1. 24th IAEA Fusion Energy Conference, San Diego, USA, October 8-13, 2012
Pedestal Modelling Based on Ideal MHD and Gyro-kinetic Stability Analyses on JET and ITER Plasmas
S. Saarelma1, M. Beurskens1, T. Casper2, I.T. Chapman1, D. Dickinson1,3, L. Frassinetti4, G.T.A. Huijsmans2, A. Kirk1, O. Kwon5, M. Leyland3, J. Lee6, A. Loarte2, Y. Na6, C.M.Roach1, R. Scannell1, H.R.Wilson3 and EFDA-JET Contributors*
JET-EFDA, Culham Science Centre, Abingdon, OX14 3DB, UK
1Euratom/CCFE Fusion Association, Culham Science Centre, OX14 3DB, Abingdon, UK, 2ITER Organization, St Paul Lez Durance – France, 3York Plasma Institute, Department of Physics, University of York, York, YO10 5DD, UK, 4Division of Fusion Plasma Physics, School of Electrical Engineering, Royal Institute of Technology, Association EURATOM-VR, Stockholm, Sweden, 5Dept. Of Physics, Daegu University, Gyungbuk, Korea, 6Dept. of Nuclear Engineering, Seoul National University, Seoul Korea, *See the Appendix of F. Romanelli et al., Proceedings of the 24rd IAEA Fusion Energy Conference 2012, San Diego, USA
JET finite-n MHD stability
The peeling ballooning stability limits are found by varying p’ and <jf> around the experimental equilibria and determining the stability by using MISHKA-1 [2]code.
Both plasmas are close to the peeling-ballooning mode stability limit just before an ELM.
Peeling-ballooning mode stability limit seems to be a robust limit for pedestal.
ITER 15 MA baseline plasmas
ITER plasmas are taken from the CORSICA simulations [6] with varying assumptions for the edge temperature: 2.5, 3.7, 5.2 and 6.5 keV. The core density is 8.5 x 1019 m-3 = 0.85 nGW.
Edge stability diagrams for Te,ped = 3.7, 5.2 and 6.5 keV cases. Stability boundaries are for g=0 (yellow) and g=w*/2 (black):
Marginal stability for g=w*/2 limit found for a intermediate case between Te,ped=5.2 and 6.5 keV cases: Te,ped=5.9 keV corresponding to pped=107 kPa.
The result is not very sensitive to the assumed width of the pedestal. The marginally stable pedestal height stays between 5.2 and 6.5 keV even if the width is increased or decreased by 30% from the value used in the CORSICA simulations (4% of the normalised poloidal flux).
The gyro-kinetic analysis of ITER plasmas finds them to be in the 2nd stable region for the KBMs (matching well with the n= ideal ballooning stability) due to the high bootstrap current.
Motivation
The H-mode pedestal is crucial for the confinement of a tokamak fusion device.
Pfus~p02, p0 ~ pped.
In order to predict the height of the pedestal, we need to understand the key physics.
Two key questions:
What sets up the pedestal pressure gradient?
What sets up the width of the pedestal?
The original ideas behind EPED1 model [1]:
Kinetic ballooning modes (KBM) limit the pressure gradient of the pedestal
Peeling-ballooning modes (PBM) limit the width of the pedestal
Temperature
Toroidal current density
Safety factor
Low fuelling #79498
High fuelling #79503
The objectives of this paper:
Take experimental JET plasmas.
Test the stability in the JET edge region against KBMs and PBMs during an ELM cycle.
Is the pedestal gradient limited by KBMs during the ELM cycle?
Is the pedestal destabilised by the PBM at the end of the ELM cycle?
Using the JET criterion for the pedestal limits, find the marginally stable ITER transport simulation.
max
Te,ped=3.7keV
Te,ped=5.2keV
Te,ped=6.5keV
max
Kinetic Ballooning Mode (KBM) stability
The (KBM) stability is studied using GS2 [3] and compared with ideal MHD n= ballooning mode stability.
JET Pedestals are found stable for n= ballooning modes and KBMs due to high bootstrap current. The “knee” of the pedestal closer to the marginality than the steep gradient region.
