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)
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) • test density dependence of error field penetration
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(!BR0(!R- relevant for ITER error fields, empirical scaling
has large error bars in prediction for acceptable error fields
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) • test density dependence of error field penetration
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(!BR0(!R
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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
Trigger of magnetic islands by external perturbation fields
• islands triggered so far in low density L-mode discharges only on ASDEX Upgrade
n=1 perturbation field
Trigger of magnetic islands by external perturbation fields
• islands triggered so far in low density L-mode discharges only on ASDEX Upgrade
n=1 perturbation field
Trigger of magnetic islands by external perturbation fields
• islands triggered so far in low density L-mode discharges only on ASDEX Upgrade
max external field (2.4 s) no perturbation (1.6 s)
q=2 surface
n=1 perturbation field
Trigger of magnetic islands by external perturbation fields
• islands triggered so far in low density L-mode discharges only on ASDEX Upgrade
• 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
n=1 perturbation field
For mode locking, plasma “wants” to rotate with , can be achieved by changing density and/or rotation profile
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Yu, Günter et al., PoP 2009 (TM1 code)
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Test Fitzpatrick‘s scaling for error field penetration
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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)
Fitzpatrick, PPCF 2012
Test Fitzpatrick‘s scaling for error field penetration
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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
Fitzpatrick, PPCF 2012
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
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