Fast Ion Beta Research Articles

Hybrid simulations of reversed shear Alfvén eigenmodes and related nonlinear resonance with fast ions in a tokamak plasma

Reversed shear Alfvén eigenmodes (RSAEs) are often observed in HL-2A reversed shear discharges with . The modes are highly localized near , and their frequencies sweep downward or upward as decreases. In this work, kinetic-magnetohydrodynamics (MHD) hybrid simulations based on experimental parameters in the HL-2A tokamak are carried out to investigate the linear stability and nonlinear dynamics of RSAEs. Linear simulations show that the frequencies of RSAEs sweep downward () first and then upward () as decreases, which is rarely seen in previous simulation work. The frequency and mode structure of the instabilities are consistent with experimental observations. For the same , the critical value of the fast ion beta required to destabilize down-sweeping RSAEs is higher than that of up-sweeping RSAEs. Both the up-sweeping and down-sweeping RSAEs are mainly driven by co-passing fast ions. The nonlinear simulation results of n = 3 and show that the frequency of the mode chirps up and down with corresponding hole-clump structures of energy perturbation appearing in the phase space. In the nonlinear phase, the dominant resonance condition becomes instead of the linear resonance condition , which can be the result of a nonlinear interaction between wave and particles. This work provides a new proof for the theory of nonlinear wave-particle resonance proposed recently (Chen and Zonca 2019 Plasma Sci. Technol. 21 125101).

Nonlinear simulation of multiple toroidal Alfvén eigenmodes in tokamak plasmas**Project supported by the National Key R&D Program of China (Grant No. 2017YFE0301900), the National Natural Science Foundation of China (Grant No. 11675083), and the Fundamental Research Funds for the Central Universities of China (Grant No. DUT18ZD101).

Nonlinear evolution of multiple toroidal Alfvén eigenmodes (TAEs) driven by fast ions is self-consistently investigated by kinetic simulations in toroidal plasmas. To clearly identify the effect of nonlinear coupling on the beam ion loss, simulations over single-n modes are also carried out and compared with those over multiple-n modes, and the wave-particle resonance and particle trajectory of lost ions in phase space are analyzed in detail. It is found that in the multiple-n case, the resonance overlap occurs so that the fast ion loss level is rather higher than the sum loss level that represents the summation of loss over all single-n modes in the single-n case. Moreover, increasing fast ion beta βh can not only significantly increase the loss level in the multiple-n case but also significantly increase the loss level increment between the single-n and multiple-n cases. For example, the loss level in the multiple-n case for βh = 6.0% can even reach 13% of the beam ions and is 44% higher than the sum loss level calculated from all individual single-n modes in the single-n case. On the other hand, when the closely spaced resonance overlap occurs in the multiple-n case, the release of mode energy is increased so that the widely spaced resonances can also take place. In addition, phase space characterization is obtained in both single-n and multiple-n cases.

A measure of fast ion beta at marginal stability in the reversed field pinch

Energetic ions are well confined in the core of the reversed field pinch and a substantial population develops rapidly during tangential neutral beam injection. A saturated fast ion density is observed within several milliseconds and coincides with the onset of energetic particle mode activity. First measurements of the fusion product profile determine the fast ion density and pressure profiles, the latter of which when combined with neutral particle analysis of the energy distribution. These are key measurements in explaining the limiting behavior of the fast ion profile in response to a combination of effects. Tearing mode activity affects the fast ion profile, and the fast ions noticeably influence the core-most tearing mode. The nonlinear situation settles into a marginally stable state where the EPM transports fast ions down a steep gradient to a region where their confinement is limited by stochastic orbit and charge exchange losses. In the state at marginal stability (achieved in one set of experimental conditions with full 1 MW neutral beam power), a critical fast ion beta gradient is measured that limits the core , or nearly four times the core thermal , but less than a strictly classical calculation predicts.

