Electromagnetic gyrokinetic simulation of turbulence in torus plasmas

Abstract

Gyrokinetic simulations of electromagnetic turbulence in magnetically confined torus plasmas including tokamak and heliotron/stellarator are reviewed. Numerical simulation of turbulence in finite beta plasmas is an important task for predicting the performance of fusion reactors and a great challenge in computational science due to multiple spatio-temporal scales related to electromagnetic ion and electron dynamics. The simulation becomes further challenging in non-axisymmetric plasmas. In finite beta plasmas, magnetic perturbation appears and influences some key mechanisms of turbulent transport, which include linear instability and zonal flow production. Linear analysis shows that the ion-temperature gradient (ITG) instability, which is essentially an electrostatic instability, is unstable at low beta and its growth rate is reduced by magnetic field line bending at finite beta. On the other hand, the kinetic ballooning mode (KBM), which is an electromagnetic instability, is destabilized at high beta. In addition, trapped electron modes (TEMs), electron temperature gradient (ETG) modes, and micro-tearing modes (MTMs) can be destabilized. These instabilities are classified into two categories: ballooning parity and tearing parity modes. These parities are mixed by nonlinear interactions, so that, for instance, the ITG mode excites tearing parity modes. In the nonlinear evolution, the zonal flow shear acts to regulate the ITG driven turbulence at low beta. On the other hand, at finite beta, interplay between the turbulence and zonal flows becomes complicated because the production of zonal flow is influenced by the finite beta effects. When the zonal flows are too weak, turbulence continues to grow beyond a physically relevant level of saturation in finite-beta tokamaks. Nonlinear mode coupling to stable modes can play a role in the saturation of finite beta ITG mode and KBM. Since there is a quadratic conserved quantity, evaluating nonlinear transfer of the conserved quantity from unstable modes to stable modes is useful for understanding the saturation mechanism of turbulence.

Kinetic ballooning modes in tokamaks and stellarators

“…The same was observed in [13], where the authors reported that the trapped electron mode is not observed in the same type of calculations for the standard Large Helical Device (LHD)…”

“…We remark that the radial wavenumber of the most unstable KBM in W7-X is in contrast with that of LHD [13] which is finite. The ITG mode also has the peak of the growth rate curve located around k x ρ s = 0 (Fig.3b).…”

“…The electrostatic ion-temperaturegradient-driven (ITG) and trapped-electron (TEM) modes have been extensively studied by means of gyrokinetic simulations [1][2][3][4][5][6][7], but KBMs have been explored less in stellarators than in tokamaks [8][9][10][11][12]. KBMs have recently been studied recently in helical plasmas [13], for a model configuration of standard LHD plasmas. In the present work we present the first numerical study of KBMs in W7-X.…”

Persistence of Ion Temperature Gradient Turbulent Transport at Finite Normalized Pressure

“…Introduction.-A finite value of normalized pressure β makes turbulence electromagnetic in magnetized plasmas, and magnetic fluctuations become important with increasing β [1][2][3][4]. The understanding of magnetic fluctuations in turbulence is an important issue in magnetic confinement and in space and astrophysics [5,6]; for instance, magnetic fluctuations have a significant impact on the normalized pressure β dependence of electromagnetic turbulent transport, which is one of the central issues in magnetized fusion plasma research, because it is linked to the fusion reaction rate and also related to the bootstrap current production that is important for steady state operation of tokamaks.…”

Nonlinear Electromagnetic Stabilization of Plasma Microturbulence

“…The impact of β on confinement is not entirely clear, with different experiments showing different scalings [1][2][3]. Moreover, the effect of β on different microturbulence regimes varies, decreasing transport in ion-temperature-gradient-driven (ITG) turbulence, while increasing transport in trapped-electron-mode (TEM) turbulence [4][5][6][7]. Fast ions can further reduce ITG turbulence [9,10].…”