Toroidicity-induced Alfven Eigenmodes Research Articles

Experiments on excitation of Alfvén eigenmodes by alpha-particles with bump-on-tail distribution in JET DTE2 plasmas

Dedicated experiments were performed in JET DTE2 plasmas for obtaining an α-particle bump-on-tail (BOT) distribution aiming at exciting Alfvén eigenmodes (AEs). Neutral beam injection-only heating with modulated power was used so that fusion-born α-particles were the only ions present in the MeV energy range in these DT plasmas. The beam power modulation on a time scale shorter than the α-particle slowing down time was chosen for modulating the α-particle source and thus sustaining a BOT in the α-particle distribution. High-frequency modes in the toroidicity-induced Alfven eigenmode (TAE) frequency range and multiple short-lived modes in a wider frequency range have been detected in these DT discharges with interferometry, soft x-ray cameras, and reflectometry. The modes observed were localised close to the magnetic axis, and were not seen in the Mirnov coils. Analysis with the TRANSP and Fokker-Planck FIDIT codes confirms that α-particle distributions with BOT in energy were achieved during some time intervals in these discharges though no clear correlation was found between the times of the high-frequency mode excitation and the BOT time intervals. The combined magneto-hydrodynamic (MHD) and kinetic modelling studies show that the high-frequency mode in the TAE frequency range is best fitted with a TAE of toroidal mode number n= 9. This mode is driven mostly by the on-axis beam ions while the smaller drive due to the pressure gradient of α-particles allows overcoming the marginal stability and exciting the mode (Oliver et al 2023 Nucl. Fusion submitted). The observed multiple short-lived modes in a wider frequency range are identified as the on-axis kinetic AEs predicted in Rosenbluth and Rutherford (1975 Phys. Rev. Lett. 34 1428).

Simulation of toroidicity-induced Alfven eigenmode excited by energetic ions in HL-2A tokamak plasmas

The toroidicity-induced Alfven eigenmode (TAE) excited by energetic (fast) ions was first simulated using the GTC code for HL-2A experiments. The simulation results indicate that the fraction of energetic ions is about 3% in the experiments. The critical density of energetic ions to excite the TAE mode is around 0.023, which is in good agreement with the theoretical expectation of 0.026. The real frequency of TAE with toroidal mode number n = 3 is around 211 kHz and is inversely proportional to the square root of electron density, which is quantitatively in agreement with the experimental observation (Ding et al 2013 Nucl. Fusion 53 043015). The frequency is in resonance with the summations of toroidal precession frequency and transit frequency of passing energetic ions, indicating that resonance with passing energetic ions is dominant for the excitation of the modes in the experiment. It is also checked by the phase space structures of (strength of energetic particle distribution function) that the TAE modes are mainly induced by passing energetic ions in HL-2A. The growth rates of TAE modes increase with fast ion density and its gradient. In addition, lower n TAE modes, such as n = 1 can also be driven by energetic ions when off-axis heating with higher beam energy is employed in the experiment. The width of radial mode structures for lower n modes is usually wider than those for higher n modes. The perpendicular wave vector of the modes and Larmor radius of ions satisfy the relation . Finally, the polarization of the mode shows that the perturbed parallel electric field is much smaller than the electrostatic parallel electric field.

MHD induced fast-ion losses on ASDEX Upgrade

A detailed knowledge of the interplay between MHD instabilities and energetic particles has been gained from direct measurements of fast-ion losses (FILs). Time-resolved energy and pitch angle measurements of FIL caused by neoclassical tearing modes (NTMs) and toroidicity-induced Alfven eigenmodes (TAEs) have been obtained using a scintillator based FIL detector. The study of FIL due to TAEs has revealed the existence of a new core-localized MHD fluctuation, the Sierpes mode. The Sierpes mode is a non-pure Alfvenic fluctuation which appears in the acoustic branch, dominating the transport of fast-ions in ICRF heated discharges. The internal structure of both TAEs and Sierpes mode has been reconstructed by means of highly resolved multichord soft x-ray measurements. A spatial overlapping of their eigenfunctions leads to a FIL coupling, showing the strong influence that a core-localized fast-ion driven MHD instability may have on the fast-ion transport. We have identified the FIL mechanisms due to NTMs as well as due to TAEs. Drift islands formed by fast-ions in particle phase space are responsible for the loss of NBI fast-ions due to NTMs. In ICRF heated plasmas, a resonance condition fulfilled by the characteristic trapped fast-ion orbit frequencies leads to a phase matching between fast-ion orbit and NTM or TAE magnetic fluctuation. The banana tips of a resonant trapped fast-ion bounce radially due to an E × B drift in the TAE case. The NTM radial bounce of the fast-ion banana tips is caused by the radial component of the perturbed magnetic field lines.

