"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