Resonant magnetic perturbation effect

on the tearing mode dynamicsin EXTRAP T2R:

experimental results and modelingL. Frassinetti, K.E.J. Olofsson, P.R. Brunsell, J.R. Drake

Alfvén Laboratory, Royal Institute of Technology KTH

Stockholm

OUTLINE

• Resonant magnetic perturbation (RMP)Resonant magnetic perturbation (RMP) Why are RMPs important? Why are RMPs studied in EXTRAP T2R?

MachineDiagnosticsFeedback system

TM dynamics with low RMP amplitudeTM dynamics with high RMP amplitudeTM locking to a RMP

Fitzpatrick theoryInterpretation of experimental results

• Modelling Modelling resultsresults

• Experimental resultsExperimental results

• EXTRAP T2REXTRAP T2R

WHY ARE RMPs IMPORTANT?

[Abdullaev, PoP 16, 030701 (2009)]

[Evans, NF 2008, 48 024002]

1. Neo-classical tearing mode stabilization RMP can interact with the NTM with stabilizing effects RMP can rotate a locked mode to move the O-point in the best position for ECCD stabilization

[La Haye, PoP 9, 2051 (2002)][Volpe, PoP 16, 102052 (2009)]

RMPs can produce stochasticity in the plasma outer region

the pressure gradient is reducedand the ELM effect mitigated. DIIID [Evans, NF 2008, 48 024002] JET [Liang, PRL 2007, 98 265004]

2. ELM suppression:

(2,1

) TM

am

plitu

de (

a.u.

) Hender NF 1992COMPASS-C

Ivers,PoP 1996 HBT-EP

time

WHY TO STUDY RMP?

2. There are many theoretical papers that investigate the interaction between an RMP and a TM

3. But recently, not so many experimental results directly investigate the RMP effect on TMs

2. RMPs can be easily produced with EXTRAP T2R feedback system

1. The mechanisms for ELM mitigation are not yet totally understood

1. EXTRAP T2R plasma is characterized by rotating TMs

WHY TO STUDY RMP in EXTRAP T2R?

EXTRAP T2R is a good device to test new feedback algorithms and study the MHD mode response to external perturbations

m=1

-30 -25 -20 -15 -10 -5

20

10

0

-10

0.3

0.2

0.1

0.0

b1,

n (m

T)

1,

n (k

rad

/s)

n

EXTRAP T2R

EXTRAP T2R is a RFP with:

• R=1.24m• a=0.18m

• Ip ≈ 80-150kA• ne ≈ 1019m-3

• Te ≈ 200-400eV

• tpulse≈ 20ms (no FeedBack)• tpulse≈ 90ms (with IS)

TM diagnosticb 4 poloidal x 64 toroidal local sensors (m=1 connected) located inside the shell. Sensitive to fast rotation.

TM

The device

(1,-12) is often larger than the other TMs

-12 -13-14

0.0 0.2 0.4 0.6 0.8 1.0r/a

0.100.080.060.040.020.00

-0.02-0.04

q(r

)

Poincare map of magnetic field lines(poloidal section)

(1,-12) island

-1.0 -0.5 0.0 0.5 1.0x/a

1.0

0.5

0.0

-0.5

-1.0

z/a

byOlofsson E.

• shell≈13.8ms (nominal) shell

EXTRAP T2R

bc

Sensor coils

Sensor coils

• SENSOR COILS 4 poloidal x 32 toroidal sensor saddle coils (m=1 connected) located inside the shell

Activecoils

Active coils

• ACTIVE COILS 4 poloidal x 32 toroidal active saddle coils (m=1 connected) located outside the shell

Digitalcontroller

• DIGITAL CONTROLLER

The feedback

plasma

external helical magnetic

perturbations shell

b1,n bc

Fourier harmonics in real time

inputto active coils

Vc(t) V1,n min[ |b1,n(t)-ref| ]

[Olofsson, Fusion Engineering and Design 84, 1455 (2009)]

m=1n=-12

0 20 40 60Time (ms)

0.6

0.4

0.2

0.0b r

1,n (

mT

)

0 20 40 60Time (ms)