Theory of Alfvén eigenmodes in shear reversed plasmas

Plasma configurations with shear reversal are prone to the excitation of unusual Alfvén eigenmodes by energetic particles. These modes exhibit a quasiperiodic pattern of predominantly upward frequency sweeping (Alfvén cascades) as the safety factor q changes in time. This work presents a theory that employs two complementary mechanisms for establishing Alfvén cascades: (1) a nonstandard adiabatic response of energetic particles with large orbits and (2) toroidal magnetohydrodynamic effects that are second-order in inverse aspect ratio. The developed theory explains the transition from Alfvén cascades to the toroidicity induced Alfvén eigenmodes (TAEs), including modifications of the TAEs themselves near the shear reversal point.

Alfven Eigenmodes in Toroidal Magnetic Confinemen. Nonlinear Simulation Study of Alfven Eigenmodes.

This article describes recent progress in nonlinear simulation studies of Alfven eigenmodes, especially of the toroidicity-induced Alfven eigenmode (TAE). Early simulations showed clearly that wave-particle trapping saturates the growth of TAE, but experimental results such as recurrent bursts and steady saturation remain unexplained. Recent simulations, which take account of particle source and collisions, can solve the mystery of these qualitatively different behaviors.

Effect of shear in toroidal rotation on toroidicity induced Alfven eigenmodes

It is found that low-n toroidicity induced Alfven eigenmodes (TAEs) excited by ion cyclotron resonance heating can be stabilized by counter-tangential neutral beam injection in JT-60U. The deformation of the radial structure of the TAE mode due to the shear in toroidal rotation is a plausible stabilizing mechanism. This mechanism is also expected to be effective in suppressing high-n TAE modes. Real time control of TAE mode amplitudes using toroidal rotation control is possible for burn control in fusion reactors

Comparison between measurements of the poloidal distribution of magnetic fluctuations and predictions of theoretical models during TAE activity

Fluctuations produced by beam-driven toroidicity-induced Alfven eigenmode (TAE) activity in the DIII-D tokamak are measured by a poloidal array of magnetic probes and compared with the wavefields computed by two theoretical models. Fluid resistive models compute continuum damped TAEs. A kinetic plasma model that retains Landau damping and finite Larmor radius effects computes global drift-kinetic Alfven eigenmodes. The phases of the probes disagree with both theoretical predictions, while the amplitudes agree best with the kinetic model

Observations of neutral beam and ICRF tail ion losses due to Alfven modes in TFTR

Experimental observations from TFTR of fast ion losses resulting from the toroidicity induced Alfven eigenmode (TAE) and the Alfven frequency mode (AFM) are presented. The AFM was driven by neutral beam ions, at low BT, and the TAE was excited by hydrogen minority ion cyclotron range of frequencies (ICRF) tail ions at higher BT. The measurements indicate that the loss rate varies linearly with the mode amplitude for both modes, and that the fast ion losses during the mode activity can be significant, with tens of per cent of the input power lost in the worst cases

Search for alpha driven TAEs at lowered ion temperature in TFTR DT discharges

An experiment was performed in TFTR DT plasmas in an attempt to destabilize the alpha particle driven toroidicity-induced Alfven eigenmodes (TAEs) by reducing their thermal ion Landau damping. The thermal ion Landau damping was reduced by transiently lowering the ion temperature using either helium (He) gas puffs or deuterium (D) or lithium (Li) pellet injection during neutral beam injection (NBI) into DT supershots. The ion temperature was successfully lowered from Ti(0) approximately=20 keV to Ti(0) approximately=10 keV in about 0.2 s; however, no alpha driven TAEs were observed. Theoretical analyses of the TAE instability of these DT discharges indicate that the alpha pressure required for TAE stability still remained greater than that actually obtained in this experiment, mainly because of the effects of beam ion Landau damping

