3D MHD simulations oN ELMs and pellet inDUCED ONES

1. 3D MHD simulations oN ELMsand pellet inDUCED ONES 6th Japan-Korea Workshop on Theory and Simulation of Magnetic Fusion Plasmas 2011.07.28 Hyunsun Han, G. Park, Sumin Yi, and J.Y. Kim

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

3. ELM simulation using MHD code ELM Cycle Pressure builds up Pedestal re-established Linear instability Non-linear eruption • precursor oscillation • pedestal/SOL perturbation • filament ejection, • filament propagation, • relative timing to relaxation 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) • A resistive MHD version of M3D is adapted from NYU • Based on the resistive MHD equation in a cylindrical coordinate • Solves 8 equations for Ref. http://w3.pppl.gov/m3d/index.php

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 results1were considered. Ref. HyunseokKim et al 2011 KPS Spring meeting

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

7. ELM simulation • Initial perturbation is added for n=12,24, … • A segment for toroidalangle as 0-30°for linear simulation (43 x 200 x 4) • τA= R0/vA≈ 0.13 μs with vA = B0/(μ0ρ0)1/2 • Typical quantities - Norm. plasma resistivity S = 1.0 x 10-6, - Norm. ion viscosity μi/ρ = 1.0 x 10-5 - Perp. thermal conductivity κ⊥ = 1.0 x 10-5

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

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

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

11. ELM simulation – Nonlinear mode Temperature contour evolution 184.4τA 282.6τA 626.2τA • 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 (fELM) beyond the intrinsic value (f0 ) fELM=83Hz f0=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 • Linear perturbation • Pellet induced localized pressure perturbation • ELM Growing

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

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

16. Simulation condition on pellet injection (3) • An artificial equilibrium is constructed based on a high performance KSTAR H-mode : 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)

17. Pellet simulation using M3D • Computing domain : 0 to 2π in toroidalaxis with 32 planes • 72x200 points on a poloidal plane • triangular mesh • Typical quantities : - τA= R0/vA≈ 0.17 μs with vA = B0/(μ0ρ0)1/2 - Norm. plasma resistivity S = 1.0 x10-6 - Norm. ion viscosity μi/ρ = 1.0 x 10-5 - Perp. thermal conductivity κ⊥ = 1.0 x 10-5

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

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

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

21. Numerical results on pellet simulation t=23.26 ELM crashes Relaxation t=0 t=12.96 • 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 : The simulation shows similar results with experimental observation - The finger-like structure is shown in density distribution plot. - Density perturbation is much larger than temperature one during ELM instability. 2. Pellet injection simulation : 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