Since 18 of December 2019 uses Nucleus credentials. Visit our help pages for information on how to Register and Sign-in using Nucleus.
May 10 – 15, 2021
Virtual Event
Europe/Vienna timezone
The Conference will be held virtually from 10-15 May 2021

Flux driven pedestal formation in tokamaks: Turbulence simulations validated against the isotope effect

May 13, 2021, 2:00 PM
4h 45m
Virtual Event

Virtual Event

Regular Poster Magnetic Fusion Theory and Modelling P6 Posters 6


clarisse bourdelle (CEA, IRFM, F-13108 Saint-Paul-lez-Durance, France.)


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


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.
Time and radially averaged (over 0.86<r/a<1) confinement time tau_E in ms with respect to the radially averaged heat flux Q_0  in arbitrary units. Note that the system is flux driven by a Gaussian shaped power source S located in the inner buffer (r/a < 0.86) to simulate the heat deposition in the core plasma. This source imposes the influx Q_0=∫S(x)dx across the simulation domain, constraining the time averaged total heat flux at equilibrium to be equal to Q_0.

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.

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.

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.
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, 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

Primary authors

clarisse bourdelle (CEA, IRFM, F-13108 Saint-Paul-lez-Durance, France.) Mr Grégory De Dominici Guillaume Fuhr (Aix-Marseille University) Mr Peter Beyer (CNRS, Aix-Marseille Univ., PIIM UMR7345, Marseille, France) Mr Laurent Chôné (Department of Applied Physics, Aalto University, Espoo, Finland) Mr Francesco Cianfrani (CNRS, Aix Marseille University) Mrs Gloria falchetto (CEA, IRFM, F-13108 St-Paul-Lez-Durance, France) Yanick SARAZIN (CEA, IRFM) Xavier Garbet (CEA)

Presentation materials