neoclassical tearing modes · neoclassical tearing modes o. sauter1, h. zohm2 1crpp-epfl, ... •...
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1NTMs , O. SauterDPG Advanced Physics School, The Physics of ITER, Bad-Honnef, Germany, Sept. 2014
Neoclassical Tearing Modes
O. Sauter1, H. Zohm2
1CRPP-EPFL, Lausanne, Switzerland2Max-Planck-Institut für Plasmaphysik, Garching, Germany
Physics of ITERDPG Advanced Physics School
22 -26 Sept, 2014, Bad Honnef, Germany
With contributions in particular from: D. Humphreys, R. La Haye, M. Maraschek, E. Poli, M. Reich
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2NTMs , O. SauterDPG Advanced Physics School, The Physics of ITER, Bad-Honnef, Germany, Sept. 2014
Outline
• Magnetic islands• Classical tearing mode -> Rutherford equation• Neoclassical tearing mode: Modified Rutherford equation (MRE)• Metastable properties (large "hysteresis" between onset/offset)• Plasma performance and NTMs• Strategies for NTM control in ITER:
Will there be more than one mode at the same time?StabilizationPreemptionAvoidanceReal-time control of NTMs:
Very complex yet simpleNew "robust" control being tested in Europe
• Conclusions
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3NTMs , O. SauterDPG Advanced Physics School, The Physics of ITER, Bad-Honnef, Germany, Sept. 2014
Outline
• Magnetic islands• Classical tearing mode -> Rutherford equation• Neoclassical tearing mode: Modified Rutherford equation (MRE)• Metastable properties (large "hysteresis" between onset/offset)• Plasma performance and NTMs• Strategies for NTM control in ITER:
Will there be more than one mode at the same time?StabilizationPreemptionAvoidanceReal-time control of NTMs:
Very complex yet simpleNew "robust" control being tested in Europe
• Conclusions
• NTMS lead to a "soft" beta limit as opposed to "hard" beta limits leading to disruption
• NTMs mainly lead to performance degradation• BUT if you push "too hard", NTMs can lead to disruption
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4NTMs , O. SauterDPG Advanced Physics School, The Physics of ITER, Bad-Honnef, Germany, Sept. 2014
, E. Poli
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5NTMs , O. SauterDPG Advanced Physics School, The Physics of ITER, Bad-Honnef, Germany, Sept. 2014
)( vnt
r⋅−∇=∂∂ρ
equation of continuity
Bjpvvtv rrrrr
×+−∇=⎟⎠⎞
⎜⎝⎛ ∇⋅+ )(
∂∂ρ force equation
jBvErrrr
η=×+ Ohm’s law
0=⎟⎠
⎞⎜⎝
⎛γρ
pdtd
equation of state
+ Maxwell‘s equations for E and B
The one fluid MHD equations
=0 if η=0 => frozen-in B lines
=0static equilibrium
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6NTMs , O. SauterDPG Advanced Physics School, The Physics of ITER, Bad-Honnef, Germany, Sept. 2014
jBvErrrr
σ1
+×−=
( ) ( )BBvEtB rrrrr
×∇×∇−××∇=×−∇=∂∂
σμ0
1
Consider equilibrium Ohm's law...
...and analyse how magnetic field can change:
( ) BBvtB rrrr
Δ+××∇=∂∂
⇒σμ0
1
Typical time scale of resistive MHD:
20 LR σμτ =
Since σ is large for a hot plasma, τR is slow (~ sec for 0.5 m) – irrelevant?
