Description
Turbulent transport is the dominant loss mechanism for heat and particles in modern magnetic-confinement-fusion experiments. To investigate the dynamics underlying this transport, gyrokinetic simulations are commonly performed in radially localized flux-tube domains. Standard practice involves identifying the dominant linear instability and comparing its behavior with that of nonlinear simulations, from which transport-relevant quantities (e.g., heat and particle fluxes) are computed.
Under reactor-relevant conditions, however, multiple linear instabilities can coexist within a single simulation. This is especially true in stellarators, where the complex magnetic-field geometry often gives rise to a larger number of destabilizing resonances than in tokamaks. As a result, it can be difficult to directly relate the nonlinear dynamics that govern turbulent transport to the underlying linear instabilities.
To address this challenge, a linear adjoint eigenmode solver has been implemented in the gyrokinetic electromagnetic numerical experiment (GENE) code. This capability enables the computation of a spectrum of direct and adjoint linear eigenmodes, which can be used to rigorously decompose a nonlinear state onto a linear-eigenmode basis. Such a decomposition facilitates investigation of the individual contributions of different linear eigenmodes to nonlinear fluctuations and offers new insights into their nonlinear saturation.
As a demonstration, simulation results are presented for the Wendelstein 7-X stellarator in the high-mirror configuration. Flux-tube simulations with kinetic ions and adiabatic electrons are performed across several ion-temperature gradients. The nonlinear distribution function is decomposed onto the computed eigenmode basis, and the resulting energy distribution across that basis is analyzed. These results are discussed in the context of developing reduced-order (e.g., quasilinear) models of turbulent transport, highlighting the ability of this approach to identify the salient dynamics that govern transport.