTR, neutron emission was measured with {sup 235}U and {sup 238}U fission chambers, silicon surface barrier diodes, spatially collimated {sup 4}He proportional counters and ZnS scintillators, and a variety of elemental activation foils. The activation foils, {sup 4}He counters and silicon diodes can discriminate between 14 MeV and 2.5 MeV neutrons. The other detectors respond to both DD and DT neutrons but are more sensitive to the latter. The proportional counters, scintillators, and some of the fission chambers were calibrated absolutely, using a 14-MeV neutron generator positioned at numerous locations inside the TFTR vacuum vessel. Although the directly calibrated systems were saturated during the highest power deuterium-tritium operation, they allowed cross-calibration of less sensitive fission chambers and silicon diodes. The estimated absolute accuracy of the uncertainty-weighted mean of these cross-calibrations, combined with an independent calibration derived from activation foil determinations of total neutron yield, is {plus_minus}7%

Characterization of off-axis fishbones

Repetitive bursting instabilities with strong frequency chirping occur in high-beta, beam-heated plasmas with safety factor q > 1 in the DIII-D tokamak. Although the mode structures differ, in many ways, the off-axis fishbones are similar to the q = 1 fishbones first observed on the Poloidal Divertor Experiment (PDX). The modes are driven by energetic trapped ions at the fast-ion precession frequency. During a burst, the frequency changes most rapidly as the mode reaches its maximum amplitude. Larger amplitude bursts have larger growth rates and frequency chirps. Unlike PDX fishbones, the decay phase is highly variable and is usually shorter than the growth phase. Also, the waveform is highly distorted by higher harmonics during the latter portion of a burst. The radial mode structure alters its shape during the burst. Like PDX fishbones, the modes expel trapped ions in a 'beacon' with a definite phase relationship relative to the mode. Seven types of loss detectors measure the beacon. The losses scale linearly with mode amplitude. The neutron rate changes most rapidly at maximum mode amplitude but, depending on the loss diagnostic, the losses often peak a few cycles later. The non-ambipolar fast-ion losses cause a sudden change in toroidal rotation frequency across the entire plasma. In addition to an overall drop, the neutron signal oscillates in response to the wave. Unlike the beacon of lost particles, which maintains a fixed phase relative to the mode, the phase of the neutron oscillations steadily increases throughout the burst, with the greatest phase slippage occurring in the highly nonlinear phase near maximum mode amplitude. © 2011 IOP Publishing Ltd

Energetic ion transport by microturbulence is insignificant in tokamaks

Energetic ion transport due to microturbulence is investigated in magnetohydrodynamic-quiescent plasmas by way of neutral beam injection in the DIII-D tokamak [J. L. Luxon, Nucl. Fusion 42, 614 (2002)]. A range of on-axis and off-axis beam injection scenarios are employed to vary relevant parameters such as the character of the background microturbulence and the value of Eb/Te , where Eb is the energetic ion energy and Te the electron temperature. In all cases, it is found that any transport enhancement due to microturbulence is too small to observe experimentally. These transport effects are modeled using numerical and analytic expectations that calculate the energetic ion diffusivity due to microturbulence. It is determined that energetic ion transport due to coherent fluctuations (e.g., Alfvén eigenmodes) is a considerably larger effect and should therefore be considered more important for ITER.United States. Dept. of Energy (DE-FC02-04ER54698)United States. Dept. of Energy (DE-FC02-99ER54512)United States. Dept. of Energy (DE-FG03-97ER54415)United States. Dept. of Energy (DE-FG02-07ER54917)United States. Dept. of Energy (DE-AC02-09CH11466)United States. Dept. of Energy (SC-G903402)United States. Dept. of Energy (DE-FG02-08ER54984)United States. Dept. of Energy ( DE-AC52-07NA27344)United States. Dept. of Energy ( DE-FG02-89ER53296)United States. Dept. of Energy (DE-FG02-08ER54999)United States. Dept. of Energy (DE-AC05-00OR22725

The Flare-energy Distributions Generated by Kink-unstable Ensembles of Zero-net-current Coronal Loops

It has been proposed that the million degree temperature of the corona is due to the combined effect of barely-detectable energy releases, so called nanoflares, that occur throughout the solar atmosphere. Alas, the nanoflare density and brightness implied by this hypothesis means that conclusive verification is beyond present observational abilities. Nevertheless, we investigate the plausibility of the nanoflare hypothesis by constructing a magnetohydrodynamic (MHD) model that can derive the energy of a nanoflare from the nature of an ideal kink instability. The set of energy-releasing instabilities is captured by an instability threshold for linear kink modes. Each point on the threshold is associated with a unique energy release and so we can predict a distribution of nanoflare energies. When the linear instability threshold is crossed, the instability enters a nonlinear phase as it is driven by current sheet reconnection. As the ensuing flare erupts and declines, the field transitions to a lower energy state, which is modelled by relaxation theory, i.e., helicity is conserved and the ratio of current to field becomes invariant within the loop. We apply the model so that all the loops within an ensemble achieve instability followed by energy-releasing relaxation. The result is a nanoflare energy distribution. Furthermore, we produce different distributions by varying the loop aspect ratio, the nature of the path to instability taken by each loop and also the level of radial expansion that may accompany loop relaxation. The heating rate obtained is just sufficient for coronal heating. In addition, we also show that kink instability cannot be associated with a critical magnetic twist value for every point along the instability threshold