80

60

40

20

0

v1,-1

2 (

km/s

)

80

60

40

20

0

vOV (

km/s

)

1.00.8

0.6

0.4

0.2

0.0

b r1,

n (

mT

)

120100

8060

40

200

Ip (

)kA

m=1n=-12

0 20 40 60Time (ms)

0.6

0.4

0.2

0.0

b r1,

n (

mT

)

At present In EXTRAP T2R RMPs are applied to study:

- effect on TM dynamics (present talk)

- effect on the plasma flow (wednsday talk)

Present RMP studies on EXTRAP T2R

TM DYNAMICS

average of all other TMs(1,-12)

Natural TM dynamics TM dynamics with low RMP amplitude

RMP ≈ 0.3mT

1- amplitude: “modulated”

RMP effect on the rotating TM:

2- velocity: “modulated”

NO RMP

0 20 40 60

0.6

0.4

0.20.0

b r1,

n (

mT

)

10080604020

0

Ip (

kA)

0.6

0.4

0.20.0

b r1,

n (

mT

)

10080604020

0

Ip (

kA)

0 20 40 60Time (ms)Time (ms)

19.60 19.65 19.70

ph

ase

Time (ms)

40

30

20

10

0

(

kra

d/s

) b

m,n (

mT

)

0.60.50.40.30.20.1

ph

ase

40

30

20

10

0

(

kra

d/s

) b

m,n (

mT

)

0.4

0.3

0.2

0.1

14.68 14.70 14.72 14.74 14.76 14.78

Time (ms)

b 1

,-1

2 (

mT

)

(kr

ad/s

)

40

30

20

10

0

0.20

0.15

0.10

0.05

0.00

AMPLIFICATIONSUPPRESSION

=0=

TM amplitudeamplitude and velocityvelocity are correlatedcorrelatedwith the phase shiftphase shift between TM and RMP

ampl.ampl. suppression

TM DYNAMICS with low RMP amplitude

decel.accelerationdecel.

Phenomenological explanation (wrong!)

Toroidal angle

bTM

Toroidal angle

Toroidal angle

bTM

bRMP

b 1

,-1

2 (

mT

)

0.5

0.4

0.3

0.2

0.1

0.0

(

krad

/s)

20

15

10

5

0

RMP ≈ 0.5mT

TM DYNAMICS with high RMP amplitude

suppression

jump

am

plifi

cati

on

deceleration

acce

lera

tion

jump

0.6

0.4

0.2

0.0

b r1

,n (

mT

)

0 20 40 60Time (ms)

1- High oscillation with “complete” suppression

2- phase jumps

b m

,n (

mT

)

0.60.50.40.30.20.1

(

krad

/s)

25201510

5029.10 29.15 29.20

Time (ms)

MODELLING

Based on Fitzpatrick [Phys. Plasmas 8 4489 (2001)]

RMPc rW c b

TMrW c b

3 coupled partial differential equations:

1. TM evolution

2. Torque balance

with

3. Helical velocity

Viscous torque EM torque

braking torque due to eddy currentsIn the wall generated by the rotating TM

braking torque due to interactionof the rotating TM with the static RMP

2TMrb TM RMP

r rb b

Poloidal section

Amplification and

deceleration

suppressionand

deceleration

suppressionand

acceleration

amplificationand

acceleration

b 1

,-1

2 (

mT

)

(kr

ad/s

)

0.30

0.20

0.10

0.00

30

20

10

0

Time (ms)0.00 0.02 0.04 0.06 0.08 0.10

ne(0)=0.9x1019m-3

FREE PARAMETERSR=0.1ms=0.65 10-7 kg/(m∙s)

INITIAL CONDITIONS0=30krad/sb

TM(0)=0.12mT

Reasonable agreement between model and experiment

MODELLING the LOW RMP case

TM amplitude is modulated

TM velocity is modulated

amplitude reduction in time(not evident on this time scale)

velocity reduction in time(not evident on this time scale)

brRMP=0.3mT

b 1

,-1

2 (

mT

)

0.20

0.15

0.10

0.05

0.00

(

krad

/s)

40

30

20

10

0

b 1

,-1

2 (

mT

)

