Two fluid simulations of RMP penetration and comparison with ...

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Two fluid simulations of RMP penetration and comparison with experiments

S. Günter

Available codes for resonant field penetration

Code Geometry Physics model

XTOR Tokamak, but no separatrix

•  two-fluid, but no polarization current •  bootstrap current •  no neoclassical rotation damping and drive •  anomalous diffusion/viscosity

JOREK Full tokamak geometry

•  two-fluid, but no polarization current •  no bootstrap current •  neoclassical rotation damping but no drive •  anomalous diffusion but no viscosity

M3D-C1 Full tokamak

geometry

•  Full two-fluid, including polarization current •  no bootstrap current •  neoclassical rotation damping/drive •  anomalous diffusion/viscosity

TM1 circular cylinder

•  Full two-fluid, including polarization current •  bootstrap current •  no neoclassical rotation damping/drive •  anomalous diffusion/viscosity

Experimental opportunities:

ASDEX Upgrade: 2x8 coils Planned upgrade (2013): rotating fields (~1 kHz), current rise time: ~2 ms

NSTX: so far 1x6 (midplane) coils

Trigger of magnetic islands by external perturbation fields

•  „clean“ experiment for forced reconnection, triggering magnetic islands (much slower than sawtooth trigger but well defined amplitude)

•  „clean“ experiment for forced reconnection, triggering magnetic islands (much slower than sawtooth trigger but well defined amplitude) •  test density dependence of error field penetration

btBtor

%&'neBtor

(!BR0(!R-  relevant for ITER error fields, empirical scaling

has large error bars in prediction for acceptable error fields

•  „clean“ experiment for forced reconnection, triggering magnetic islands (much slower than sawtooth trigger but well defined amplitude) •  test density dependence of error field penetration

btBtor

%&'neBtor

(!BR0(!R

btBtor

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(9/5R0(1/4

Fitzpatrick, PPCF 2012

-  relevant for ITER error fields, empirical scaling has large error bars in prediction for acceptable error fields

-  so far no theoretical explanation for the density dependence, and weak empirical basis for αs

-  Recent theory by Fitzpatrick can be tested

•  islands triggered so far in low density L-mode discharges only on ASDEX Upgrade

n=1 perturbation field

max external field (2.4 s) no perturbation (1.6 s)

q=2 surface

•  very small rotation at the rational surface

•  plasma rotation speeded up to lock the electron fluid

max external field (2.4 s) no perturbation (1.6 s)

q=2 surface

For mode locking, plasma “wants” to rotate with , can be achieved by changing density and/or rotation profile

!ne( )'

ne / r!!!ExB

" #µD$

*0,eExB ωω −=

Yu, Günter et al., PoP 2009 (TM1 code)

electron direction

ion direction pl

Test Fitzpatrick‘s scaling for error field penetration

btBtor

%&'!"*'neBtor

(9/5R0(1/4

Experiments: •  First test physics scaling (β ρ*) using measured plasma parameters

and – if found – explore relevant parameter range -  density variation -  Ohmic vs. ECRH heated discharges

•  Test validity of applied scaling law (neo-Alcator assumed in Fitzpatrick‘s paper) -  scaling law should connect Ohmic regime with low density L mode -  affects density scaling even if physics model for penetration is right -  momentum confinement assumed to be proportional to energy

confinement (but in Ohmic discharges dominated by electron transport)

Test Fitzpatrick‘s scaling for error field penetration

btBtor

%&'!"*'neBtor

(9/5R0(1/4

Theory: compare theory (β ρ* scaling) with code results Theory assumes that ion polarization current is the main stabilizing effect, minimum code requirements •  plasma inertia (at least in the vicinity of the rational surfaces) –

discuss PIES project! •  anomalous viscosity

To determine the plasma rotation against the perturbation field: •  Neoclassical viscosity and rotation drive

Edge ergodization on ASDEX Upgrade ?

Vacuum fields ergodic, but no evidence for ergodization inside plasma separatrix: -  no significant changes in pressure gradient nor rotation profiles (pedestal density

increases) -  ELM suppression works anyway

Chirikov parameter

W. Suttrop, 2012

Edge ergodization on ASDEX Upgrade ?

Vacuum fields ergodic, but no ergodization observed inside plasma separatrix: probably due to high rotation velocity of electron fluid

E. Viezzer, 2012

Evans et al., NF 2008

In the pedestal region plasma rotates in the electron diamagnetic drift direction: •  torque to force plasma rotation into ion diamagnetic direction •  reduction of density gradient

AUG (higher density) results in contradiction to low density discharges on DIII-D

low density discharges planned on AUG

Edge ergodization on NSTX?

ELMs triggered by RMPs (due to larger pressure gradients?)

J. Canik et al., NF 2010

Example: JOREK simulations for ITER edge

M. Becoulet et al., 2012

Combine topics of error field penetration and island excitation by sawteeth/fishbones:

•  Experiments on exciting magnetic islands by external fields and background MHD activity, examine details of plasma perturbation (see talk by Igoshine)

•  Simulations using appropriate codes

-  M3D-C1/TM-1 for sawtooth dynamics and seed island trigger

-  M3D-C1/TM-1/PIES for test of Fitzpatrick‘s results (ion polarization current for PIES needed)

Understand modification of the pedestal by external error fields: •  try to find edge ergodization in low-density ASDEX Upgrade

discharges, situation for NSTX?

•  Simulations by XTOR, JOREK, possibly M3D-C1 and PIES

Two fluid simulations of RMP penetration and comparison with ...

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