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

3D MHD SIMULATIONS ON ELMSAND PELLET INDUCED ONES

Contents

Introduction

Natural ELM simulation

Pellet triggered ELM

simulation

Summary

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

M3D code

Original M3D code was written by W. Park (PPPL) in early 1980s

Code improvement has been ongoing continu-ously 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 , , ,p B v

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 results1 were

considered.

Ref. Hyunseok Kim et al 2011 KPS Spring meeting

ELM simulation - Computing condition

Reconstructed equilibrium is checked for its edge-stability

30 30 30 1010 10 10 1010

0 0 0 3030 10 10 1010

0 0 0 00 0 30 30 5

0 0 0 00 0 0 5 5

0 0 0 00 0 0 5 5

0 0 0 00 5 5 5 5

0 0 0 55 5 5 5 5

0

Pressure gradient, max

Currentdensity<j //>max.

3 3.5 4 4.5 50.6

0.7

0.8

0.9

1

1.1

1.2

1.3

6.5E-026.0E-025.5E-025.0E-024.5E-024.0E-023.5E-023.0E-022.5E-022.0E-021.5E-021.0E-025.0E-033.0E-032.6E-031.7E-031.0E-030.0E+00

N

currentdensity

0 0.2 0.4 0.6 0.8 1

0.2

0.4

0.6

0.8

1

Ohmic

bootstrap

N

Pressure[Pa]

0 0.2 0.4 0.6 0.8 1

2000

4000

6000

8000

10000

12000 [Pressure]

[Current]

[Result of ELITE code]

ELM simulation

Initial perturbation is added for n=12,24, … A segment for toroidal angle as 0-30°for linear

simulation

1 1.5 2 2.5

-1

0

1

• 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

(43 x 200 x 4)

artificial chopping

KE as a function of time

Time ( A )

K.E.(t)

20 40 60 80-12.5

-12.0

-11.5

-11.0

-10.5

-10.0

-9.5

ELM simulation – Linear mode

Perturbed poloidal magnetic flux

ELM simulation – Nonlinear mode

A segment for toroidal angle as 0-90°

Time (A)

K.E.(t)

200 220 240 260 280 300

-6.4

-6.2

-6

-5.8

-5.6

-5.4

-5.2

-5

ELM crashes

Number of poloidal plane is increased as 16. (i.e. 43x200x16)

Relaxation

Pressure.

-0.02 -0.01 0 0.01 0.02 0.03 0.04

184.4τA

282.6τA

626.2τA

Pressure profiles

ELM simulation – Nonlinear mode

-0.2 0 0.2 0.4 0.6

0

0.5

1

1.5

184.4τA

-0.2 0 0.2 0.4 0.6

0

0.5

1

1.5

-0.2 0 0.2 0.4 0.6

0

0.5

1

1.5

Density contour evolution

Finger-like structure is seen during ELM crash.

282.6τA 626.2τA

ELM simulation – Nonlinear mode

-0.2 0 0.2 0.4 0.6

0

0.5

1

1.5

-0.2 0 0.2 0.4 0.6

0

0.5

1

1.5

-0.2 0 0.2 0.4 0.6

0

0.5

1

1.5

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.

Pellet induced ELMs

ELM pace making enhancing the ELM frequency (fELM) be-yond 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 injec-tion using a nonlinear 3D MHD code (M3D).

Idea for simulation on pellet induced ELMs

Simulation process for a spontaneous ELM

ELM

Linear perturbation

Growing

Pellet induced localized pressure perturbation

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. )

-0.5 0 0.5

-0.5

0

0.5

Simulation condition on pellet injection (2)

Initial conditions

-0.5 0 0.5

-0.5

0

0.5

-0.5 0 0.5

-0.5

0

0.5

-0.5 0 0.5

-0.5

0

0.5

-0.5 0 0.5

-0.5

0

0.5

-0.5 0 0.5

-0.5

0

0.5

Density Temperature Pressure

After 100 time step Density Temperature Pressure

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

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 :

- τA = R0/vA ≈ 0.17 μs with vA = B0/(μ0ρ0)1/2

- 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

Initial density distribution in 3D

Pellet simulation using M3D

Initial condition: Density perturbation by injected pellet

- Peak density ~ 169 x back-ground density

- r=0.46m on outer midplane with rp=4cm - The distribution is also per-turbed toroidally

-4 -3 -2 -1 0 1 2 3 40

0.2

0.4

0.6

0.8

1

1.2

Toroidal direction (rad.)

Amplitude

26

Density contour evolution

10.3τA 25.3τA 35.6τA

Massive particles are ejected from the plasma during the evolution of pellet cloud

91.7τA

Numerical results on pellet simulation

10.3τA 25.3τA 35.6τA 91.7τA

Temperature contour evolution

Perturbed temperature is quickly stabilized than per-turbed density

Numerical results on pellet simulation

Midplane (m)

Density

0.35 0.4 0.45 0.5

0.25

0.3

0.35

t=0

t=12.96

t=23.26

Numerical results on pellet simulation

ELM crashes

Time (A)

K.E.

50 100 150 200

-7.5

-7.0

-6.5

-6.0

-5.5

-5.0

-4.5

-4.0

-3.5

Relaxation

The unstable period by the pellet injection is relatively short.

: Peaked kinetic energy is rapidly decreased. Local density minimum means the ejection of den-sity blob.

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 balloon-ing 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