Neoclassical Tearing Modes · Neoclassical Tearing Modes O. Sauter1, H. Zohm2 1CRPP-EPFL, ... •...

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1 NTMs , O. Sauter DPG Advanced Physics School, The Physics of ITER, Bad-Honnef, Germany, Sept. 2014 Neoclassical Tearing Modes O. Sauter 1 , H. Zohm 2 1 CRPP-EPFL, Lausanne, Switzerland 2 Max-Planck-Institut für Plasmaphysik, Garching, Germany Physics of ITER DPG 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

Transcript of Neoclassical Tearing Modes · Neoclassical Tearing Modes O. Sauter1, H. Zohm2 1CRPP-EPFL, ... •...

Page 1: Neoclassical Tearing Modes · Neoclassical Tearing Modes O. Sauter1, H. Zohm2 1CRPP-EPFL, ... • Classical tearing mode -> Rutherford equation ... crashes after long sawtooth periodPublished

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

Page 2: Neoclassical Tearing Modes · Neoclassical Tearing Modes O. Sauter1, H. Zohm2 1CRPP-EPFL, ... • Classical tearing mode -> Rutherford equation ... crashes after long sawtooth periodPublished

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

Page 3: Neoclassical Tearing Modes · Neoclassical Tearing Modes O. Sauter1, H. Zohm2 1CRPP-EPFL, ... • Classical tearing mode -> Rutherford equation ... crashes after long sawtooth periodPublished

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

Page 4: Neoclassical Tearing Modes · Neoclassical Tearing Modes O. Sauter1, H. Zohm2 1CRPP-EPFL, ... • Classical tearing mode -> Rutherford equation ... crashes after long sawtooth periodPublished

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

Page 6: Neoclassical Tearing Modes · Neoclassical Tearing Modes O. Sauter1, H. Zohm2 1CRPP-EPFL, ... • Classical tearing mode -> Rutherford equation ... crashes after long sawtooth periodPublished

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

Page 7: Neoclassical Tearing Modes · Neoclassical Tearing Modes O. Sauter1, H. Zohm2 1CRPP-EPFL, ... • Classical tearing mode -> Rutherford equation ... crashes after long sawtooth periodPublished

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

Page 8: Neoclassical Tearing Modes · Neoclassical Tearing Modes O. Sauter1, H. Zohm2 1CRPP-EPFL, ... • Classical tearing mode -> Rutherford equation ... crashes after long sawtooth periodPublished

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

Page 9: Neoclassical Tearing Modes · Neoclassical Tearing Modes O. Sauter1, H. Zohm2 1CRPP-EPFL, ... • Classical tearing mode -> Rutherford equation ... crashes after long sawtooth periodPublished

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

Page 10: Neoclassical Tearing Modes · Neoclassical Tearing Modes O. Sauter1, H. Zohm2 1CRPP-EPFL, ... • Classical tearing mode -> Rutherford equation ... crashes after long sawtooth periodPublished

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

Bp

)()(~)(~)('0

ρρρρ ϕ

ρ

ϕϕϕ jIjdSjq p∫ ++

Page 11: Neoclassical Tearing Modes · Neoclassical Tearing Modes O. Sauter1, H. Zohm2 1CRPP-EPFL, ... • Classical tearing mode -> Rutherford equation ... crashes after long sawtooth periodPublished

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

Page 12: Neoclassical Tearing Modes · Neoclassical Tearing Modes O. Sauter1, H. Zohm2 1CRPP-EPFL, ... • Classical tearing mode -> Rutherford equation ... crashes after long sawtooth periodPublished

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

Page 13: Neoclassical Tearing Modes · Neoclassical Tearing Modes O. Sauter1, H. Zohm2 1CRPP-EPFL, ... • Classical tearing mode -> Rutherford equation ... crashes after long sawtooth periodPublished

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

Chang et al, 1994, "belt-model"

degradation

Provides accurate simple measure of wsat

Page 14: Neoclassical Tearing Modes · Neoclassical Tearing Modes O. Sauter1, H. Zohm2 1CRPP-EPFL, ... • Classical tearing mode -> Rutherford equation ... crashes after long sawtooth periodPublished

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

Page 18: Neoclassical Tearing Modes · Neoclassical Tearing Modes O. Sauter1, H. Zohm2 1CRPP-EPFL, ... • Classical tearing mode -> Rutherford equation ... crashes after long sawtooth periodPublished

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

Page 19: Neoclassical Tearing Modes · Neoclassical Tearing Modes O. Sauter1, H. Zohm2 1CRPP-EPFL, ... • Classical tearing mode -> Rutherford equation ... crashes after long sawtooth periodPublished

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)

Page 20: Neoclassical Tearing Modes · Neoclassical Tearing Modes O. Sauter1, H. Zohm2 1CRPP-EPFL, ... • Classical tearing mode -> Rutherford equation ... crashes after long sawtooth periodPublished

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

Page 21: Neoclassical Tearing Modes · Neoclassical Tearing Modes O. Sauter1, H. Zohm2 1CRPP-EPFL, ... • Classical tearing mode -> Rutherford equation ... crashes after long sawtooth periodPublished

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

Page 22: Neoclassical Tearing Modes · Neoclassical Tearing Modes O. Sauter1, H. Zohm2 1CRPP-EPFL, ... • Classical tearing mode -> Rutherford equation ... crashes after long sawtooth periodPublished

