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Tearing modes control in RFX-mod:
status and perspectives
P.Zanca, R.Cavazzana, L.Piron, A.Soppelsa
Consorzio RFX, Associazione Euratom-ENEA sulla Fusione, Padova, Italy
Milestones
• Intelligent Shell: egde radial field control (2005)
• Clean Mode Control (de-aliasing of the measurement): TM wall-unlocking (2007)
• Coils amplifiers improvements: maximum current and rensponse time (2008, 2010)
• MHD model of the feedback (RFXlocking) (2007-2010)
Optimizations
• Edge radial field reduction: get closer to the ideal-shell limit (determined by vessel/copper shell)
• Increase the QSH duration: non-zero reference for the dominant mode
• m=2, n=1 control in tokamak dicharges
Optimizations
• Edge radial field reduction: get closer to the ideal-shell limit (determined by vessel/copper shell)
• Increase the QSH duration: non-zero reference for the dominant mode
• Control in tokamak dicharges
Model-based optimization for m=1
0
0,2
0,4
0,6
0,8
1
8 10 12 14 16
Kd Model-based
Kd Empir.
RF
X u
nit
n
400
500
600
700
800
900
Kp Model-based
Kp Empir.
RF
X u
nit
Latency reduction
m=1,n=8-16 br(a)
Empirical gains
0.8
1
1.2
1.4
1.6
8 10 12 14 16
Experiment
ideal shell limit
mT
n
Latency reduction
m=1, n=8-16 br(a)
Empirical gains
0.8
1
1.2
1.4
1.6
8 10 12 14 16
Experimentideal shell limitsimulation T=400s t=1.2ms
mT
n
Latency reduction
m=1, n=8-16 br(a)
Empirical gains
0.8
1
1.2
1.4
1.6
8 10 12 14 16
Experimentideal shell limitsimulation T=400s t=1.2mssimulation T=125s t=125s
mT
n
Derivative control
• db/dt is currently obtained numerically from b
• Acquisition of the derivative signal db/dt is preferable
• This allows a better PD gains optimization
Dynamic decoupler
• The dynamic decoupler reduces the side-harmonic components of the magnetic field produced
• A “modal” decoupler could be designed considering a limited number of harmonics (i.e. only the poloidal sidebands)
I coilm
,n (A
)B rm
,n (T
)
decoupler ON
m=1, n=-7 m=0, n=7m=1, n=7 m=2, n=7
bφ systematic errors correction
• Unavoidable misalignment of the pick-up coils determines a spurious Ip contribution to bφ
• Real-time subtraction of this term
Similar for m=±1,2
M=0 control • Little affected by the feedback
• High gains test on m=0, n<6 has not shown any improvement on F shallow discharges
• m=0 control at deeper F still to be investigated
• m=0 n≥7 spurious contribution should be removed by the dynamic decoupler
M=0, n<6 feedback with the toroidal circuit
• Enhance the natural reaction of the 12 toroidal sectors to the m=0 low n TM
• Present circuit too slow to follow the m=0 dynamic (2.5ms delay according to 2006 experiments)
• Upgrade of the internal circuit control by reducing the latency
Independent feedback on br and bφ
Iref = Kr br + Kφ bφ
• Suggested by J.Finn and co-workers
• A more general control could allow finding a new optimum
• Preliminary RFXlocking simulations are planned
Feedback on the plasma response
bplasma = br – bcoils(vacuum)
• bcoils from the cylindrical model used in the de-aliasing or from a state-space model which includes the shell frequency response
• The hope is to reduce the TM amplitude at the resonant surface
• According to RFXlocking edge br is comparable to the standard feedback case upon PD gains optimization
Synopsis
• Control system upgrade
Latency reduction
db/dt acquisition
Improved toroidal circuit control
• New algorithms
Dynamic decoupler
bφ sistematic errors removal
M=0 low n control with the toroidal circuit (partially developed)
Plasma response
Independent br bφ feedback
• Other schemes
M=0 control at deep F
Non-zero reference control to sustain QSH
} Gains optimization
Spare
RFXlocking
• Semi-analitical approach in cylindrical geometry
• Newcomb’s equation for global TMs profiles
• Resonant surface amplitudes imposed from experiments estimates
• Viscous and electromagnetic torques for phase evolution
• Radial field diffusion across the shell(s)
• Feedback equations for the coils current
Model-based optimization
Simulation of the derivative control
0,03
0,04
0,05
0,06
0,07
2 4 6 8 10 12 14
brs
1,7 =12mT w=0.1s
Kd=0
Kd=
c K
p
Kd= 2
c K
p
Kd= 3
c K
p
b^ a
-Kpa/(0.96)
ideal shell
plasma
Sensors CoilsVessel
Feedback limit
plasma
Sensors CoilsVessel
Feedback limit
plasma
Sensors
br=0 everywhere: impossible
CoilsVessel
Feedback limit
Single-shell: discrete feedback
ttt jj 1 Δt = latency of the system
;1,,1
,,1
, j
nmr
nmdj
nmr
nmpjj
nmc tb
dt
dKtbKttV
External coils: discrete feedback τw=100ms
0,03
0,04
0,05
0,06
0,1
0,2
2 6 10 14
w=100mscontinuous
t=10-6
t=10-5
t=10-4
t=10-3
< b
^ f >
-Kp rwi
/(0.96)
a)
ideal-shell limit
External coils: discrete feedback τw=10ms
0,03
0,04
0,05
0,06
0,1
0,2
2 6 10 14
w=10ms
continuous
t=10-6
t=10-5
t=10-4
< b
^ f >
-Kp rwi
/(0.96)
a)
ideal-shell limit
External coils: discrete feedback τw=1ms
0,03
0,04
0,05
0,06
0,1
0,2
2 6 10 14
w=1ms
continuous
t=10-6
t=10-5
< b
^ f >
-Kp rwi
/(0.96)
ideal-shell limit
a)
Edge radial field control by feedback
0
5
10
15
0 0,02 0,04 0,06 0,08 0,1
w=100ms
rwi
=0.475m rf=r
wi
rwi
=0.5125m rf=r
wi
RFX-mod experiment
max
[1(
)] (
mm
)
time(s)
RFXlocking simulation of the plasma response
Control system + internal control latency: 2.5 msPower supply time constant: 3 ms
Toroidal circuit dynamic response
Simulation of power supply behaviour with latency = 1.6 ms - Kp = 0.04
Simulation of power supply behaviour with latency = 0.1 ms - Kp = 0.7
Toroidal circuit dynamic response
br(rm,n) vs br(a) experimental
0
0,01
0,02
0,03
0,04
0,05
0,06
0
0,002
0,004
0,006
0,008
0,01
0,012
0,02 0,03 0,04 0,05 0,06 0,07 0,08 0,09 0,1
br1_mn(7) br1_ra(7)br
1_m
n(7)
br1_ra(7)
time
0,22
0,23
0,24
0,25
0,26
0,27
0,28
0,29
0 0.5 1 1.5 2 2.5 3
m=1 n=-8
b^
a
c(ms)
Edge radial field .vs. current time constant
Normalized edge radial field: no rf dependence
0,04
0,06
0,080,1
0,3
8 10 12 14 16 18
w=100ms
ideal shellrf=r
wi=0.475m
rf=a=0.459m
b^ a
-n
m=1
