Global approach to the spectral problem of microinstabilities in tokamak plasmas using a gyrokinetic model

Abstract

A solution to the full two-dimensional eigenvalue problem of electrostatic microinstabilities in a tokamak plasma is presented in the framework of gyrokinetic theory. The approach is the generalization of methods previously developed for a cylindrical system [S. Brunner and J. Vaclavik, Phys. Plasmas 5, 365 (1998)]. By solving the spectral problem in a special Fourier space adapted to the curved geometry, orbit width as well as Larmor radius can be kept to all orders. For a first numerical implementation, a large aspect ratio plasma with circular concentric magnetic surfaces is considered. A root finding algorithm for identifying the eigenfrequencies, based on a higher order Nyquist method, enables straightforward implementation on a parallel computer. Illustrative results for ion temperature gradient-related instabilities are presented. These include scaling studies of the radial width, and toroidicity and magnetic shear scans, as well as the effects of nonadiabatic trapped electron dynamics.

Momentum transport in the vicinity of qmin in reverse shear tokamaks due to ion temperature gradient turbulence

“…Further ITG mode exhibit a slab-like feature in the negative-sheared magnetic configuration as shown by a gyrokinetic pseudospectral global code GLOGYSTO. 46 So ITG modes in sheared slab geometry are considered in this work. As mentioned before, the presence of q-curvature inherently break the hk k i symmetry, leading to net parallel momentum generation without regard to the E Â B symmetry breaking mechanism.…”

Role of nonadiabatic untrapped electrons in global electrostatic ion temperature gradient driven modes in a tokamak

“…Theoretical formulations used here are an extension of those studied in Ref. 4 and 17 with a major change, namely the addition of the proper gyrokinetic nonadiabatic passing electron response to the electrostatic potential fluctuation. As our interest is in passing nonadiabatic electron dynamics, here we present a description of the electrostatic formulation.…”

“…For example, for typical DIII-D-like parameters, the global electrostatic toroidal gyrokinetic spectral model GLOGYSTO 4,5 and time-evolving gyrokinetic codes 6 report typical toroidal mode numbers in the range 3 ഛ n ഛ 15 with eigenmode width and structure occupying a good fraction of the minor radius a. These eigenmodes span several mode rational surfaces ͑MRS͒ r = r MRS defined as k ʈm,n ͑r = r MRS ͒ = 0.…”

“…8 The code EM-GLOGYSTO was generalized by including fully gyrokinetic nonadiabatic passing ion and electron dynamics which couple to A Ќ fluctuations, 9 Shafranov shift effects, 10 followed by trapped electron dynamics coupled to A Ќ fluctuations. 4,11 It has been shown that when passing drift kinetic electrons couple only to A ʈ , 7 finite-␤ effects have a benign effect on ITGs with adiabatic electron response. Within the same model, Alfvén ITGs ͑AITGs͒ or kinetic ballooning modes ͑KBMs͒ 3,12-16 become more unstable with increasing ␤.…”

Role of Trapped Electrons on Global Gyrokinetic Linear Stability of Collisionless Microtearing Modes

“…The model assumptions and formulation are detailed in Refs. [15,16,17,18,19,20] and references thereof. In this work, many of the recent results described in Ref.…”