Fishbone Mode Excited by Deeply Trapped Energetic Beam Ions in EAST**supported by the National Magnetic Confinement Fusion Science Program of China (Nos. 2013GB101001, 2014DFG61950 and 2013GB112003) and National Natural Science Foundation of China (Nos. 11175211 and 11275233)

This paper describes the fishbone mode phenomena during the injection of high-power neutral beams in EAST (Experimental Advanced Superconducting Tokamak). The features of the fishbone mode are presented. The change in frequency of the mode during a fishbone burst is from 1 kHz to 6 kHz. The nonlinear behavior of the fishbone mode is analyzed by using a prey-predator model, which is consistent with the experimental results. This model indicates that the periodic oscillations of the fishbone mode always occur near the critical value of fast ion beta. Furthermore, the neutral beam analysis for the discharge is done by using the NUBEAM module of the TRANSP code. According to the numerical simulation results and theoretical calculation, it can be concluded that the fishbone mode is driven by the deeply trapped energetic beam ions in EAST.

Double fishbone instability excited by energetic ions with m = n = 1 in a reversed magnetic shear tokamak plasmas

Double fishbone mode excited by energetic particles at q = 1 rational surfaces is studied, with the minimum of the safety factor qmin<1. The dispersion relation of the mode is derived based on energy principle and the radial displacement structure is calculated by an iterative method self-consistently. It is found that the double fishbone mode has a two-step mode structure similar to that of double kink modes. For qmin→1, the sharp slope of the ξr distribution at the rational surfaces is smoothened. The effects of the magnetic shear, the minimum of safety factor, the fast ion beta, and the precession frequency on the plasma displacement and growth rate are also analyzed, respectively.

Energetic ion beta scaling of q ≳ 1 non-resonant modes in tokamak plasmas with a weak magnetic shear configuration

Fast ion beta scaling of non-resonant modes (NRMs) with a safety factor profile close to but above unity ( 1) in tokamak plasmas with a reversed magnetic shear configuration, particularly those with a weak shear ( ~ 0) of around , are analysed in this study. It is found that, in three different regimes of magnetic shear configuration, the fast ion beta scaling of the NRM growth rate are: (1) in the small but finite regime, (2) , in the = 0 regime, and (3) in an almost flat q-profile regime. The scalings suggest that the growth rate of the mode is related to the fast ion beta and weakens as the q-profile is flattened. The dispersion relation of NRM in the = 0 regime is then derived and analysed.

Non-resonant fishbone instabilities of qmin ≳ 1 in tokamak plasmas with weakly reversed magnetic shear

In this study, we theoretically explore properties of non-resonant fishbone (NRF) instabilities with a safety factor profile slightly above unity (qmin ≳ 1) in tokamak plasmas with reversed magnetic shear configuration. From the dispersion relation of the NRF mode, it is found that the growth rate of the mode in general reversed shear scenarios with qmin ≳ 1 depends on fast ion beta βh in a power law of , different from that of ∼βh in a conventional positive magnetic shear configuration. Meanwhile, due to the slow ion precession and small continuum damping in ITER-like tokamaks with reversed shear, the mode has a lower trigger threshold than those with monotonously positive magnetic shear. In addition, the ion diamagnetic drift has been found to destabilize the fast ion-driven NRF mode. Other effects such as the shape of the q-profile, characterized by values of qmin and q(0), neutral beam energy, magnetohydrodynamic potential energy and the fraction of fast ions on the instability threshold are also discussed. Nonlinear behavior of the mode is further analyzed using a modified model.

Role of convective amplification of n = 1 energetic particle modes for N-NB ion dynamics in JT-60U

