Nonlinear evolution of the toroidal Alfvén instability using a gyrofluid model*

Abstract

Discrete shear Alfvén modes such as the TAE (toroidal Alfvén eigenmode) are susceptible to destabilization by energetic alpha populations and neutral beams; this can lead to enhanced fast ion losses and degraded heating efficiencies. A gyrofluid model with Landau closure has been developed for understanding both the linear and nonlinear phases of these instabilities. The linear wave–particle resonances necessary to excite Alfvén instabilities are included in a coupled set of fluid equations. This model is used to analyze several nonlinear saturation mechanisms that arise from mode coupling effects. The effects of shear flow velocity generation (through the Reynolds stress) and localized current generation (leading to modifications in the q profile) are specifically examined.

The toroidicity-induced Alfvén eigenmode structure in DIII-D: Implications of soft x-ray and beam-ion loss data

“…The eigenfunction is altered by coupling to other plasma waves, 10-12 by energetic particles 11,[13][14][15][16][17] and by sheared rotation profiles. 18 Experimentally, there have been many studies of various properties of the TAE ͑Ref. 19͒ but accurate measurements of the TAE eigenfunction are rare.…”

Alpha particle physics experiments in the Tokamak Fusion Test Reactor

“…the effect of TAE modes on the internal redistribution of alphas in TFTR. Some progress has been made in the theory of this interaction [28,29,[183][184][185][186][187], and in interpreting the TAE-induced transport of NBI or RF tail ions due to TAE modes [188][189][190][191]. The results of such studies would help to clarify the degree to which collective alpha effects will affect the confinement of reactor-grade tokamak plasmas.…”

Recent JET experiments on Alfvén eigenmodes with intermediate toroidal mode numbers: measurements and modelling of n = 3 toroidal Alfvén eigenmodes with the TAEFL code*

“…This exercise included the contribution of various numerical codes, ranging from perturbative MHD models such as those employed in CASTOR(-K) [32,33] and NOVA(-K) [34,35], to those employing a warm dielectric tensor model like LEMan [15,16] to fully gyro-fluid models such as that used in TAEFL [17,18] and linear gyro-kinetic models as that employed in LIGKA [36]. Many aspects of these studies have been presented elsewhere [7,8,14,19]; therefore, here we specifically focus only on the analysis performed with the TAEFL code.…”

“…The TAEFL code [17,18] is a reduced MHD initial value code that uses gyrofluid closure techniques for the energetic ions to incorporate the Landau resonance effects that destabilize Alfvén modes. Since only unstable modes can be analyzed by TAEFL, the technique used in this comparison with the JET data for stable n=3 modes, was to start with an unstable Alfvén mode, vary the fast ion drive and extrapolate back to zero drive in order to determine an effective damping rate.…”

“…In this paper we focus on a further theoretical analysis of the damping rate measurements for the n=3 TAEs previously reported in [6] using the TAEFL code [17,18]. As the TAEFL and LEMan estimation of the damping rate of the modes is based on different numerical algorithms, this work is important not only as a code-to-code benchmark, but also in that it indicates whether the essential physics mechanisms are retained in the numerical calculations, irrespective of the actual details of the calculations themselves.…”