1. 6 th Japan-Korea Workshop on Theory and Simulation of Magnetic Fusion Plasmas 2011.07.28 Hyunsun Han, G. Park, Sumin Yi, and J.Y. Kim 3D MHD SIMULATIONS ON ELMS AND PELLET INDUCED ONES

2. Contents Introduction Natural ELM simulation Pellet triggered ELM simulation Summary

3. ELM simulation using MHD code precursor oscillation pedestal/SOL perturbation filament ejection, filament propagation, relative timing to relaxation Non-linear eruption Linear instability Pressure builds up Pedestal re-established ELM Cycle ELM dynamics

4. M3D code Original M3D code was written by W. Park (PPPL) in early 1980s Code improvement has been ongoing continuously  Two-fluid model (L. Sugiyama)  Hybrid model including hot particle (G. Fu) Ref. http://w3.pppl.gov/m3d/index.php A resistive MHD version of M3D is adapted from NYU  Based on the resistive MHD equation in a cylindrical coordinate  Solves 8 equations for

5. ELM simulation - Computing condition Initial equilibrium is constructed considering a KSTAR H-mode #4200 is selected. - First ELMy H-mode shot in KSTAR - Most reviewed and analyzed shot - Plasma transport simulation results 1 were considered. Ref. Hyunseok Kim et al 2011 KPS Spring meeting

6. ELM simulation - Computing condition Reconstructed equilibrium is checked for its edge-stability Ohmic bootstrap [Pressure] [Current] [Result of ELITE code]

7. ELM simulation Initial perturbation is added for n=12,24, … A segment for toroidal angle as 0-30°for linear simulation τ A = R 0 /v A ≈ 0.13 μs with v A = B 0 /(μ 0 ρ 0 ) 1/2 Typical quantities - Norm. plasma resistivity S = 1.0 x 10 -6, - Norm. ion viscosity μ i /ρ = 1.0 x 10 -5 - Perp. thermal conductivity κ ⊥ = 1.0 x 10 -5 (43 x 200 x 4)

8. artificial chopping KE as a function of time ELM simulation – Linear mode Perturbed poloidal magnetic flux

9. ELM simulation – Nonlinear mode A segment for toroidal angle as 0-90° ELM crashes Number of poloidal plane is increased as 16. (i.e. 43x200x16) Relaxation 184.4τ A 282.6τ A 626.2τ A Pressure profiles

10. ELM simulation – Nonlinear mode 184.4τ A Density contour evolution Finger-like structure is seen during ELM crash. 282.6τ A 626.2τ A

11. ELM simulation – Nonlinear mode Temperature contour evolution 184.4τ A 282.6τ A 626.2τ A Temperature distribution reflects the tangled magnetic field structure Radial extent is not larger than that of density.

12. Pellet induced ELMs ELM pace making enhancing the ELM frequency (f ELM ) beyond the intrinsic value (f 0 ) f ELM =83Hzf 0 =51Hz P.T. Lang et al, NF (2005) We want to know the ELM trigger mechanism by pellet injection using a nonlinear 3D MHD code (M3D).

13. Idea for simulation on pellet induced ELMs Simulation process for a spontaneous ELM ELM Linear perturbation Growing Pellet induced localized pressure perturbation

14. Simulation condition on pellet injection (1) It is assumed : The details of the ablation processes are not considered Ref.) H.R. Strauss et al Physics of Plasma 7 (2000) 250 G. T. A. Huysmans et al PPCF 51 (2009) 124012 the ablation and ionization time scale are short the injection process is adiabatic : The pellet impart no energy to the plasma ( p=const. )

15. Simulation condition on pellet injection (2) Initial conditions Density Temperature Pressure After 100 time step Density Temperature Pressure

16. Simulation condition on pellet injection (3) : Initial equilibrium is arbitrarily generated using TOQ code and xplasma in the NTCC library - Edge pedestals are modeled using a tanh function. - Bootstrap current is included using the Sauter model. (Phys. Plasmas 1999) An artificial equilibrium is constructed based on a high performance KSTAR H-mode

17. Pellet simulation using M3D Computing domain : 0 to 2π in toroidal axis with 32 planes 72x200 points on a poloidal plane triangular mesh Typical quantities : - τ A = R 0 /v A ≈ 0.17 μs with v A = B 0 /(μ 0 ρ 0 ) 1/2 - Norm. plasma resistivity S = 1.0 x 10 -6 - Norm. ion viscosity μ i /ρ = 1.0 x 10 -5 - Perp. thermal conductivity κ ⊥ = 1.0 x 10 -5

18. Initial density distribution in 3D Pellet simulation using M3D Initial condition: Density perturbation by injected pellet - Peak density ~ 169 x background density - r=0.46m on outer midplane with r p =4cm - The distribution is also perturbed toroidally Toroidal direction (rad.) Amplitude

19. 26 Density contour evolution 10.3τ A 25.3τ A 35.6τ A Massive particles are ejected from the plasma during the evolution of pellet cloud 91.7τ A Numerical results on pellet simulation

20. 10.3τ A 25.3τ A 35.6τ A 91.7τ A Temperature contour evolution Perturbed temperature is quickly stabilized than perturbed density Numerical results on pellet simulation

21. t=0 t=12.96 t=23.26 Numerical results on pellet simulation ELM crashes Relaxation The unstable period by the pellet injection is relatively short. : Peaked kinetic energy is rapidly decreased. Local density minimum means the ejection of density blob.

22. Summary 1. ELM simulation 2. Pellet injection simulation - The finger-like structure is shown in density distribution plot. - Density perturbation is much larger than temperature one during ELM instability. : The simulation shows similar results with experimental observation : Injected pellet in an H-mode pedestal can lead to the destabilization of a ballooning mode - Massive particles are ejected from the plasma during the evolution of pellet cloud - The unstable state becomes stabilized in a relatively short period Further simulation is required to identify the characteristics on the ELMs