The hybrid code MEGA is used to simulate an abrupt large-amplitude event (ALE) in JT-60U shot E039672 that was strongly driven by a pair of negative-ion-based neutral beams (N-NBs). This configuration is known to be unstable to energetic particle modes (EPMs) with toroidal mode number n = 1. The purpose of this study is to look for a threshold with respect to the on-axis fast ion beta value, βh0, beyond which the EPM undergoes convective amplification (CA) and causes significant fast ion transport. This is motivated by the hypothesis that such a threshold may work as a trigger mechanism for relaxation events, such as ALE. In order to facilitate quantitative comparisons with the experiment, a realistic geometry and bulk pressure is used. Furthermore, MEGA is initialized with a fast ion distribution computed for JT-60U by an orbit-following Monte-Carlo code, and a passive vacuum region allows particles to travel without encountering artificial loss boundaries. Consistently with the experiment, the simulation predicts a burst time of about 0.3 ms and peak magnetic fluctuation levels around δBϑ/B < 10−3 at the plasma boundary. As βh0 is increased, a gradual increase in the CA of the EPM and in the convective transport of both resonant and nonresonant particles is found. The absence of a sharp transition between low- and high-amplitude fluctuations leads to the conclusion that the onset of CA does not suffice as a trigger mechanism for ALE.

Absorption of fast waves at moderate to high ion cyclotron harmonics on DIII-D

The absorption of fast Alfvén waves (FW) by ion cyclotron harmonic damping in the range of harmonics from 4th to 8th is studied theoretically and with experiments in the DIII-D tokamak. A formula for linear ion cyclotron absorption on ions with an arbitrary distribution function which is symmetric about the magnetic field is used to estimate the single-pass damping for various cases of experimental interest. It is found that damping on fast ions from neutral beam injection can be significant even at the 8th harmonic if the fast ion beta, the beam injection energy and the background plasma density are high enough and the beam injection geometry is appropriate. The predictions are tested in several L-mode experiments in DIII-D with FW power at 60 MHz and at 116 MHz. It is found that 4th and 5th harmonic absorption of the 60 MHz power on the beam ions can be quite strong, but 8th harmonic absorption of the 116 MHz power appears to be weaker than expected. The linear modelling predicts a strong dependence of the 8th harmonic absorption on the initial pitch-angle of the injected beam, which is not observed in the experiment. Possible explanations of the discrepancy are discussed.

Collective fast ion instability-induced losses in National Spherical Tokamak Experiment

A wide variety of fast ion driven instabilities are excited during neutral beam injection (NBI) in the National Spherical Torus Experiment (NSTX) [Nucl. Fusion 40, 557 (2000)] due to the large ratio of fast ion velocity to Alfvén velocity, Vfast∕VAlfvén, and high fast ion beta. The ratio Vfast∕VAlfvén in ITER [Nucl. Fusion 39, 2137 (1999)] and NSTX is comparable. The modes can be divided into three categories: chirping energetic particle modes (EPM) in the frequency range 0 to 120kHz, the toroidal Alfvén eigenmodes (TAE) with a frequency range of 50kHz to 200kHz, and the compressional and global Alfvén eigenmodes (CAE and GAE, respectively) between 300kHz and the ion cyclotron frequency. Fast ion driven modes are of particular interest because of their potential to cause substantial fast ion losses. In all regimes of NBI heated operation we see transient neutron rate drops, correlated with bursts of TAE or fishbone-like EPMs. The fast ion loss events are predominantly correlated with the EPMs, although losses are also seen with bursts of multiple, large amplitude TAE. The latter is of particular significance for ITER; the transport of fast ions from the expected resonance overlap in phase space of a “sea” of large amplitude TAE is the kind of physics expected in ITER. The internal structure and amplitude of the TAE and EPMs has been measured with quadrature reflectometry and soft x-ray cameras. The TAE bursts have internal amplitudes of ñ∕n=1% and toroidal mode numbers 2&amp;lt;n&amp;lt;7. The EPMs are core localized, kink-like modes similar to the fishbones in conventional aspect ratio tokamaks. Unlike the fishbones, the EPMs can be present with q(0)&amp;gt;1 and can have a toroidal mode number n&amp;gt;1. The range of the frequency chirp can be quite large and the resonance can be through a fishbone-like precessional drift resonance, or through a bounce resonance.