MHD: consequences of Ohm's law
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7NTMs , O. SauterDPG Advanced Physics School, The Physics of ITER, Bad-Honnef, Germany, Sept. 2014
Reconnection in a hot fusion plasma
A change of magnetic topology is only possible through reconnection
• opposing field lines reconnect and form new topological objects• requires finite resistivity in the reconnection region
Due to high electrical conductivity, magnetic flux is frozen into plasma
⇒ magnetic field lines and plasma move together
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8NTMs , O. SauterDPG Advanced Physics School, The Physics of ITER, Bad-Honnef, Germany, Sept. 2014
Reconnection on ‘rational’ magnetic surfaces
Helical field (i.e. ‚poloidal‘ field relative to resonant surface) changes sign:
• reconnection of helical flux can form new topological objects - islands
Typical q-profile
Corresponding Bhel
Bhel = Bpol(1-q/qres)
Corresponding Bpol
position of q=2
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9NTMs , O. SauterDPG Advanced Physics School, The Physics of ITER, Bad-Honnef, Germany, Sept. 2014
Reconnection on ‘rational’ magnetic surfaces
Torus has double periodicity
• instabilities with poloidal and toroidal 'quantum numbers'
m = 1
m = 2
m = 3
‚Resonant surfaces‘ prone to instabilites with q = m/n
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10NTMs , O. SauterDPG Advanced Physics School, The Physics of ITER, Bad-Honnef, Germany, Sept. 2014
0))(1(
)(0
=−
+Δ ψμ
ψθ rqm
nBdr
rdj
MHD description of tearing mode formation
Deformation of flux surfaces opens up island of width W
• Tearing Mode equation (∇p = j x B) singular at resonant surface:implies kink in magnetic flux ψ, jump in B
⇒ current sheet on the resonant surfaceψ(r): helical magnetic flux
j(r): current profile
q(r): field line helicity profile
m,n: mode quantum numbers
ψ(r): helical magnetic flux
j(r): current profile
q(r): field line helicity profile
m,n: mode quantum numbers
j ~ q' => ψ ~ q''ψ ~ w2
2πR*q
2πa
Bϕ
Bp
)()(~)(~)('0
ρρρρ ϕ
ρ
ϕϕϕ jIjdSjq p∫ ++
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11NTMs , O. SauterDPG Advanced Physics School, The Physics of ITER, Bad-Honnef, Germany, Sept. 2014
MHD description of "classical" tearing mode formation
Solution of tearing mode equation can be made continuous, but has a kink• implied surface current will grow or decay depending on equilibrium j(r)
• the parameter defining stability is Δ‘ = ((dψ/dr)right – (dψ/dr)left) / ψ
• if Δ‘ > 0, tearing mode is linearly unstable – this is related to ∇jresonant surface
"resistive"layer
"outer"layer
"outer"layer
ψ solution
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12NTMs , O. SauterDPG Advanced Physics School, The Physics of ITER, Bad-Honnef, Germany, Sept. 2014
• for small ∇p, current gradient (Δ') dominates
⇒ 'classical Tearing Mode', current driven(most of the time stable except if q profile is "tweaked", which is why resistiveMHD was never a big thing up to end 1990s for tokamak interpretation)
• for larger ∇p, pressure gradient dominates:
⇒ 'Neoclassical Tearing Mode', pressure driven
• adding an externally driven helical current can stabilise
2321 'W
IaWpaadt
dW externres −∇+Δ=τ
Equation for the growth rate of a finite size island of width w:
Tearing Modes – nonlinear growth
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13NTMs , O. SauterDPG Advanced Physics School, The Physics of ITER, Bad-Honnef, Germany, Sept. 2014
Magnetic islands deteriorate performances
Local transport stays same outside islandBut "short-circuit" across island4
3
4a
w s
E
E ρττ
=Δ
Chang et al, 1994, "belt-model"
degradation
Provides accurate simple measure of wsat
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14NTMs , O. SauterDPG Advanced Physics School, The Physics of ITER, Bad-Honnef, Germany, Sept. 2014
, E. Poli
B*
B*+δBr
.Bs~j//
( ) θθθθ ρρ BqqBBB s
s
ss −−≈−=
'*
Perturbed Bootstrap is driving term=>Neoclassical
xδjbs
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15NTMs , O. SauterDPG Advanced Physics School, The Physics of ITER, Bad-Honnef, Germany, Sept. 2014
