Influence of Equilibrium Shear Flow on Peeling-Ballooning Instability and ELM Crash

1. Influence of Equilibrium Shear Flow on Peeling-Ballooning Instability and ELM Crash Pengwei Xi1,2, Xueqiao Xu2, Xiaogang Wang1, Tianyang Xia2,3 1FSC, School of Physics, Peking University, Beijing, China. 2Lawrence Livermore National Laboratory, Livermore, CA 94550, USA 3Institute of Plasma Physics, Chinese Academy of Sciences, Hefei, China Presented at 6th US-PRC Magnetic Fusion Workshop San Diego, CA, USA, July 10-12, 2012 This work was performed under the auspices of the U.S. Department of Energy by Lawrence Livermore National Security, LLC, Lawrence Livermore National Laboratory under Contract DE-AC52-07NA27344, and is supported by the China Scholarship Committee under contract N0.2011601099. LLNL-PRES-563575 1

2. Outlines • Research Motivation • Simulation Setups • Simulation Results • Linear • Nonlinear • Summary 3

3. Research Motivation: Dramatic influence of shear flow on ELM behavior 1 Fig1. ELM image from MAST (Scannell .RPlasma Phys. Control. Fusion 49 1431) 2 Fig2. Ideal MHD simulation about shear flow influence on peeling-ballooning mode (H.R.Wilson, Plasma Phys. Control. Fusion 48 (2006) A71–A84) 3 Fig3. Experiment shows rotation frequency can change ELM frequency significantly. (N.Oyama, Nucl. Fusion 45 (2005) 871–881) 4

4. SimulationEquations: 3-fields reduced MHD equations with equilibrium EXB flow Kelvin-Helmholtz term Net flow Resistivity/Hyper-resistivity In our simulation, we assume ion diamagnetic flow is balanced by the first part of EXB flow Ion diamagnetic effect 5

5. Total Erprofiles for EXB flow at H-mode pedestal Counter-direction flow Co-direction flow Rigid flow 6

6. Simulation Results: Rigid flow only leads to Doppler shift but doesn’t change peeling-ballooning mode growth rate 10

7. Ideal MHD: Flow shear strongly stabilizes high-n ballooning modes and weakly destabilizes low-n peeling modes N=15 N=15 High-n modes are twisted and the radial extension is limited by shear flow, while this effect becomes weaker for modes with lower mode number. N=30 N=30 7

8. Destabilizing effect of Kelvin-Helmholtz term depends on mode number and flow shear, and is different from its role in neutral fluid Step function In neutral fluid, shear flow with step function profile cause strong Kelvin-Helmholtz instability. But in our simulation, the destabilizing effect from Kelvin-Helmholtz term disappear when flow shear is vary large. Gradient of equilibrium vorticity 9

9. Nonlinear simulation: shear flow can reduce ELM size and limit the radial extension of profile collapse Resistivity, hyper-resistivity and ion-diamagnetic effects are included in nonlinear simulation 10

10. Nonlinear simulation: shear flow can reduce ELM size and limit the radial extension of profile collapse Without shear flow With shear flow 11

11. Nonlinear simulation: Without Kelvin-Helmholtz term 12

12. Nonlinear simulation: With Kelvin-Helmholtz term 13

13. Nonlinear simulation: For large flow shear case, Kelvin-Helmholtz term reduces mode number at nonlinear phase W/O KH With KH Initial perturbation has mode number n=15 Before ELM crash With KH W/O KH After ELM crash 22 14

14. Nonlinear simulation: Kelvin-Helmholtz term becomes dominant for middle flow shear value and leads to larger ELM crash The competition between flow shear stabilizing effect and Kelvin-Helmholtz destabilizing effect decides the overall influence of shear flow on ELM 15

15. Summary • Linear simulation results • Flow shear has strong stabilizing effect on high n mode and is destabilizing for low n modes for ideal MHD; • Kelvin-Helmholtz term is destabilizing and the effects depends on mode number and shear; • Nonlinear simulation result • Flow shear can reduce ELM size and limit profile collapse; • Kelvin-Helmholtz term is dominant for intermediate flow shear value and leads to larger ELM size; Flow shear 16