Beam anisotropy effect on Alfvén eigenmode stability in ITER-like plasmas

This work studies the stability of the toroidicity-induced Alfvén eigenmodes (TAE) in the proposed ITER burning plasma experiment, which can be driven unstable by two groups of energetic particles, the 3.5 MeV α-particle fusion products and the tangentially injected 1 MeV beam ions. Both species are super-Alfvénic but they have different pitch angle distributions and the drive for the same pressure gradients is typically stronger from co-injected beam ions as compared with the isotropically distributed α-particles. This study includes the effect of anisotropy of the beam ion distribution function on TAE growth rate directly via the additional velocity space drive and indirectly in terms of the enhanced effect of the resonant particle phase space density. For near parallel injection TAEs are marginally unstable if the injection aims at the plasma centre, where the ion Landau damping is strong, whereas with the off-axis neutral beam injection the instability is stronger with the growth rate near 0.5% of the TAE mode frequency. In contrast, for perpendicular beam injection TAEs are predicted to be stabilized in nominal ITER discharges.In addition, the effect of TAEs on the fast ion beta profiles is evaluated by introducing a fast ion redistribution toy model based on a quasi-linear diffusion theory, which uses analytic expressions for the local growth and damping rates. These results illustrate the parameter window that is available for plasma burn when TAE modes are excited.

Additional Beta due to Fast Fusion Products in D-3HeFusion Plasma

An analytical formula for the additional beta due to fast fusion-bornions is derived by using the slowing-down approximation from theFokker-Planck equation under the assumption of negligible loss term. Itis found that the fast ion beta in a D-3He fusion plasma at atypical temperature of 55 keV is about 20% of the thermal beta, whichis the same ratio as that obtained in a D-T plasma at 20 keV.

Observation of modes at frequencies near the second Alfvén gap in the Tokamak Fusion Test Reactor

Modes have been observed near the frequency of the second Alfvén gap during off-axis H-minority heating experiments in the circular cross-section Tokamak Fusion Test Reactor. The observation of these modes is surprising in that the second gap, which is generally opened with ellipticity, is expected to be small, of order (r/R)2. A model is proposed in which the second gap is opened by the fast ion beta, which is shown to be able to introduce mode coupling, much as toroidal effects introduce mode coupling for Toroidal Alfvén Eigenmodes (TAE). With the low inferred energy of the fast ion tail (30–50 keV), the fast ion bounce resonance condition is assumed to drive the modes. The modes are seen with and without accompanying TAE mode activity.

Recent progress in high performance and steady-state experiments on the Japan Atomic Energy Research Institute Tokamak-60 Upgrade with W-shaped divertor

In the Japan Atomic Energy Research Institute (JAERI) Tokamak-60 Upgrade [H. Shirai and the JT-60 Team, Phys. Plasmas 5, 1712 (1998)], high performance and steady-state experiments have been conducted in the W-shaped divertor. The equivalent deuterium-tritium (D-T) fusion multiplication factor, QDTeq, was enhanced transiently up to 1.25 in the reversed shear plasma. The reduction in particle diffusivity in the internal transport barriers (ITB) region of the reversed shear plasma was confirmed as well as the thermal diffusivity. It was also confirmed that the correlation length of density fluctuations is reduced inside the ITB of density. The performance with a confinement-enhancement factor (H-factor, H89) of 2.2 and QDTeq of 0.16 was sustained in a quasi-steady-state in the high-poloidal-beta (βp) and high confinement mode (H-mode) regime. The reversed shear configuration with ITBs was sustained by injecting the lower-hybrid waves combined with neutral beam injection and fully noninductive current drive in the reversed shear plasmas was realized for the first time. The driven current by the negative-ion-based neutral beam (NNB) injection increased up to 0.6 MA. The H-mode transition was triggered with the NNB injection and the H-mode with H89∼1.6–1.8 was sustained. The toroidicity-induced Alfvén eigenmode was excited for a volume-averaged fast ion beta, 〈βh〉, as low as ∼0.1%.

トロイダル磁場閉じ込めにおけるアルヴェン固有モードに関する物理的課題 3.トカマクプラズマにおける実験と課題

Experimental studies of Alfvén eigenmodes in tokamaks and related critical issues are reviewed. Excitation and identification of Alfvén eigenmodes, threshold fast ion beta for excitation, their stability, mode structure and impact on plasma confinement are discussed.

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