The interaction of EPs and MHD modes is an intrinsically multi-scale process, which is addressed by WP4. Here, we focus on tearing modes (TM) because, in addition to interact with EPs, TM can lead to loss of confinement or even major disruptions. Therefore, a considerable effort is devoted to improving our theoretical understanding and to developing experimental tools to prevent its appearance and/or control its growth in current experiments and in future fusion devices like ITER. In this proposal, we will therefore study how the tearing mode affects the transport of EPs and how EPs stabilize or destabilize tearing modes. We will concentrate on energetic ions, while electrons will be kept thermal. The study will be divided into three parts. First, a study will be conducted by means of reduced models for the excitation of the tearing mode using a fully fluid description for the thermal plasma. This reduced model will provide the time evolution of the perturbation spectrum. Together with this model, the equations of motion of gyro-centers will be integrated in a separate module for passive tracers leading to the quantification of the transport of EPs in the presence of tearing modes. This module already exists for axisymmetric modes such as geodesic acoustic modes (GAMs) and has been used to study the transport of gyro-centers in the presence of energetic GAMs⁶⁰. The module will have to be upgraded to include non-axisymmetric modes. The analysis of both passing and trapped particles will be carried out. Second, the analysis of the impact of EPs on the linear and nonlinear stability of the tearing mode will be conducted using reduced models treating the thermal plasma (ions and electrons) as a fluids but retaining the retroaction of energetic ions, described kinetically, following previous works^61-64. As a first step, the kinetic behaviour of thermal ions, and in particular finite orbit width effects, can be modeled in the fluid framework. Third, few selected global electromagnetic simulations using the gyrokinetic Vlasov code GKW^65-67 will be performed in order to compare full-kinetic results and those of the hybrid models, validating the reduced approach used before. In these simulations all the three different species will be described kinetically, using isotropic Maxwellian for the initial distribution functions.

Milestones:
WP4-M1 - Derivation of a nonlinear reduced fluid model of the tearing mode excitation (Dec. 2019).
WP4-M2 - Non-linear simulations of tearing mode with energetic ions (Dec. 2020).
WP4-M3 - Comparison between self-consistent GKW simulations and reduced EP transport model (Dec. 2020).

Deliverables:
WP4-D1 - Linear stability analysis of tearing modes with energetic ions (2019).
WP4-D2 - Upgrade of the test-particle tracking module to include non-axisymmetric modes (2020).
WP4-D3 - Assess the impact of energetic ions on the stabilization/destabilization of the tearing mode and the induced energetic ion transport (2020).

Bibliography