Toroidicity-induced Alfven Eigenmodes Modes Research Articles

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.

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

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

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.

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.

Doppler shift of the TAE mode frequency in DIII-D

The Doppler shift caused by toroidal plasma rotation in DIII-D complicates a comparison of the frequency of toroidicity-induced Alfven eigenmodes (TAE) to theoretical predictions, but also separates toroidal modes in frequency space and provides information about the radial location of the modes. Two independent techniques for estimating the mode frequency and Doppler shift are presented: one based upon the spectrum of multiple toroidal modes and one that utilizes the measured toroidal rotation of the plasma. Both methods indicate the presence of multiple TAE modes located between the q=1 and y=3/2 surfaces. The frequencies determined by the two methods agree within 20%, consistent with their estimated uncertainties.

Stability of neutral beam driven TAE modes in DIII-D

The observed characteristics of toroidicity induced Alfven eigenmodes (TAE) in DIII-D tokamak discharges are compared in detail with predictions of various theories of TAE mode stability, and good qualitative agreement is found. The observed range of unstable toroidal mode numbers (n approximately 3-6) is consistent with theoretical predictions. For DIII-D parameters, low mode numbers are damped by coupling to the stable Alfven continuum, while high mode numbers are clamped by electron kinetic effects including coupling to kinetic Alfven waves. A threshold for destabilization is observed experimentally at a fast ion beta of approximately 1%. The predicted driving and damping rates, estimated from experimental data, balance within about a factor of two for discharges at the threshold. It is demonstrated experimentally that the damping of TAE modes can be increased by current profile control, in this case with a peaked current profile produced by a negative current ramp, in qualitative agreement with theoretical predictions. A possible stabilizing effect of discharge elongation is also observed

Simulations of deuterium-tritium experiments in TFTR

A transport code (TRANSP) is used to simulate future deuterium-tritium (DT) experiments in TFTR. The simulations are derived from 14 TFTR DD discharges, and the modelling of one supershot is discussed in detail to indicate the degree of accuracy of the TRANSP modelling. Fusion energy yields and alpha particle parameters are calculated, including profiles of the alpha slowing down time, the alpha average energy, and the Alfven speed and frequency. Two types of simulation are discussed. The main emphasis is on the DT equivalent, where an equal mix of D and T is substituted for the D in the initial target plasma, and for the D0 in the neutral beam injection, but the other measured beam and plasma parameters are unchanged. This simulation does not assume that alpha heating will enhance the plasma parameters or that confinement will increase with the addition of tritium. The maximum relative fusion yield calculated for these simulations is QDT ~ 0.3, and the maximum alpha contribution to the central toroidal β is βα(0) ~ 0.5%. The stability of toroidicity induced Alfven eigenmodes (TAE) and kinetic ballooning modes (KBM) is discussed. The TAE mode is predicted to become unstable for some of the simulations, particularly after the termination of neutral beam injection. In the second type of simulation, empirical supershot scaling relations are used to project the performance at the maximum expected beam power. The MHD stability of the simulations is discussed

Destabilization of Tokamak Pressure-Gradient Driven Instabilities by Energetic Alpha-Particle Populations

This paper reports on alpha-particle populations that can significantly alter existing magnetohydrodynamic (MHD) instabilities in tokamaks through kinetic effects and coupling to otherwise stable shear Alfven waves. Resonances of the trapped alpha-particle precessional drift, with the usual ballooning mode diamagnetic frequency ({omega}{sub *i}/2) and the toroidicity-induced Alfven eigenmode (TAE), are considered. These are examined for noncircular tokamaks in the high-n ballooning limit using an isotopic alpha-particle slowing down distribution and retaining the full-energy and pitch-angle dispersion in the alpha-particle drift frequency. Applying this to the Compact Ignition Tokamak (CIT) and the International Thermonuclear Experimental Reactor (ITER) indicates that ballooning instabilities can persist at betas below the ideal MHD threshold. These are especially dominated by the destabilization of the TAE mode. In addition, a hybrid fluid-particle approach for simulating alpha-particle effects on pressure-gradient driven instabilities is described.

Alpha-Particle Effects on LOW-n Magnetohydrodynamic Modes

This paper reports that the NOVA-K code is employed to study the effects of alpha particles on two types of magnetohydrodynamic (MHD) modes: the stabilization of ideal MHD internal modes and the excitation of resonant internal modes, and the alpha-particle destabilization of toroidicity-induced Alfven eigenmodes (TAEs) via transit resonances. Analytical theories are also presented to help explain the NOVA-D results. The trapped alpha particles are found to destabilize the n = 1 internal mode and lower the total beta threshold. The circulating alpha particles can strongly destabilize TAE modes via inverse Landau damping associated with the spatial gradient of the alpha-particle pressure.