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Flux driven pedestal formation in tokamaks:
Turbulence simulations validated against the isotope effect
C. Bourdelle1, G. De Dominici1, G. Fuhr2, P. Beyer2, L. Chôné3, F. Cianfrani2, G. L. Falchetto1, X. Garbet1, Y. Sarazin1
1 CEA, IRFM, F-13108 St-Paul-Lez-Durance, France
2 CNRS, Aix-Marseille Univ., PIIM UMR7345, Marseille, France
3 Department of Applied Physics, Aalto University, Espoo, Finland
E-mail: clarisse.bourdelle@cea.fr
Spontaneous pedestal formation above a power threshold at the edge of magnetically confined plasma is modelled for the first time in flux driven three-dimensional fluid simulations of electromagnetic turbulence with the code EMEDGE3D 1. The model implemented in EMEDGE3D is based on nonlinear fluid equations for the charge, energy balance and Ohm's law, the three transported fields being the electrostatic potential, the electron pressure and the magnetic potential 2.
Three key ingredients of the edge turbulent transport are simultaneously included in the flux driven simulations, applied on realistic L mode edge parameters, namely:
- an edge turbulence modelling accounting for resistive ballooning modes as well as drift waves [3,4,5,6]
- the electromagnetic effects on edge turbulence [3,4,5,6]
- a force balance radial electric field accounting for a realistic neoclassical poloidal velocity profile, i.e. with a realistic L mode edge radial variation of collisionality (from banana to Pfirsch-Schlüter regimes) [7,8]
The existence of a threshold on the injected power above which a pedestal forms is recovered. The pedestal formation is shown to be due to the E×B shear of the turbulence, following the BDT criterion [9]. The neoclassical friction and the Reynolds stresses are of the same order, while the Maxwell stress is negligible.
![From [1]. Time averaged profiles of, (a) the equilibrium electron pressure in arbitrary units, (b) the equilibrium radial electric field in arbitrary units, for a heat source lower than the threshold (Q_0=40, dashed line) and a heat source above the threshold (Q_0=55 full line). 1<r/a<1.02 corresponds to the RHS buffer zone.](http://irfm.cea.fr/Pisp/clarisse.bourdelle/Fig2.jpg)
The validity of the physics embedded in the fluid turbulence modelled is further challenged by changing Deuterium for Tritium. A lower threshold value on the power leading to the formation of a pedestal is observed in T versus D, similarly to experimental observations. The E×B quenching is made easier in T due to longer turbulence auto-correlation time.
![From [1]. Radially averaged confinement time over the simulation domain, tau_E in ms with respect to the radially averaged heat flux Q_0 in arbitrary units. For Deuterium (as shown in Fig.1) in black dotted line, for Tritium in yellow dashed line.](http://irfm.cea.fr/Pisp/clarisse.bourdelle/Fig6.jpg)
Even though the fluctuation level of the pressure is around 5 to 10% when approaching the separatrix in L mode, the quasilinear approximation is found to be valid. As in gyrokinetic L mode edge modelling [6], in the fluid EMEDGE3D simulations, the linear and non-linear cross-phases agree with each other [5]. Moreover, the Kubo number (the ratio between the turbulence auto-correlation time and the time-of-flight of the particle, here the eddy turnover time) is estimated and shown to be consistently lower than unity..
The validity of the quasilinear approximation up to the separatrix gives perspectives towards a reduced quasilinear model adapted to the L-mode edge region, as long as such a reduced model accounts for the two important effects of electromagnetic destabilization and stabilizing diamagnetic coupling.
This work has been carried out within the framework of the EUROfusion Consortium and has received funding from the Euratom research and training programme 2014-2018 and 2019-2020 under grant agreement No 633053. The views and opinions expressed herein do not necessarily reflect those of the European Commission.
References
1 G. De Dominici, G. Fuhr, P. Beyer, C. Bourdelle, L. Chôné, F. Cianfrani, G. L. Falchetto, X. Garbet, Y. Sarazin, submitted to Physical Review Letters, available on ArXiv https://arxiv.org/abs/1912.09792v1, 2019.
2 G. Fuhr, P. Beyer, S. Benkadda, and X. Garbet. Physical Review Letters,101(19), 2008.
3 B. N. Rogers, J. F. Drake, and A. Zeiler. Physical Review Letters, 81(20):4396_4399, 1998.
[4] B. D. Scott. Physics of Plasmas, 12(6), 2005.
[5] G. De Dominici, G. Fuhr, C. Bourdelle et al, Nuclear Fusion, 59(12):126019 2019.
[6] N. Bonanomi, C. Angioni, P.C. Crandall et al, Nuclear Fusion, 59(12):126025, 2019.
[7] L. Chôné, P. Beyer, Y. Sarazin, G. Fuhr, C. Bourdelle, S. Benkadda. Physics of Plasmas, 21(7):070702, 2014.
[8] G. Y. Park, S. S. Kim, Hogun Jhang, P. H. Diamond, T. Rhee, X. Q. Xu., Physics of Plasmas, 22(3), 2015.
[9] H. Biglari, P. H. Diamond, P. W. Terry. Physics of Fluids B: Plasma Physics, 2(1):1_4, 1990.
| Affiliation | CEA |
|---|---|
| Country or International Organization | France |