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)

Page 23: Neoclassical Tearing Modes · Neoclassical Tearing Modes O. Sauter1, H. Zohm2 1CRPP-EPFL, ... • Classical tearing mode -> Rutherford equation ... crashes after long sawtooth periodPublished

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"

Page 24: Neoclassical Tearing Modes · Neoclassical Tearing Modes O. Sauter1, H. Zohm2 1CRPP-EPFL, ... • Classical tearing mode -> Rutherford equation ... crashes after long sawtooth periodPublished

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

Page 25: Neoclassical Tearing Modes · Neoclassical Tearing Modes O. Sauter1, H. Zohm2 1CRPP-EPFL, ... • Classical tearing mode -> Rutherford equation ... crashes after long sawtooth periodPublished

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

Page 26: Neoclassical Tearing Modes · Neoclassical Tearing Modes O. Sauter1, H. Zohm2 1CRPP-EPFL, ... • Classical tearing mode -> Rutherford equation ... crashes after long sawtooth periodPublished

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

Page 27: Neoclassical Tearing Modes · Neoclassical Tearing Modes O. Sauter1, H. Zohm2 1CRPP-EPFL, ... • Classical tearing mode -> Rutherford equation ... crashes after long sawtooth periodPublished

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

Page 28: Neoclassical Tearing Modes · Neoclassical Tearing Modes O. Sauter1, H. Zohm2 1CRPP-EPFL, ... • Classical tearing mode -> Rutherford equation ... crashes after long sawtooth periodPublished

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)

Page 29: Neoclassical Tearing Modes · Neoclassical Tearing Modes O. Sauter1, H. Zohm2 1CRPP-EPFL, ... • Classical tearing mode -> Rutherford equation ... crashes after long sawtooth periodPublished

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)

Page 30: Neoclassical Tearing Modes · Neoclassical Tearing Modes O. Sauter1, H. Zohm2 1CRPP-EPFL, ... • Classical tearing mode -> Rutherford equation ... crashes after long sawtooth periodPublished

30NTMs , O. SauterDPG Advanced Physics School, The Physics of ITER, Bad-Honnef, Germany, Sept. 2014

, E. Poli

Page 31: Neoclassical Tearing Modes · Neoclassical Tearing Modes O. Sauter1, H. Zohm2 1CRPP-EPFL, ... • Classical tearing mode -> Rutherford equation ... crashes after long sawtooth periodPublished

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

Page 32: Neoclassical Tearing Modes · Neoclassical Tearing Modes O. Sauter1, H. Zohm2 1CRPP-EPFL, ... • Classical tearing mode -> Rutherford equation ... crashes after long sawtooth periodPublished

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

Page 33: Neoclassical Tearing Modes · Neoclassical Tearing Modes O. Sauter1, H. Zohm2 1CRPP-EPFL, ... • Classical tearing mode -> Rutherford equation ... crashes after long sawtooth periodPublished

33NTMs , O. SauterDPG Advanced Physics School, The Physics of ITER, Bad-Honnef, Germany, Sept. 2014

Page 34: Neoclassical Tearing Modes · Neoclassical Tearing Modes O. Sauter1, H. Zohm2 1CRPP-EPFL, ... • Classical tearing mode -> Rutherford equation ... crashes after long sawtooth periodPublished

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

Page 35: Neoclassical Tearing Modes · Neoclassical Tearing Modes O. Sauter1, H. Zohm2 1CRPP-EPFL, ... • Classical tearing mode -> Rutherford equation ... crashes after long sawtooth periodPublished

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

Page 36: Neoclassical Tearing Modes · Neoclassical Tearing Modes O. Sauter1, H. Zohm2 1CRPP-EPFL, ... • Classical tearing mode -> Rutherford equation ... crashes after long sawtooth periodPublished

36NTMs , O. SauterDPG Advanced Physics School, The Physics of ITER, Bad-Honnef, Germany, Sept. 2014

Simple to add to present feedback control

Page 37: Neoclassical Tearing Modes · Neoclassical Tearing Modes O. Sauter1, H. Zohm2 1CRPP-EPFL, ... • Classical tearing mode -> Rutherford equation ... crashes after long sawtooth periodPublished

37NTMs , O. SauterDPG Advanced Physics School, The Physics of ITER, Bad-Honnef, Germany, Sept. 2014

Simple to add to present feedback control

Page 38: Neoclassical Tearing Modes · Neoclassical Tearing Modes O. Sauter1, H. Zohm2 1CRPP-EPFL, ... • Classical tearing mode -> Rutherford equation ... crashes after long sawtooth periodPublished

38NTMs , O. SauterDPG Advanced Physics School, The Physics of ITER, Bad-Honnef, Germany, Sept. 2014

Page 39: Neoclassical Tearing Modes · Neoclassical Tearing Modes O. Sauter1, H. Zohm2 1CRPP-EPFL, ... • Classical tearing mode -> Rutherford equation ... crashes after long sawtooth periodPublished

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

Page 40: Neoclassical Tearing Modes · Neoclassical Tearing Modes O. Sauter1, H. Zohm2 1CRPP-EPFL, ... • Classical tearing mode -> Rutherford equation ... crashes after long sawtooth periodPublished

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