Experimental study of toroidicity induced Alfven eigenmode (TAE) stability at high q(0)

Experiments to destabilize the toroidicity induced Alfven eigenmode (TAE) by energetic alpha particles were performed on the Tokamak Fusion Test Reactor using deuterium and tritium fuel. To decrease the alpha particle pressure instability threshold, discharges with an elevated value of q(0)>1.5 were used. By raising q(0), the radial location of the low toroidal mode number TAE gaps moves towards the magnetic axis and into alignment with the region of maximum alpha pressure gradient, thereby (in theory) lowering the value of the central alpha particle beta alpha required for instability. No TAE activity was observed when beta alpha (0) reached 0.08% in a discharge with fusion power of 2.4 MW. Calculations predict that the alpha driven TAE was weakly unstable

Non-linear analysis of the toroidicity induced Alfven eigenmode

A fast and efficient numerical algorithm using energy conservation is developed to study the interaction of high energy particles with a toroidicity induced Alfven eigenmode (TAE). A Hamiltonian guiding centre code is used to simulate the alpha particle motion and a non-linear delta f scheme is employed to calculate the wave-particle energy exchange. For a single TAE mode, the particle radial excursion is much less than the spacing between the resonances produced by the poloidal harmonics for International Thermonuclear Experimental Reactor parameters. Modification of the particle distribution leading to mode saturation is observed. A TAE is found in some cases to cause loss through induced ripple trapping

Alfven frequency modes at the edge of TFTR plasmas

An Alfven frequency mode (AFM) is very often seen in TFTR neutral beam heated plasmas as well as in ohmic plasmas. This quasi-coherent mode has so far only been seen on magnetic fluctuation diagnostics (Mirnov coils). A close correlation between the plasma edge density and the mode activity (frequency and amplitude) has been observed, which indicates that the AFM is an edge localized mode with r/a>0.85. No direct impact of this mode on the plasma global performance or on fast ion loss (e.g., the alpha particles in DT experiments) has been observed. This mode is not the conventional TAE (toroidicity induced Alfven eigenmode). The present TAE theory cannot explain this observation. Other possible explanations are discussed

Overview of Alfven eigenmode experiments in JET

Results from the first experiments to drive Alfven eigenmodes (AEs) with antennas external to a tokamak plasma are presented. In ohmically heated plasma discharges, direct experimental measurements of the damping of toroidicity induced AEs (TAEs) have allowed an identification of different regimes corresponding to different dominant TAE absorption mechanisms with a wide range of damping rates, 10-3 ⩽ γ/w ⩽ 10-1. In plasmas heated by ion cyclotron resonance heating, neutral beam injection heating, lower hybrid heating and high plasma current ohmic heating, a new class of weakly damped Alfven eigenmodes, the kinetic Alfven eigenmodes, predicted in theoretical models that include finite Larmor radius and finite parallel electric field effects, has been identified experimentally

Energetic particle drive for toroidicity-induced Alfven eigenmodes and kinetic toroidicity-induced Alfven eigenmodes in a low-shear tokamak

The structure of toroidicity-induced Alfven eigenmodes (TAE) and kinetic TAE (KTAE) with large mode numbers is analysed and the linear power transfer from energetic particles to these modes is calculated in the low-shear limit when each mode is localized near a single gap within an interval whose total width Delta out is much smaller than the radius rm of the mode location. Near its peak where most of the mode energy is concentrated, the mode has an inner scale length Delta in, which is much smaller than Delta out. The scale Delta in is determined by toroidicity and kinetic effects, which eliminate the singularity of the potential at the resonant surface. This work examines the case when the drift orbit width of energetic particles Delta b is much larger than the inner scale length Delta in, but arbitrary compared to the total width of the mode. It is shown that the particle-to-wave linear power transfer is comparable for the TAE and KTAE modes in this case. The ratio of the energetic particle contributions to the energetic particle drive for the TAE and KTAE modes is then roughly equal to the inverse ratio of the mode energies. It is found that in the low-shear limit the energetic particle drive for the KTAE modes can be larger than that for the TAE modes.

