1. 1 Lawrence Livermore National Laboratory Influence of Equilibrium Shear Flow on Peeling-Ballooning Instability and ELM Crash Pengwei Xi 1,2, Xueqiao Xu 2, Xiaogang Wang 1, Tianyang Xia 2,3 1 FSC, School of Physics, Peking University, Beijing, China. 2 Lawrence Livermore National Laboratory, Livermore, CA 94550, USA 3 Institute of Plasma Physics, Chinese Academy of Sciences, Hefei, China Presented at 6 th 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. 2 Lawrence Livermore National Laboratory Research Motivation Simulation Setups Simulation Results –Linear –Nonlinear Summary Outlines 3

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

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

5. 5 Lawrence Livermore National Laboratory Total E r profiles for EXB flow at H-mode pedestal 6 Counter-direction flowCo-direction flowRigid flow

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

7. 7 Lawrence Livermore National Laboratory 7 Ideal MHD: Flow shear strongly stabilizes high-n ballooning modes and weakly destabilizes low-n peeling modes 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=15 N=30

8. 8 Lawrence Livermore National Laboratory 9 Destabilizing effect of Kelvin-Helmholtz term depends on mode number and flow shear, and is different from its role in neutral fluid Gradient of equilibrium vorticity 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.

9. 9 Lawrence Livermore National Laboratory 10 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 Lawrence Livermore National Laboratory 11 Nonlinear simulation: shear flow can reduce ELM size and limit the radial extension of profile collapse Without shear flowWith shear flow

11. 11 Lawrence Livermore National Laboratory 12 Nonlinear simulation: Without Kelvin-Helmholtz term

12. 12 Lawrence Livermore National Laboratory 13 Nonlinear simulation: With Kelvin-Helmholtz term

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

14. Lawrence Livermore National Laboratory 15 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 Lawrence Livermore National Laboratory 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; 16 Flow shear