Modelling control P. Piovesan, A. Soppelsa in collaboration with L. Grando, G. Marchiori, L. Marrelli, L. Piron, D. Terranova, P. Zanca Consorzio RFX, Euratom-ENEA Association, Padova, Italy

The goal … The main goal is to realize an IDEAL SHELL through magnetic feedback B r =0 at r=a (plasma radius) + helical boundary conditions? (L. Marrelli and A. Boozer talks)

The goal … and real life Our main goal is to realize an IDEAL SHELL through magnetic feedback But in real life we have to face some facts: –Discrete active and sensor coils  ALIASING OF SIDEBAND HARMONICS –Gaps, portholes, …  MODE COUPLING, ERROR FIELDS –Active coils and sensors are coupled –Finite penetration time of B r through the shell –Finite bandwidth and current limits of power supplies + active coils –Shell proximity –… B r =0 at r=a (plasma radius) + helical boundary conditions? (L. Marrelli and A. Boozer talks)

Where we are … Clean Mode Control  b r cleaned from the SIDEBAND HARMONIC aliasing due to the discreteness of the active coils and sensors Mode unlocking  current up to 1.6MA  helical states with improved confinement AM b  i,j b r i,j Poloidal index: i=1,…,4 Toroidal index: j=1,2,…,48 I i,j I ref i,j State-space Simulink e.m. model of the wall + feedback system (by G. Marchiori, A. Soppelsa) Power supply + coil controller Inductance matrix among active coils and sensors from vacuum measurements FFT -1 C I ref m,n PID mode controller PID gains chosen to induce mode rotation and phase unlocking, based on simulations with the torque-balance code RFXlocking (by P. Zanca) - CLEAN FFT b r,cl i,j b r,cl m,n m = -1,0,1,2 n = 0,1,…,24 + b r,ref m,n Sideband cleaning + extrapolation to r=a

Where we are going … When increasing the current above 1.6MA, we may encounter the current limit of the active coil power supplies –Related with self-organization to the helical state (1,-7) –Some coil power may be saved by reducing the CMC gains –RFXlocking code predicts that extrapolation to r=a needs more current without improving control (P. Zanca, PPCF 2009) –Alternative strategies should be tested at 1.5MA first I P (MA) current on m=1,n mode (A) power supply saturation (1, -7) (1, -8) (1, -9)

Ultimate limit of CMC? How far is CMC from IDEAL SHELL performance? The secondary mode scaling is favourable, while the (1,-7) mode may fix the ultimate limit Error fields may also play a role I P (MA) Max. m=1 displacement of LCFS (mm) n = -1,…,-23 n = -7 RFXlocking (with 3 shells) may provide an estimate of the ultimate CMC limit, within some assumptions (e.g. uniform wall) Quantitative comparisons with the experiment are ongoing (L. Piron, P. Zanca) K P, proportional gain on (1,-7) Max. m=1 displacement of LCFS (mm) Simulation Experiment

CMC optimization Recent modelling with RFXlocking suggests that several optimizations of the CMC controller are possible: –Tuning of derivative gains  20% reduction of b r for the (1,-7) mode and other modes (more details in D. Terranova and G. Marchiori talk) –Remove complex gains? –Extend CMC to all modes? –Higher gains on m=0 modes at deep F Alternative approaches? –Could stopping the mode rotation allow a further reduction of b r ? –Chose gains to induce an ordered rotation of locked mode? we are here b r (a) / b r (res) for (1,-7) mode

Error fields at toroidal gaps Major EFs identified  Should we avoid or correct them or both? Main EF due to vertical field penetration through the two toroidal gaps: –Locked mode prefers gaps, especially during the start-up phase, but also during flattop –Effects on secondary modes and/or QSH? Locked mode angle toroidal index radial magnetic field (T) M -1 b ref i,j M ~ b r i,j  b ref i,j I i,j First correction tests with the dynamic pseudo- decoupler are promising and suggest some possible optimizations: –Less derivative action to reduce noise on output –Toroidal symmetry assumption may be too strong –All mutual inductances should be measured

