Pressure-gradient-induced Alfven eigenmodes: II. Kinetic excitation with ion temperature gradient

The kinetic excitation of ideal magnetohydrodynamic (MHD) discrete Alfven eigenmodes in the second MHD ballooning stable domain is studied in the presence of a thermal ion temperature gradient (ITG), using linear gyrokinetic particle-in-cell simulations of a local flux tube in shifted-circle tokamak geometry. The instabilities are identified as alpha-induced toroidal Alfven eigenmodes (alpha-TAE); that is, bound states trapped between pressure-gradient-induced potential barriers of the Schroedinger equation for shear Alfven waves. Using numerical tools, we examine in detail the effect of kinetic thermal ion compression on alpha-TAEs; both non-resonant coupling to ion sound waves and wave-particle resonances. It is shown that the Alfvenic ITG instability thresholds (e.g., the critical temperature gradient) are determined by two resonant absorption mechanisms: Landau damping and continuum damping. The numerical results are interpreted on the basis of a theoretical framework previously derived from a variational formulation. The present analysis of properties and structures of Alfvenic fluctuations in the presence of steep pressure gradients applies for both positive or negative magnetic shear and can serve as an interpretative framework for experimental observations in (future) high-performance fusion plasmas of reactor relevance.Comment: 25 pages, 9 figure

Dynamics of resistive double tearing modes with broad linear spectra

The nonlinear evolution of resistive double tearing modes (DTMs) with safety factor values q=1 and q=3 is studied in a reduced cylindrical model of a tokamak plasma. We focus on cases where the resonant surfaces are a small distance apart. Recent numerical studies have shown that in such configurations high-m modes are strongly unstable. In this paper, it is first demonstrated that linear DTM theory predicts the dominance of high-m DTMs. A semi-empirical formula for estimating the poloidal mode number of the fastest growing mode, m_peak, is obtained from the existing linear theory. Second, using nonlinear simulations, it is shown that the presence of fast growing high-m modes leads to a rapid turbulent collapse in an annular region, whereby small magnetic island structures form. Furthermore, consideration is given to the evolution of low-m modes, in particular the global m=1 internal kink, which can undergo nonlinear driving through coupling to fast growing linear high-m DTMs. Factors influencing the details of the dynamics are discussed. These results may be relevant for the understanding of the magnetohydrodynamic (MHD) activity near the minimum of q and may thus be of interest to studies concerned with stability and confinement in advanced tokamaks.Comment: 11 pages, 10 figure

Large-mode-number magnetohydrodynamic instability driven by sheared flows in a tokamak plasma with reversed central shear

The effect of a narrow sub-Alfvenic shear flow layer near the minimum q_min of the tokamak safety factor profile in a configuration with reversed central shear is analyzed. Sufficiently strong velocity shear gives rise to a broad spectrum of fast growing Kelvin-Helmholtz (KH)-like ideal magnetohydrodynamic (MHD) modes with dominant mode numbers m,n ~ 10. Nonlinear simulations with finite resistivity show magnetic reconnection near ripples caused by KH-like vortices, the formation of turbulent structures, and a flattening of the flow profile. The KH modes are compared to double tearing modes (DTM) which dominate at lower shearing rates. The possible application of these results in tokamaks with internal transport barrier is discussed.Comment: 4 pages, 4 figure

Nonlinear evolution of the m=1 internal kink mode in the presence of magnetohydrodynamic turbulence

The nonlinear evolution of the m=1 internal kink mode is studied numerically in a setting where the tokamak core plasma is surrounded by a turbulent region with low magnetic shear. As a starting point we choose configurations with three nearby q=1 surfaces where triple tearing modes (TTMs) with high poloidal mode numbers m are unstable. While the amplitudes are still small, the fast growing high-m TTMs enhance the growth of the m=1 instability. This is interpreted as a fast sawtooth trigger mechanism. The TTMs lead to a partial collapse, leaving behind a turbulent belt with q ~= 1 around the unreconnected core plasma. Although, full reconnection can occur if the core displacement grows large enough, it is shown that the turbulence may actively prevent further reconnection. This is qualitatively similar to experimentally observed partial sawtooth crashes with post-cursor oscillations due to a saturated internal kink.Comment: 14 pages, 13 figure

Fast growing double tearing modes in a tokamak plasma

Configurations with nearby multiple resonant surfaces have broad spectra of linearly unstable coupled tearing modes with dominant high poloidal mode numbers m. This was recently shown for the case of multiple q = 1 resonances [Bierwage et al., Phys. Rev. Lett. 94 (6), 65001 (2005)]. In the present work, similar behavior is found for double tearing modes (DTM) on resonant surfaces with q >= 1. A detailed analysis of linear instability characteristics of DTMs with various mode numbers m is performed using numerical simulations. The mode structures and dispersion relations for linearly unstable modes are calculated. Comparisons between low- and higher-m modes are carried out, and the roles of the inter-resonance distance and of the magnetic Reynolds number S_Hp are investigated. High-m modes are found to be destabilized when the distance between the resonant surfaces is small. They dominate over low-m modes in a wide range of S_Hp, including regimes relevant for tokamak operation. These results may be readily applied to configurations with more than two resonant surfaces.Comment: 11 pages, 15 figure

Benchmark of multi-phase method for the computation of fast ion distributions in a tokamak plasma in the presence of low-amplitude resonant MHD activity

The transport of fast ions in a beam-driven JT-60U tokamak plasma subject to resonant magnetohydrodynamic (MHD) mode activity is simulated using the so-called multi-phase method, where 4 ms intervals of classical Monte-Carlo simulations (without MHD) are interlaced with 1 ms intervals of hybrid simulations (with MHD). The multi-phase simulation results are compared to results obtained with continuous hybrid simulations, which were recently validated against experimental data (Bierwage et al., 2017). It is shown that the multi-phase method, in spite of causing significant overshoots in the MHD fluctuation amplitudes, accurately reproduces the frequencies and positions of the dominant resonant modes, as well as the spatial profile and velocity distribution of the fast ions, while consuming only a fraction of the computation time required by the continuous hybrid simulation. The present paper is limited to low-amplitude fluctuations consisting of a few long-wavelength modes that interact only weakly with each other. The success of this benchmark study paves the way for applying the multi-phase method to the simulation of Abrupt Large-amplitude Events (ALE), which were seen in the same JT-60U experiments but at larger time intervals. Possible implications for the construction of reduced models for fast ion transport are discussed