# Development and application of a multiscale model for the magnetic fusion edge plasma region

- Entwicklung und Anwendung eines Multiskalenmodells zur Beschreibung des Plasmas in der Randschicht von magnetischen Fusionsanlagen

Hasenbeck, Felix; Kull, Hans-Jörg (Thesis advisor); Reiter, Detlev (Thesis advisor)

*Jülich : Forschungszentrum Jülich GmbH, Zentralbibliothek, Verlag (2016)*

Book, Dissertation / PhD Thesis

In: Schriften des Forschungszentrums Jülich. Reihe Energie & Umwelt 307*Page(s)/Article-Nr.: 188 Seiten : Illustrationen, Diagramme*

Dissertation, RWTH Aachen, 2015

Abstract

Plasma edge particle and energy transport perpendicular to the magnetic field plays a decisive role for the performance and lifetime of a magnetic fusion reactor. For the particles, classical and neoclassical theories underestimate the associated radial transport by at least an order of magnitude. Drift fluid models, including mesoscale processes on scales down to tenths of millimeters and microseconds, account for the experimentally found level of radial transport; however, numerical simulations for typical reactor scales (of the order of seconds and centimeters) are computationally very expensive. Large scale code simulations are less costly but usually lack an adequate model for the radial transport.The multiscale model presented in this work aims at improving the description of radial particle transport in large scale codes by including the effects of averaged local drift fluid dynamics on the macroscale profiles. The multiscale balances are derived from a generic multiscale model for a fluid, using the Braginskii closure for a collisional, magnetized plasma, and the assumptions of the B2 code model (macroscale balances) and the model of the local version of the drift fluid code ATTEMPT (mesoscale balances). A combined concurrent-sequential coupling procedure is developed for the implementation of the multiscale model within a coupled code system. An algorithm for the determination of statistically stationary states and adequate averaging intervals for the mesoscale data is outlined and tested, proving that it works consistently and efficiently.The general relation between mesoscale and macroscale dynamics is investigated exemplarily by means of a passive scalar system. While mesoscale processes are convective in this system, earlier studies for small Kubo numbers K << 1 have shown that the macroscale behavior is diffusive. In this work it is demonstrated by numerical experiments that also in the regime of large Kubo numbers K >> 1 the macroscale transport remains diffusive. An analytic expression for the diffusion coefficient D is found, being consistent with results from percolation theory.The multiscale model and the coupling procedure are benchmarked with a one-dimensional test problem which consists of coupling the local version of the drift fluid code ATTEMPT to a 1D macroscale code to determine the time-dependent evolution of the flux surface averaged density in radial direction in the tokamak edge region. The reference simulation is given by a simulation of the non-local version of ATTEMPT, accounting for both the mesoscale and the macroscale evolution. Results of the coupled code simulations show that the macroscale evolution of the density and the radial particle flux can be reproduced with typical uncertainties of 6 and 22%, respectively. Time savings with respect to the non-local simulations are of a factor of ten for a typical macroscale evolution time of 10 milliseconds while a speedup factor of the order of 50 is achievable for an edge region with a radial extent of ~ 30 cm and typical radial profile lengths of ~ 5 cm.The multiscale model for two-dimensional, stationary problems is realized by coupling of the B2 code and the local version of the ATTEMPT code. The results of the corresponding coupled code simulations for experiments at the tokamak TEXTOR provide plasma profiles in agreement with experimental measurements with uncertainties regarding the electron density and electron temperature measured at the outer midplane around 10 to 25%. Poloidally and radially dependent profiles of the radial particle diffusion coefficients D, self-consistently determined by B2-ATTEMPT, have typical values of 0.3 to 0.9 m^2/s and are within a 10 to 30% range of effective diffusion coefficients employed in B2-EIRENE simulations to fit simulation results to measured density profiles. The poloidal dependence of D as given by the B2-ATTEMPT simulations accounts for the experimentally confirmed ballooning character of radial transport with D at the low field side, being up to a factor two larger than on the high field side.

### Identifier

- ISBN: 978-3-95806-120-0
- URN: urn:nbn:de:hbz:82-rwth-2016-013380
- RWTH PUBLICATIONS: RWTH-2016-01338