More sophisticated feedforward EF correction schemes, to be applied also during plasma, may be designed and tested: –The m=0,n=1 current in the shell is measured and should be proportional to the EF Feedforward EF correction –A pseudo-decoupler may be designed, starting from the inductance matrix among currents in the Field Shaping windings and radial field sensors –ANSYS simulations of the two gaps to determine the fine structure of the EF FFT -1 AM CLEAN FFT + C - b  i,j b r i,j I i,j I ref i,j b r,cl i,j b r,cl m,n b r,ref m,n I ref m,n F + I EF,ref i,j I shell Feedforward correction of error fields

EFs at the equatorial gap The radial magnetic field penetrates faster through the equatorial gap, which may cause significant poloidal mode coupling Is this comparable to the coupling introduced by toroidal geometry? time (s) b  1,n (a) (mT) b r 1,n (a) (mT) I 1,n (A) time (s) Phase difference among b  1,n (a) and b r 1,n (a) m=1, n=-7 + m=1, n=0 m=0, n=7 m=1, n=+7 m=2, n=7

Reduced modal decoupler To correct the EFs at the equatorial gap, a dynamic (or static) modal decoupler is being designed: –Start with reduced dimensions, e.g. m=1, n=-7 only  effects on QSH? –Then try to extend it to the main secondary modes M -1 C e r m,n I ref m,n b r,req m,n ~

Advanced virtual shell The virtual shell scheme on the other hand may have some advantages: –Does it make sense to Fourier decompose EFs and act on them as if they were modes? AM + C VS - b r i,j I i,j I ref i,j b r,ref i,j

Advanced virtual shell AM + C VS - I i,j I ref i,j b r,ref i,j CLEAN b r,cl i,j b r i,j The virtual shell has some advantages: –Does it make sense to Fourier decompose EFs and act on them as if they were modes? A Clean-VS scheme may be designed: –With sideband cleaning (presently without extrapolation to r=a)

Advanced virtual shell AM + C VS - I i,j I ref i,j b r,ref i,j CLEAN b r,cl i,j b r i,j The virtual shell has some advantages: –Does it make sense to Fourier decompose EFs and act on them as if they were modes? A Clean-VS scheme may be designed: –With sideband cleaning (presently without extrapolation to r=a) –With different gains in different positions, to compensate for gaps and other features

Advanced virtual shell AM + C - I i,j I ref i,j b r,ref i,j CLEAN b r,cl i,j b r i,j D The virtual shell has some advantages: –Does it make sense to Fourier decompose EFs and act on them as if they were modes? A Clean-VS scheme may be designed: –With sideband cleaning –With different gains in different positions, to compensate for gaps and other features –OR with a dynamic pseudo-decoupler (to be re-designed on cleaned measurements)

Advanced virtual shell The virtual shell has some advantages: –Does it make sense to Fourier decompose EFs and act on them as if they were modes? A Clean-VS scheme may be designed: –With sideband cleaning –With different gains in different positions, to compensate for gaps and other features –OR with a dynamic pseudo-decoupler (to be re-designed on cleaned measurements) Is it worth developing all of this at plasma radius? –Mutual inductances among active coils and “virtual sensors” at r=a are needed: Can they be measured from mutual inductances among active coils and b  sensors? Very detailed and good measurements of mutual inductances would be needed Can they be estimated from FEM e.m. codes, such as CARIDDI?

Hybrid scheme More physics-driven control schemes may be designed, based on proper combinations of the VS, MC, and FF schemes introduced above (once these have been all investigated separately):

Hybrid scheme M b  i,j b r i,j I i,j I ref i,j A - b r,ref m,n Filter n>n 0 Filter n<n 0 + CLEAN FFT b r,cl i,j b r,cl m,n SIDEBAND CLEANING + EXTRAPOLATION TO r=a F I EF,ref i,j I shell i,j FEEDFORWARD ERROR FIELD CORRECTION DFFT -1 C I ref m,n MC + PSEUDO-DECOUPLER ++ CDCD I ref 1,-7 MODE DECOUPLER ON m=1, n=-7 or most important m=1 modes FFT -1 More physics-driven control schemes may be designed, based on proper combinations of the VS, MC, and FF schemes introduced above (once these have been all investigated separately):