]...),('),(')('),(' +Δ+Δ+Δ+Δ ωρωρρωρ wwww mnswallsechspols
+Δ+Δ+Δ+Δ= )(')(')(')('[ wwwwdtdw
cdsGGJsbsssR
s ρρρρτρ
Modified Rutherford Equation (MRE)
Many terms can contribute to total // current within island
Main terms discussed and compared with experiment on 1st line
"classical" + bootstrap + curvature + polarisation + (EC)CDGlasser-Greene-Johnson
wall and mode coupling can also be important
in particular, efficient locking of 2/1 mode
Despite limits of MRE, method/coeff. described in Sauter et al PoP 1997 and PPCF 2002 + Ramponi PoP 1999 for Δ'wall describes essentially all exp. Results+prediction
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16NTMs , O. SauterDPG Advanced Physics School, The Physics of ITER, Bad-Honnef, Germany, Sept. 2014
~1 (for wcd~w)
Considering main contributions
:'
1MREΔ
×sρ
To obtain self-consistent solutionwith confinement degradation
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17NTMs , O. SauterDPG Advanced Physics School, The Physics of ITER, Bad-Honnef, Germany, Sept. 2014
NTMs are metastable: require seed island
w structure of steady-state MRE (no CD)
2arg
20,0
)(1)(~
msat
p
p
wwww
twf
++−= ∞β
β
)(~ wf
wmarg=3cmwsat∞0=30cm
t=0 ->βp(t)/βp0 = 1
βp(t)/βp0=2wmarg/wsat∞0 (=0.2 in this case) 0,0,
argarg, 2 p
sat
mmp w
wββ
∞
=w [cm]
ITER expected 2/1 parameters
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18NTMs , O. SauterDPG Advanced Physics School, The Physics of ITER, Bad-Honnef, Germany, Sept. 2014
5 0 5 3 6
β n
P N B I( 1 0 7 W )
n = 2 P e r tu r b e d r a d ia l f i e ld c a u s e s s o f t s to p
T im e ( s )
D e c l in e in τ E a t ( 3 ,2 ) a n d la r g e d e c l in e a t ( 2 ,1 )
N B n = 2 r e d u c e s s a w te e th
2 /1 s t a b i l i s e d a t lo w b e ta
n = 1
3/2 NTMs lead to 10-20% losses
2/1 NTMs lead to greaterlosses and to disruptions
Typical effects of NTMs
Sketch of time evolution
Hender, chap 3, NF 2007
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19NTMs , O. SauterDPG Advanced Physics School, The Physics of ITER, Bad-Honnef, Germany, Sept. 2014
Standard Scenario: Sawteeth and Mode Locking
2/1
3/24/3
• As discussed in ST session, crashes after long sawtooth periodcan trigger several modes
• Modes can lock rapidly (within0.4s in this JET case)
JET #58884
0.4s
0
1
2 JET #58884
n=1n=2
0
1
2
0
5000
SX
R
0
5
10
14 15 16 17 18 190
5
ICR
H
time [s]
NBI
βN
Modes locks(no disruption)
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20NTMs , O. SauterDPG Advanced Physics School, The Physics of ITER, Bad-Honnef, Germany, Sept. 2014
NTMs in ITER – predictions for Q=10 scenario
Q=10 operationpoint
Full stabilisationwith 7 MW
Full stabilisationwith 20 MW
ITER burn curves in the presenceof ECCD at q=3/2 and q=2
(O. Sauter and H. Zohm, EPS 2005, alsoPlasma Phys. Contr. Fusion 52 (2010))
HH=1.0
Impact on Q in case of continuous stabilisation (worst case):
• Q drops from 10 to 5 for a (2,1) NTM and from 10 to 7 for (3,2) NTM
• with 20 MW needed for stabilisation, Q recovers to 7, with 10 MW to Q > 8
• note: if NTMs occur only occasionally, impact of ECCD on Q is small
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21NTMs , O. SauterDPG Advanced Physics School, The Physics of ITER, Bad-Honnef, Germany, Sept. 2014
What are we controlling?
0 20 40 60 80 1000
10
20
30
time [s]
2/1 island width time evolution
0 20 40 60 80 1000.5
0.55
0.6
0.65
time [s]
βp
Predicted 2/1 in ITER
1. Island starts• At large wseed from ST trigger• At small wseed• Without trigger from q profile
(Δ'>0)
2. Island grows and rotates or locks• Growth rate depends on beta• Beta drop depends on ρres, w• Locking depends on β, q95, and
error field
1
3. Island saturates or plasma disrupts• Depends on island size• On proximity to beta limit• On w versus a-ρres (on q95)• On island overlap
23
Conf. degradation
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22NTMs , O. SauterDPG Advanced Physics School, The Physics of ITER, Bad-Honnef, Germany, Sept. 2014
How are we controlling?
