Microtearing modes in tokamak discharges

Journal article, 2016

Microtearing modes (MTMs) have been identified as a source of significant electron thermal transport in tokamak discharges. In order to describe the evolution of these discharges, it is necessary to improve the prediction of electron thermal transport. This can be accomplished by utilizing a model for transport driven by MTMs in whole device predictive modeling codes. The objective of this paper is to develop the dispersion relation that governs the MTM driven transport. A unified fluid/kinetic approach is used in the development of a nonlinear dispersion relation for MTMs. The derivation includes the effects of electrostatic and magnetic fluctuations, arbitrary electron-ion collisionality, electron temperature and density gradients, magnetic curvature, and the effects associated with the parallel propagation vector. An iterative nonlinear approach is used to calculate the distribution function employed in obtaining the nonlinear parallel current and the nonlinear dispersion relation. The third order nonlinear effects in magnetic fluctuations are included, and the influence of third order effects on a multi-wave system is considered. An envelope equation for the nonlinear microtearing modes in the collision dominant limit is introduced in order to obtain the saturation level. In the limit that the mode amplitude does not vary along the field line, slab geometry, and strong collisionality, the fluid dispersion relation for nonlinear microtearing modes is found to agree with the kinetic dispersion relation. Published by AIP Publishing. [http://dx.doi.org/10.1063/1.4953609] I. INTRODUCTION Micro-instabilities can result in turbulence that influences energy confinement in tokamak discharges. One such micro-instability is the microtearing mode (MTM), a tearing-parity mode centered on high-order rational surfaces. Microtearing instability can provide a significant contribution to the electron thermal transport in low-aspect ratio tokamaks.1–5 The MTMs lead to a tearing and subsequent reconnection of the magnetic field. MTMs are shortwavelength ion scale (low kh) electromagnetic instabilities that are driven by electron temperature gradients.6–8 It was proposed that when the magnetic field has a component in the same direction as the electron temperature gradient, a current is driven in the direction of the magnetic field line, which can destabilize MTMs. These modes propagate in the electron diamagnetic drift direction and depend on the electron ion collisionality.9,10 Consequently, transport driven by MTM instabilities depends on both the electron ion collision frequency and the electron temperature gradient. The research carried out in this paper indicates that when the electrostatic effects are included, MTMs also depend on the density gradient.