Systematic linear-stability assessment of Alfvén eigenmodes in the presence of fusion α-particles for ITER-like equilibria

Abstract

A systematic approach to assess the linear stability of Alfvén eigenmodes in the presence of fusion-born alpha particles is described. Because experimental results for ITER are not available yet, it is not known beforehand which Alfvén eigenmodes will interact more intensively with the alpha-particle population. Therefore, the number of modes that need to be considered in stability assessments becomes quite large and care must be exercised when choosing the numerical tools to work with, which must be fast and efficient. In the presented approach, all possible eigenmodes are first found after intensively scanning a suitable frequency range. Each solution found is then tested to find if its discretization over the radial grid in use is adequate. Finally, the interaction between the identified eigenmodes and the alpha-particle population is evaluated with the drift-kinetic code CASTOR-K, in order to assess their growth rates and hence their linear stability. The described approach enables one to single out the most unstable eigenmodes in a given scenario, which can then be handled with more specialized tools. This selection capability eases the task of evaluating alpha-particle interactions with Alfvén eigenmodes, either for ITER scenarios or for any other kind of scenario planning.

Numerical investigation of non-perturbative kinetic effects of energetic particles on toroidicity-induced Alfvén eigenmodes in tokamaks and stellarators

“…Radiative damping by the background-plasma is described by a fourth-order operator [13,14]. Here, a term derived in Ref.…”

Comprehensive evaluation of the linear stability of Alfvén eigenmodes driven by alpha particles in an ITER baseline scenario

“…We focus on eigenmodes with toroidal mode number n ranging from 1 to 50 in order to stay within the limits of the drift-kinetic ordering for alpha particles, i.e., k ⊥ ρ α < 1 where k ⊥ is the AE perpedicular wavenumber and ρ α is the gyroradius of the alpha particles [8]. We further restrict our analysis to AEs whose eigenfrequency falls in one of the first three gaps of the ideal shear Alfvén wave continuum, namely (ordered by increasing frequency) the Toroidicity induced AE (TAE) gap, the Ellipticity induced AE (EAE) gap, and the Non-circular triangularity-induced AE (NAE) gap [1,15,16].…”

“…In CASTOR-K, the distribution function of every particle population p is modelled with the product of a function of s and a function of energy E [10,8],…”

“…Concerning the energy distribution f p (E), while DT ions, He ashes and electrons have been described by Maxwellian distributions [8], a slowing-down distribution which is determined by the effects of electron and ion drag on alpha particles [19,20,21,22] has been used to describe the alpha-particle population,…”

“…In this article the stability of AEs is systematically addressed for the 15 MA ELMy H-mode ITER baseline scenario [5,6,7,8] making use of a recently introduced framework [8] that is based on the hybrid MHD drift-kinetic code CASTOR-K [9,10], which is the key element in our suite of numerical codes. Growth rates are computed systematically for all possible eigenmodes taking into account the alpha-particle drive, the Landau damping due to the DT …”