ITER 2/1 mode
Sauter, PPCF 2010
Add CD on ρ2/1
Compute P requiredfor various models:wcdwmargpol typeχ⊥ typeCW or 50%
Criteria for ITER:
wcd≤5cmAND
ηNTMwcd≥5cm(ηNTM=jcd/jbs≥1)
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23NTMs , O. SauterDPG Advanced Physics School, The Physics of ITER, Bad-Honnef, Germany, Sept. 2014
Why and when do we intervene?
Pre-emptive ECCD stab. on ρres Start of |ρdep-ρres| - wcd/2<w/2
2/1 mode in ITER starting/triggered at t=0
Lock level 2
Lock level 1
ΔQ>10%
• Lots of "conditions" and constraints to take into account• Extra plots are to be added:
• Proximity to disruption, mode freq. vs time (fast diagn. used to predict locked mode)• Confinement degradation/proximity to H-L transition, etc
• Using real-time control+simulation, these will also be known predictively• Calculations within few ms and prediction for next 10-20s => opens new "control space"
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24NTMs , O. SauterDPG Advanced Physics School, The Physics of ITER, Bad-Honnef, Germany, Sept. 2014
Mode coupling: usually favourable
4/3 mode triggered by sawtooth crash is seen to stabilize 3/2 modeobserved in JET and TCV, similar to FIR-NTMs seen on AUG and with XTOR
Sauter, PPCF 2002; Raju PPCF 2003
Bi-coherence confirmnonlinear coupling
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25NTMs , O. SauterDPG Advanced Physics School, The Physics of ITER, Bad-Honnef, Germany, Sept. 2014
Scalings for predictions for ITER
• Scalings of βp,onset hard to use as prediction since• Couples seed island and bootstrap drive• Needs similar trigger mechanisms• Very hard to predict triggered island size
• Use ramp-down experiments to perform scalings of:• wsat(βp,max) (allows test of bootstrap drive and Δ')• βp,marg (includes also effects of stabilising terms)• wmarg ( stab. terms and provides info size of trigger)
• Then can test the physics against these scalings• βp,marg scaling: ITER metastable to both 3/2 and 2/1 modes
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26NTMs , O. SauterDPG Advanced Physics School, The Physics of ITER, Bad-Honnef, Germany, Sept. 2014
Importance of trigger mechanism
NTM onset
ΔτST↑
Controlling sawteeth changes significantly βonset
+90: phase: βN,onset≈1-90: No NTM with βN up to 2
1st harmonic minority ICRH
2nd harmonic ICCD
Sauter et al, PRL 2002
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27NTMs , O. SauterDPG Advanced Physics School, The Physics of ITER, Bad-Honnef, Germany, Sept. 2014
Power ramp-down studies
mar
gina
l β
βN,marg< L-H threshold
q 95=
2.54
cas
e do
es n
ot d
isru
pt e
ven
with
2/1
mod
e
onsetmarg
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28NTMs , O. SauterDPG Advanced Physics School, The Physics of ITER, Bad-Honnef, Germany, Sept. 2014
NTMs Avoidance technique required in JET high performance: control of 1st sawteeth
2/1 NTM triggered leads to end of shot (soft-stop)
Lack of sawtoothcontrol actuators is a difficulty for these scenarios (high current and shape)
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29NTMs , O. SauterDPG Advanced Physics School, The Physics of ITER, Bad-Honnef, Germany, Sept. 2014
"Ultimate" control of NTMs: ECCD
Why ECCD in ITER? (4 ports dedicated to NTM stab.)