Global marginal stability of TAEs in the presence of fast ions

The global stability of toroidicity induced Alfven eigenmodes (TAEs) in the presence of fast ions in realistic tokamak fusion-grade plasmas is analysed with a global, perturbative approach. Volume averaged fast particle betas for marginal stability are obtained and analysed for a wide range of plasma parameters such as the fast ion radial density profile width, the ratio of birth velocity to the Alfven velocity on axis and the bulk plasma beta. There is evidence of different stability behaviour of two types of TAEs ('internal' or 'external')

Stability Analysis of Toroidicity-Induced Alfvén Eigenmodes in TFTR Deuterium-Tritium Experiments

The toroidicity-induced Alfven eigenmodes (TAE) are found to be stable in the Tokamak Fusion Test Reactor (TFTR) deuterium-tritium plasmas. The dominant stabilizing mechanisms are beam ion Landau damping and radiative damping. A core localized TAE mode is shown to exist near the center of the plasma at small magnetic shear and finite plasma beta, which can be destabilized by energetic alpha particles in future TFTR DT experiments. With additional instability drive from fast minority ions powered by ion cyclotron radio frequency, both the global and core localized TAE modes can be readily destabilized.

Direct measurement of the damping of toroidicity-induced Alfvén eigenmodes.

This Letter presents the first direct experimental measurements of the damping of toroidicity-induced Alfven eigenmodes (TAE), carried out in the JET tokamak. These measurements were obtained during the first experiments to drive these modes with antennas external to a tokamak plasma. Different regimes corresponding to different dominant TAE absorption mechanisms with a wide range of damping rates, 10(-3) less than or equal to gamma/omega less than or equal to 10(-1), have been identified in Ohmically heated plasma discharges.

Observation of TAE activity in JET

High-frequency magnetic activity with characteristics expected of toroidicity-induced Alfven eigenmodes (TAEs) has been observed in JET discharges heated by neutral beam injection and ion cyclotron resonance heating. The mode frequency is found to scale in the expected way with the magnetic field and plasma density and the frequency spectra show the characteristic multi-mode TAE structures seen in other devices. A correlation between fast-particle loss levels and the mode amplitude is also suggested by the data.

Investigation of high-n TAE modes excited by minority-ion cyclotron heating in JT-60U

Toroidicity-induced Alfven eigen (TAE) modes are observed during minority-ion cyclotron resonance heating (ICRH) in the JT-60U. The toroidal mode numbers of TAE modes are identified as 7, 8, 9, 10 and 11 from the Doppler shift in the TAE modes with scanning toroidal rotation at a plasma current of 3 MA. The toroidal mode number of TAE modes tends to increase during a giant sawtooth by ICRH with a decreasing safety factor for the central region. The TAE mode number increases with plasma current, so that nine TAE modes are observed sequentially during a giant sawtooth at a plasma current of 4 MA, where the maximum toroidal mode number is estimated to be at least 13. There are no Alfven continuum gaps for TAE modes in the safety-factor ranges of i-1/2n<q<i+1/2n, (i=1, 2, 3, ...), except for the gaps in ellipticity-induced Alfven eigen (EAE) modes, where n is the toroidal mode number of TAE modes. Therefore, control of the q profile might provide a means of avoiding TAE modes, as long as the pressure gradient of the high-energy ions is localized.

Damping of toroidal Alfvén modes in DIII-D

The previously developed single-gap kinetic theory for toroidicity-induced Alfvén eigenmodes (TAE) is extended and applied to Doublet III-D [J. L. Luxon and L. G. Davis, Fusion Technol. 8, 441 (1985)] experimental data. It is found that the theory gives reasonable agreement with the data when an appropriate magnetohydrodynamic boundary condition is accounted for. As is shown, this boundary condition is equivalent to an appropriate real frequency shift relative to the continuum gap. The correct eigenfunction near the gap, and thus the correct damping, is obtained by using the gap structure calculated from an equilibrium reconstruction that includes low aspect ratio, noncircularity, and finite beta effects, combined with an experimentally measured frequency. In the considered experimental cases, the damping is well into the nonideal regime.