JET Experiment (d=0.42, Bt=2.7T, Ip=2.5MA, PNBI=16MW, Type I ELMs)
#79498: low fuelling, G=0.5 x 1022 el/s. #79503:high fuelling, G=3.0 x 1022 el/s
Pedestal High Resolution Thomson Scattering data is collected through the ELMing H-mode period at 20Hz, divided into 4 bins based on the normalised time in the ELM cycle (the first bin 0-10% ignored as too close to the ELM crash) and a fitted with a modified tanh-function:
STABLE
UNSTABLE
Low fuelling
<1, unstable, >1 stable
#79498,
low fuelling
#79503,
high fuelling
knee
End of ELM cycle, Bootstrap-current scan
knee
High fuelling
Exp. current
The effect of the conducting wall on the ELM triggering instabilities
ITER will have a close fitting wall made of Beryllium that is a good conductor.
The wall is constructed of modules, which means that the effect on large low-n instabilities is reduced. However, it is possible to affect the more local high-n peeling-ballooning modes.
Micro-tearing modes (MTM)
In MAST unstable MTMs were found at the top of the pedestal [4][5]. As density gradient widens towards the core, they become stabilised.
In JET pedestal top, the MTMs are subdominant to twisting parity modes.
The MTMs at the top of the JET pedestal are not very elongated along the field line (unlike MTMs in the core region). They are not stabilised by the decreasing collisionality.
The increasing density gradient stabilises the MTMs.
The MTM characteristics match with those found on MAST pedestal top [4]
Wall geometry
Wall effect on n=15 peeling-ballooning mode (Te,ped=6.5keV). rwall=(1+C) x rplasma
The ITER first wall is on the border of significantly affecting the peeling-ballooning modes (vacuum vessel alone has no effect).
The stability limits are not affected, but the ELM dynamics may by changing the ideally growing modes into more slowly growing resistive wall modes.
Profile evolution during an ELM cycle:
High fuelling:
Te profile does not change
ne,ped increases
Pedestal width stays constant
pmax first increases, then saturates
Low fuelling:
Both Te,ped and ne,ped increase
Pedestal width gets narrower
pmax increases through the ELM cycle
Growth rate spectrum at the top of the pedestal
MTM Growth rate at the top of the pedestal as a function of density gradient
Equilibrium reconstruction (HELENA)
The fitted profiles are shifted so that Te,sep agrees with the power balance calculations.
We assume Ti=Te (the effect of this assumption on stability is small), Zeff has a flat profile and that the inductively driven current is fully diffused to follow the neoclassical conductivity profile. The bootstrap current is calculated self-consistently from the profiles.
The plasma boundary is taken to match the free-boundary EFIT everywhere except near X-point where the boundary is rounded.
Conclusions
The JET pedestal height is limited by the peeling-ballooning modes. No unstable KBMs are found.
Micro-tearing modes are unstable at the pedestal top.
ITER pedestal is limited to Te,ped=5.9keV (corresponding to pped=107 kPa) by the peeling-ballooning limit. No unstable KBMs are found in the pedestal region of the ITER equlibria.
The Beryllium wall in ITER has the potential to affect the ELM triggering peeling-ballooning modes.
References
Snyder P.B., et al. Phys. Plasmas 16 (2009)
Mikhailovskii A.B. et al., Plasma Phys. Rep. 23 (1997) 844
M Kotschenreuther, et al. Comput. Phys. Commun 88 (1995) 128
C.M. Roach. et al., TH/5-1 in this conference
D, Dickinson et al. Phys. Rev. Lett. 108, (2012)
T. Casper et al. Proc. 23rd Int. Conf. on Fusion Energy 2010 (Daejeon, South Korea, 2010) (Vienna: IAEA) ITR/P1-19
This work was funded by the RCUK Energy Programme under grant EP/I and the European Communities under the contract of Association between EURATOM and CCFE and carried out within the framework of the European Fusion Development Agreement. The views and opinions expressed herein do not necessarily reflect those of the European Commission.
24th IAEA Fusion Energy Conference, San Diego, USA, October 8-13, 2012