• ECCD can drive localised current• Deposition location is well defined and depends essentially on launching mirrors
• Mirrors can be oriented in real-time to control NTMs
• Aim:• Replace missing bootstrap current by driving jCD in O-
point of island• (Modify jtot to decrease further Δ') (in theory)
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30NTMs , O. SauterDPG Advanced Physics School, The Physics of ITER, Bad-Honnef, Germany, Sept. 2014
, E. Poli
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31NTMs , O. SauterDPG Advanced Physics School, The Physics of ITER, Bad-Honnef, Germany, Sept. 2014
ECCD Localized at Islands Can Replace Missing Bootstrap Current and Stabilize NTM
2900
j (A/cm2)
w 7 cmfrom ECE radiometer
jECCD
jBS
126
20
15
10
5
00.5 0.6
ISLAND
0.7 0.8
128130132134136
56789
10
n = 2 Mirnov (G)
R (cm) of 2 e
3000 3100Time (ms)
3200 3300 3400
~
fc
DIII-D Experiment
ρ=r/a
• ECCD deposition must be accurately positioned at q=m/n rational surface where NTM island forms
• Alignment accuracy required in DIII-D ~ 1 cm
• EC total current drive (for 2 MW injected) ~30 kA ~2%IP
• NTM control achieved at ASDEX-U, JT-60U, DIII-D, FT-U
D. Humphreys, R. La Haye
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32NTMs , O. SauterDPG Advanced Physics School, The Physics of ITER, Bad-Honnef, Germany, Sept. 2014
NTM Control Requires Achieving and Sustaining Dynamic Island/ECCD Alignment
Detect Mode Onset
Locate Island Locate ECCD Deposition
Align
Detect Island Suppression
Maintain Alignment
Target Lock
Active Tracking
Yes
No No
OR
Search&Suppress
D. Humphreys, R. La Haye
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33NTMs , O. SauterDPG Advanced Physics School, The Physics of ITER, Bad-Honnef, Germany, Sept. 2014
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34NTMs , O. SauterDPG Advanced Physics School, The Physics of ITER, Bad-Honnef, Germany, Sept. 2014
Main problem: there is always some mismatch between ρec,dep and ρm/n due to equilibrium reconstruction, launcher inaccuracies, changes in density profiles, etc
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35NTMs , O. SauterDPG Advanced Physics School, The Physics of ITER, Bad-Honnef, Germany, Sept. 2014
New control strategy developed on TCV
•Add a systematic sweep around target position•Limits systematic errors, use slow growth of tearing modes (resistive timescale)
•Works for both preemption and stabilization, scales for ITER•Allows more precise physics studies => better prediction for ITER
2/1 stabilization with robust control
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36NTMs , O. SauterDPG Advanced Physics School, The Physics of ITER, Bad-Honnef, Germany, Sept. 2014
Simple to add to present feedback control
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37NTMs , O. SauterDPG Advanced Physics School, The Physics of ITER, Bad-Honnef, Germany, Sept. 2014
Simple to add to present feedback control
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38NTMs , O. SauterDPG Advanced Physics School, The Physics of ITER, Bad-Honnef, Germany, Sept. 2014
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39NTMs , O. SauterDPG Advanced Physics School, The Physics of ITER, Bad-Honnef, Germany, Sept. 2014
ITER scenarios and NTMs
• Standard scenario:• Monotonic q profile, medium to high shear:
-> quite stable in shaped plasmas• In H-mode, quite "meta"-stable• Sawteeth stabilized by fast particles:
-> large seed islands can be triggered at ST crashes• Should control sawteeth
• Hybrid and advanced scenarios• Flat or reversed q profile:
-> quite unstable to classical tearing(no need for seed islands)
• bN quite large -> more "meta-stable"-> need NTM preemption and stabilization
• ITER plasma rotation is small -> quite prone to mode locking
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40NTMs , O. SauterDPG Advanced Physics School, The Physics of ITER, Bad-Honnef, Germany, Sept. 2014
Conclusions
• Basic physics of NTMs well understood• Modified Rutherford Equation allows us to understand main physics
mechanisms• Detailed "first principles" calculations should not rely on MRE but on 3D
MHD codes coupled to kinetic codes• Nevertheless "fitted" MRE can be used for predictive calculations• In burning plasmas, performance will decide best strategy for NTM
control. Note small modes can have large effect on neutron rate.• Best strategy depends on scenario, mode onset and available actuators• 2/1 mode is clearly main mode to avoid/control• Detrimental effect of multiple modes not expected• Apart from 2/1 locking, one has time to control NTMs• Sawtooth control for standard scenario and preemptive ECCD for hybrid
and advanced scenarios seem best at present• New robust NTM control strategy can do the job on ITER