For the development of a reduced description for EP transport in fusion plasmas, which preserves all the necessary physics ingredients, as well as for code validation efforts, it is crucial to adopt clearly defined reference cases, where the physics processes of interest are identified. This was done in the case of the NLED ER Project¹¹, which could produce positive feedback on the experimental activity as discussed in the Accompanying Document. The further development of reference cases aimed at the benchmark activity combined with comparisons with the reduced model description is the focus of the sub-work-package WP3.1. Meanwhile, as different codes are based on different physics models and approaches, each code involved in the present proposal has a dedicated sub-work-package. However, all codes will jointly take part to the benchmark activity combined with the comparison of numerical simulation results with the reduced EP transport model description, following the various levels of approximation described in WP1 and WP2. Through this activity, we will assess the relevance of various elements in the multi-level description of the nonlinear processes involved in EP transport.

WP3.1 Reference case setup: Recently, the experimental scenario underlying the NLED/NAT AUG reference case³⁴ has been further developed to reach a stationary flat-top phase (Oct. 2017). In this phase, one can analyze the EP transport on time scales considerably longer than the slowing down time. It is proposed to adopt the previous NLED case according to this new data and to create a sufficiently generic base case for theory-code-experiment comparisons. In addition it is proposed to extend the previous studies on the standard ITER scenario (15MA) and to set up a DEMO-type burning plasma case. Further, DTT (intermediate to high-n) and JT-60SA-type (low-n, high-beta) scenarios will be considered. For simplicity, and for making benchmark possible with codes using simplified geometry, “circular magnetic flux surface“ equivalent cases will be provided.

WP3.2 EUTERPE code: EUTERPE⁴⁶ is a nonlinear three-dimensional global electro magnetic particle-in-cell code being able to handle multiple species and collisions. Due to the enormous complexity in Stellarator geometry, simplified versions have been developed: a fluid-electron model (FLUID-EUTERPE) has shown to mitigate the cancellation problem in electromagnetic simulations and CKA-EUTERPE is a nonlinear hybrid model using pre-calculated eigenfunctions to determine the wave-particle energy transfer, similar to the HAGIS model⁴⁷, however in 3D geometry. In the comparison with the reduced EP transport model description, EUTERPE will be particularly useful in testing the development of a reliable collision model.

WP3.3 HAGIS/LIGKA code: The HAGIS/LIGKA⁴⁸ code package has been extensively used to determine the linear mode properties, single- and multi-mode saturation levels for various Alfvén-type perturbations. Thus, the output of this package can be used to estimate the quasilinear transport in the most simplistic limit, and compare this estimate to nonlinear hybrid simulations. Presently, a wave-wave interaction model including some aspects of zonal flow physics is implemented and benchmarked with more complete codes (ENR NAT¹²). By construction, LIGKA can provide linear AE properties with different fidelity by using a hierarchy of analytical, semi-analytical and numerical methods, allowing very fast and automated overview-type analysis over a broad range of the relevant parameter space. Within the present project proposal, HAGIS/LIGKA can help to select the most relevant scenarios and analyze their sensitivity.

WP3.4 HYMAGYC code: HYMAGYC⁴⁹ is analogous to XHMGC (see WP3.6), but suited for applications to general axisymmetric magnetic equilibria, even in high-β plasmas (perturbed vector potential fully retained). The MHD module solves resistive MHD linear equations including the kinetic response of a single energetic-particle population evolved according to fully gyrokinetic equations of motion expanded up to order O(ε_g²), with ε_g being the gyrokinetic ordering parameter. In the comparisons with the reduced EP transport models, HYMAGYC can provide a test of the importance of a fully compressible gyrokinetic description.

WP3.5 ORB5 code: ORB5, originally written for electrostatic ITG turbulence⁵⁰, now has all extensions made in the NEMORB project fully implemented⁵¹ (including the electro-magnetic effects, and the capability of dealing with many particle species). ORB5 has been successfully tested for the dynamics of zonal structures^52,53, and has also been successfully tested for the SAW dynamics, with verifications against analytical theory, and benchmarks against other codes^54-56. Within this project proposal, ORB5 can contribute to the comparison with the reduced EP transport model description taking into account the interaction of AEs and zonal structures in the presence of turbulence.

WP3.6 XHMGC code: XHMGC^57-59 is a non-perturbative nonlinear hybrid MHD- particle initial value code, for equilibria with shifted circular magnetic surfaces. The kinetic response by several (up to three) particle populations is included, accounting for EP and/or kinetic thermal plasma effects. Finite Larmor radius effects are neglected, while magnetic drift orbit widths are fully retained. Thermal ion compressibility and diamagnetic effects are also included. XHMGC can serve as test bench for the reduced EP transport models in simplified geometry.

Milestones:
WP3-M1 - Finishing selection of reference cases and relevant plasma scenarios for code benchmarking and testing of reduced EP transport models; finishing linear stability analysis by all codes involved (Dec. 2019).

Deliverables:
WP3-D1 - Well documented reference cases for various scenarios; data base providing linear stability properties for all participating codes (2019).
WP3-D2 - Demonstration of applicability of the developed transport models to the selected scenarios (2020).
WP3-D3 - Analysis of the reference scenarios using the developed models, demonstrating their validity and range of applicability (2020).

Bibliography