What is the rotation dependence of error field thresholds?Rotation dependence of EF thresholds R J Buttery, Orlando, EFW 2007 Mode rotation • Mode born slightly slower than CER carbon

Rotation dependence of EF thresholds R J Buttery, Orlando, EFW 2007

2007 Error Field Workshop, Orlando, Florida

What is the rotation dependenceof error field thresholds?

R J Buttery1

T.C. Hender1, R. J. La Haye2, T. Scoville2

and the DIII-D and JET teams.

1EURATOM/UKAEA Fusion Association, Culham Science Centre, UK.2General Atomics, San Diego, USA

Work conducted under the European Fusion Development Agreementand jointly funded by EURATOM, the UK EPSRC, Swiss NSF, and US DOE.


NTM/TM triggering – Error Field role

• Error fields act to brake rotation and then drive tearing

– Criteria for mode based on error field torque overcomingplasma rotation to allow tearing to accelerate

– threshold scales as Bpen ~BT w0 t A (t rec / t v)1/2 ~ w0 (visco-resistive)or may be w00.5 (ideal viscous)

– w0 is ‘natural’ MHD fluid rotation

• Increased rotation raisesthresholds

– So modes not a problem inmost co NB plasmas

– …but a concern if youcancel fluid rotation? (w0=0)

0

2

4

6

8

0 2 4 6 8 10PHeat (MW)

Pen

etr

ati

on

fie

ld (

G) NBI

ICRH


Momentum injection variedwith neutral beams on JET:

– Error fields ramped toinduce locked mode

– Despite considerablerange in plasma rotation…

– …Error field thresholdvariation is modest

•‘Sweet spot’ with verylow threshold not found…

– Contrasts with traditionalEF theory:

Bpen ~BT w0 t A (t rec / t v)1/2

…although finer NBI scans givesome encouragement at low

rotation

0

1

2

3

4

5

6

-2 -1 0 1 2 3

PNBI (MW)

Saw

too

th P

recu

rso

r F

req

(kH

z)

JETNBI power scan- density and intrinsic corrected

0

1

2

3

4

5

6

7

8

-2 -1 0 1 2 3

NBI (MW)

Bp

en

(A

)

Norm B

RBE exp

Series3

Series1

Reverse Bcounter NBI

Normal Bco NBI

Rotation:

EF threshold:


But error fields role may be worse at high beta

• At high beta, error fields couple more strongly to theplasma

– Increased resonant responsebrakes plasma rotation

– Decreased locked modethreshold [La Haye 1991]

• This poses a double concern for ITER!

– Rotation braking by error field may further perturb NTMstability physics

– Lower rotation may lower EF thresholds further at high b


Error fields help trigger tearing modes at high beta

• DIII-D and JET show a lowering of 2/1 NTM thresholds withincreased error field and co-NB:

(corrected for ne & Bt variation)

0

2

4

0 4 8B 21 (G)

bN

Rotating onset q>4Rotating onset q<4Locked onset q>4Locked onset q<4Fit x 2̂

DIII-D 2/1 NTMs

• Note difference in locking behaviour– JET: error field rapidly brake plasma and cause locked modes

• Interplay of bN accessible and error field amplitude

– DIII-D: zone of rotating mode onset with decreased b thresholds• Not error field penetration, but changes to NTM stability physics

– How will this manifest with low torque injection?

JET 2/1 mode thresholds

(B21 corrected linearly

for density)

0

2

4

0 4 8B21 (Gauss)

!N

Rotating onset

no error field

Locked onset

with EFCCs

Locked onset

with saddles

(H mode)

(L mode)(Ohmic)

all q95~3.4

JET 2/1 mode thresholds

(B21 corrected linearly

for density)

0

2

4

0 4 8B21 (Gauss)

!N

Rotating onset

no error field

Locked onset

with EFCCs

Locked onset

with saddles

(H mode)

(L mode)(Ohmic)

all q95~3.4


Differences in DIII-D/JET error field effects lie inharmonic mix

• JET error fields havemore 1/1 field

– Increased brakingmay explain locking

• DIII-D 100% co beamscan used C coils

– Some uncertainty inintrinsic error

• Esp with JET shape

• DIII-D ~30% net cobeam scan used I coils

– Very low m=1, more m=3

0

1

2

3

0 1 2 3

poloidal harmonic number, m

Fie

ld s

tre

ng

th

rela

tiv

e t

o m

=2

JET saddles

JET EFCCD3D C coil

D3D intrinsic

D3D standardand JET-likeshapes

JET shape


New studies usingDIIII-D beambalancing…


DIII-D beam balancing studies

Error field seems todrop threshold slightly

– but effect not highlypronounced…

– and modes usuallyform rotating…

2/1 NTM bN thresholds fall as net torque is reduced:

0

1

2

3

-4 -2 0 2 4 6

Neutral Beam Torque (Nm)

!N (

21

NT

M o

ns

et)

Optimal Error Correction

No Error Correction

x-1 Enhanced Error Field


Born locked

DIII-D

cocounter

b N (2

/1 N

TM o

nset

)

sawtoothingELMy H modes


Trend confirmed in initial mode rotation speed

0

1

2

3

-5 0 5 10 15

2/1 NTM rotation at mode onset /kHz

!N (

21

NT

M o

ns

et)