0.50

0.40

0.30

0.20

0.10

0.00

(kr

ad/s

) 15

10

5

0

Time (ms)0.20 0.22 0.24 0.26 0.28 0.30

Reasonable agreement between model and experiment

MODELLING the HIGH RMP case

brRMP=0.5mT

TM amplitude is modulated

TM velocity is modulated

amplitude increases in time

Phase jumps

ne(0)=0.9x1019m-3

FREE PARAMETERSR=0.1ms=0.65 10-7 kg/(m∙s)

INITIAL CONDITIONS0=50krad/sb

TM(0)=0.01mT

b 1

,-1

2 (

mT

)

0.50

0.40

0.30

0.20

0.10

0.00

(

krad

/s)

20

15

10

5

0

b 1

,-1

2 (

mT

)

0.50

0.40

0.30

0.20

0.10

Time (ms)

30.40 30.45 30.50 30.55

EXPERIMENT brRMP=0.4mT

TM LOCKING TO A RMP

-Low RMPLow RMP amplitude “weak” oscillationoscillation in the TM amplitude and velocity

-High RMPHigh RMP amplitude “strong” modulation in the TM amplitude and phase jumpsphase jumps

IS IT ALWAYS SO SIMPLE?IS IT ALWAYS SO SIMPLE?

lockinglockingoscillationsoscillations jumpsjumps lockinglockingoscillationsoscillations jumpsjumps

MODEL brRMP=0.4mT

R=0.1ms=0.65 10-7 kg/(m∙s) ne(0)=0.9x1019m-3

0=25krad/sb

TM(0)=0.2mT

b

1,-

12 (

mT

)

0.50

0.40

0.30

0.20

0.10

Time (ms)

0.00 0.05 0.10 0.15 0.20 0.20

SCALING OF THE TM DYNAMIC PROPERTIES WITH THE RMP AMPLITUDE

TM amplitude:

1- Suppression1- Suppression for “low” RMP amplitudes

2- Amplification2- Amplification for “high” RMP amplitudes

TM dynamics:

1- Full rotation1- Full rotation for “low” RMP amplitudes

2- Jumps2- Jumps for “high” RMP amplitudes

3- Locking3- Locking for “very high” RMP amplitudes

time averaged amplitude

Angle covered by the TM during one rotation

b 1

,-1

2 (

mT

)

0.50

0.40

0.30

0.20

0.10

0.00

0.0 0.2 0.4 0.6 0.8 1.0br

1,-12 (mT)

br1,-12 (mT)

0.0 0.2 0.4 0.6 0.8 1.0

SCALING OF THE TM DYNAMIC PROPERTIES WITH THE RMP AMPLITUDE

TM amplitude:

1- Suppression1- Suppression for “low” RMP amplitudes

2- Amplification2- Amplification for “high” RMP amplitudes

TM dynamics:

1- Full rotation1- Full rotation for “low” RMP amplitudes

2- Jumps2- Jumps for “high” RMP amplitudes

3- Locking3- Locking for “very high” RMP amplitudes

time averaged amplitude

Angle covered by the TM during one rotation

b 1

,-1

2 (

mT

)

0.50

0.40

0.30

0.20

0.10

0.00

0.0 0.2 0.4 0.6 0.8 1.0br

1,-12 (mT)

br1,-12 (mT)

0.0 0.2 0.4 0.6 0.8 1.0

CONCLUSIONS

• An external RMP can affect the rotating TM and the corresponding magnetic island

• The RMP producesRMP produces: TM amplitude amplification or suppression TM velocity acceleration or deceleration

• “Low” RMP amplitude “weak” oscillationoscillation in the TM amplitude and velocity• “High” RMP amplitude “strong” modulation in the TM amplitude and phase jumpsphase jumps• The locking to a RMP can be a complicated mechanism

• The Fitzpatrick modelFitzpatrick model gives a reasonable explanationreasonable explanation of these phenomena It is a useful tool for testing advanced feedback algorithmuseful tool for testing advanced feedback algorithm for TM control

• Work in progress and future work:

1- RMP with another helicity 2- RMP effect on plasma flow 3- …

depending on the phase shift