"Mode dynamics and active control studies andexperiments on RFX-mod"

Acknowledgement to the RFX and Extrap-T2R teams

10th Workshop on MHD Stability Control, Madison (WI) 31 October - 2 November 2005

R. Paccagnella

OutlineOutline

• Control system in RFX-mod• Theoretical Models predictions• Virtual shell experiments:

-mode spectrum-RWM & tearing behaviour-plasma sawtoothing

• Conclusions

Control system in RFX-mod

Sensor coil array:

48x4=192saddle coils Each coilhas 90° poloidal, 360/48=7.5°toroidal extent

SENSORS COILS

Active coil array:

48x4=192 saddle coils Each coilhas 90° poloidal, 360/48=7.5°toroidal extent

Full surface coverage

50 msec (Bv) Cu thin shell

Control system in RFX-mod

4 x 48 radial flux sensors

4 x 48 coils

Measured and Controlled harmonics:

m=0,2 0 <= n <= +24 m = 1 -23 <= n <= +24

Digital controller:

“Virtual Shell” VS : i-th measured rad. Flux zeroed by i-th active coil

Mode control:

Magnetic sensors-> FFT-> harmonics -> gains -> invFFT -> coils responsem,n

• 3D MHD feedback studies using (amodified) DEBS code

• Linear cylindrical model with a discretecoil system

• 3D MHD feedback studies using (amodified) DEBS code

• Linear cylindrical model with a discretecoil system

Theoretical Models

3D DEBS code:3D DEBS code:

•Nonlinear visco-resistive MHD

•cylindrical geometry

•finite difference in radius, Fourier in θ and φ(pseudo-spectral)

• up to 2 “thin” resistive walls

• jump conditions on the external coils for each m,n(coils produce “clean” harmonics)

•Nonlinear visco-resistive MHD

•cylindrical geometry

•finite difference in radius, Fourier in θ and φ(pseudo-spectral)

• up to 2 “thin” resistive walls

• jump conditions on the external coils for each m,n(coils produce “clean” harmonics)

R. Paccagnella, D. Schnack, M. Chu, Phys. of Plasmas 9 (2002)234

Mode control

RFP RWM control ok!

10-10

10-9

10-8

10-7

10-6

10-5

0.0001

0.001

0.01

-30 -20 -10 0 10 20 30

n

externalRWMs

dynamomodes

Fig.5

Non resonant RWMs

NonlinearSpectrum (DEBS)

m=1 modes

3D spectrum agrees w. linearpredictions:

3D spectrum agrees w. linear3D spectrum agrees w. linearpredictions:predictions:

Linear growth rates

No non-linear coupling of RWMs

RFX-mod & linear theory :RFX-mod & linear theory :RFX-mod & linear theory :

0

0.2

0.4

0.6

0.8

1

1.2

1.4

-14 -13 -12 -11 -10 -9 -8 -7 -6 -5 -4 -3 -2 1 2 3 4 5 6 7 8 9 10 11

#17262

gamma*tauw (linear results)normalized spectral m=1 amplitudes

gam*tauw

n

RWMs No Control

@ 30 msec

Too early forExp. RWMs

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

20 40 60 80 100 120 140 160

expfit#17302

b(-6)_exp

b(-6)_lin

b(-5)_exp

b(-5)_lin

b(-4)_exp

b(-4)_lin

time (msec)

[mT]

Internally non-resonant RWMs

RFX-mod & linear theory :RFX-mod & linear theory :RFX-mod & linear theory :

No Control on RWMs

3D simulations & RFX-mod :3D simulations & RFX-mod :3D simulations & RFX-mod :

Good Control in 3D runs(control applied only on RWMs)

Good Control in VS shots on RFX-mod

4 10-5

5 10-5

6 10-5

7 10-5

8 10-5

9 10-510-4

2 10-4

0.04 0.06 0.08 0.1 0.12 0.14 0.16

brE_stat_17216-410

1,-5

1,-6

1,-4

1,-7

1,-8

1,-9

1,-10

1,2

1,3

1,4

time

[ mT ]

10-8

10-7

10-6

10-5

10-4

10-3

1.3 1.35 1.4 1.45 1.5 1.55

Wr( 1, -4)

Wr( 1, -5)

Wr( 1, -6)

Wr( 1, -7)

Wr( 1, -8)

Wr( 1, -9)

Wr( 1,-10)

Wr( 1, 4)

Wr( 1, 2)

Wr( 1, 3)

Time

3D simulations of induced SH & RFX-mod experiment :

3D simulations of induced SH3D simulations of induced SH & RFX-mod experiment : & RFX-mod experiment :

0 20 40 60 80 100 120 140 160 180 200

0.5

1

1.5

2

2.5

t (ms)

amplitude[ brad

n ]

m=1

-1-2-3-4

-5-6-7-8-9

Controlled 1/-7 in RFX-mod

10-9

10-8

10-7

10-6

10-5

0.0001

0.001

0.5 1 1.5 2 2.5

eps42wf3_4/f5_10Wr( 0, 1)Wr( 0, 2)Wr( 1, 1)Wr( 1, 2)Wr( 1, 3)Wr( 1, 4)Wr( 1, 5)Wr( 1, -1)Wr( 1, -2)Wr( 1, -3)Wr( 1, -4)Wr( 1, -5)Wr( 1, -6)Wr( 1, -7)Wr( 1, -8)Wr( 1, -9)Wr( 1,-10)Wr( 1,-11)Wr( 1,-12)Wr( 1,-13)

Time

Controlled 1/-7 in DEBS

#17520

R. Paccagnella, Proc. of Theory of Fusion Plasma Joint Varenna-Lausanne International Workshop, ISPP-20, 73 (2002) (ed. SIF Bologna, Italy)

-30 -20 -10 0 10 20 300

0.5

1shot # 17520@ time (msec)= 100

Discretized coils system

Linear feedback stabilization model(cylindrical)

N

n n+ k N(k=+/-1, +/-2 ..)

Aliasing effect

m m+ j M(j=+/-1, +/-2 ..)

M

Linear feedback stabilization model

R. Paccagnella, D. Gregoratto, A. Bondeson, Nucl. Fusion 42(2002) 1102.

))((

)()1(

)(2 '

'

22

2

,

2

,wm

fm

wnm

w

fanm nK

nK

n

m

s

nM

ε

ε

εγτ

εεπ+

−−=

''''' ' ''1 nmnmMlmm Npnn nmmn

sensmn MSFIb

P ∑ ∑== += +=

Forms factorof coils and sensors

The transfer function has a pole for MHD unstable modesγ ◊ complex(to allow slow rotation)

m,n

ExtrapT2 vs. Linear feedback stabilization model:

D. Gregoratto, et. al. Phys. of Plasmas 12 (2005) 092510.

Sawtoothing on RFX-mod :thermal effects

SawtoothingSawtoothing on RFX-mod : on RFX-mod :thermal effectsthermal effects

40 50 60 70 80 90 100 110100

150

200

250

300

350

400

450

500

550 SXR

m=0,n=1

#17116

m/n=0/1 & SXR

0 10 20 30 40 50 60 70 80 90 1000

50

100

150

200

250

300

350

400

450

500

SXR

m=1,n=-7

m=1,-7 & SXR

In antiphase

In phase

Conclusions

• Linear and nonlinear models for RFP w. feedback in the cylinder: satisfactory models validation with

experiments (to be completed in RFX-mod)

• VS in RFX gives simultaneous control onmodes amplitudes as predicted by theory

(shots up to 280-290 msec = 5 τw achieved)