No Error Correction

x-1 Error Correction


DIII-D

counter-co

b N (2

/1 N

TM o

nset

) Error field seems todrop threshold slightly

– but effect not highlypronounced…

– and modes usuallyform rotating…

– Error fields act tobrake plasma…

2/1 NTM bN thresholds fall as net torque is reduced:


Error fields act to brake plasma

• Error fields slow plasmarotation and lower NTMb thresholds

• But do not directly drivelocked modes

– Most low torque casesstart in rotating state

2/1 NTM Rotation vs Torque

-6

-4

-2

0

2

4

6

8

10

12

14

-4 -2 0 2 4 6

Neutral Beam Torque /Nm21 N

TM

ro

tati

on

/kHz


No Error Correction



#126689:430Hz 2/1 NTM-1Nm torque


Comparison of low and high torque:no increased error sensitivity

• Compare previous all co-scan with points at ~+1.7Nm torque

0

1

2

3

4

0 2 4 6 8

B21 (G)

!N

Rotating onset

Locked onset

Low torque

Linear (Rotating

onset )Linear (Low

torque)

Raw data

(no corrections)

– Note some uncertainty in intrinsic error - treat as an unknown…

– Low torque points use I coils; high torque points use C coils

– But gradients clearly similar or weaker than high torque points

(corrected for ne

& Bt variation)

0

1

2

3

4

0 2 4 6 8

B21 (G)

!N

Rotating onset q>4Rotating onset q<4Locked onset q>4Locked onset q<4Low torqueFit x 2̂Linear (Low torque)

Blue point xvalues arerelative to optimalcorrection


(Density ramp down gives estimate of intrinsic error)

• Optimal I coil correctionaccesses 42% lowerdensity

– I coil field applies 1.1Gof 2/1 field in our study

– Intrinsic error is of order1.5G of 2/1 field

– This is approximate -ignores sidebandcompletely

Locked modeonset:

Density

I coil error correction: optimal / none


Is there much higher rotation shear? …not really

• Co and counter beams may depositdifferently, so balancing may makeprofile sheared…

– Could help make plasmamore resilient to tearing?

CERFIT q=2 tor rot shear vs q=2 rot

-140

-100

-60

-20

20

-4 0 4 8 12

CER q=2 rotation /kHz

q=

2 r

ot

sh

ear kHz/m


Summary

• Theory: Error fields expected to induce modes more readilyat low rotation

– Experiment: some evidence for this but not the expectedlinear dependence

• New torque scan experiment reveals 2 surprising things

– No region of where modes systematically form locked

– Error fields have modest effect on TM thresholds

• Questions:

– Are medium bN plasmas somehow more stable to EF modes?

– Is torque balancing introducing rotation shear?

– Is rotation dependence in EF theory linear?


0

1

2

3

-4 -2 0 2 4 6

Neutral Beam Torque (Nm)

!N (

21

NT

M o

ns

et)


No Error Correction



Born locked

DIII-D

cocounter

b N (2

/1 N

TM o

nset

)

sawtoothingELMy H modes

Key Question

Is low torque really notsensitive to EFs?

– Vital question for ITERoperational limits

– And real puzzle fortheorists!

• Perhaps there is nosweet spot where zerorotation gives zerothreshold?

Key area of parameter space to explore:

These areas should be exploredexperimentally…

?


Additionalmaterial…


Mode rotation

• Mode born slightly slowerthan CER carbon rotation

-4

0

4

8

12

-4 0 4 8 12

CER q=2 rotation /kHz

2/1

NT

M r

ota

tio

n /kHz


Torque cf rotation

• Note offset due to intrinsicplasma rotation

-6

0

6

12

18

24

-4 0 4

Torque /Nm

CE

R r

ota

tio

n /kHz

q=2

core

q~1.5


CERq measure at locked mode

Average CER Rotation profiles just

after mode locks (+stdevs plotted)

-3

-2

-1

0

1.85 1.95 2.05 2.15

Radius (m)

CE

R R

ota

tio

n /kH

z

CERQ T2-7 combinations

CERQ T18-22 combinations


Error field physics raises further concern

•Modes form when resonant surface is braked by resonantresponse to EF to ~half it’s natural frequency

– tiny static island induced by EF

– viscous forces try to keep bulk plasma rotating slipping about island

• this opposes island growth

– torque exerted through island and viscosity by EF brakes plasma

– if rotation slows enough, island can grow, increasing torque andbifurcating to a locked mode state

– threshold scales as Bpen ~BT w0 t A (t rec / t v)1/2

• w0 often taken to be electron diamagnetic rotation

•Expect cancelling natural q=2 rotation should lower thresholds– didn’t see in normal B operation on JET so look in reverse B...


But error field role may be worse at high beta

• At high beta, error fields couple more strongly to theplasma

– Increased resonant responsebrakes plasma rotation

[Strait et al., IAEA 2002]

Documents

What is the rotation dependence of error field thresholds?Rotation dependence of EF thresholds R J Buttery, Orlando, EFW 2007 Mode rotation • Mode born slightly slower than CER carbon