Recent Results on RFX-mod control experiments in RFP and tokamak configuration L.Marrelli Summarizing contributions by M.Baruzzo, T.Bolzonella, R.Cavazzana, Y. In, G.Marchiori, P.Martin, E.Martines, M.Okabayashi, R.Paccagnella, P.Piovesan, L.Piron, A.Soppelsa, D.Terranova, P.Zanca
Outline RFP control of Tearing modes/shax states - Independent control for b r and b t - Dealing with coupled harmonics in controlled helical boundary SHAx states: Dynamic Decoupler Stationary operations in RFX-mod Very low q (q<2) tokamak with active control - The role of the feedback variable Clean vs Raw control - Simple model explanation
Background Known facts on Control of Tearing Modes in the RFP - Clean Mode Control induces a slow rotation of wall-locked tearing modes and jumps of the residual slinky [1] - The dynamics of single mode b edge (amplitude and phase) is well reproduced by the RFXlocking (cylindrical) code. The amplitude of the TMs at the resonance (b core ) is an input - Minimum b edge have been characterized by extensive single mode simulations and experiments Using extrapolated radial field Optimizing gains for TM harmonics - Feedback laws explored so far can only reduce the proportionality constant α i.e. Active Control cannot act as an ideal shell at an arbitrary radius [1] P.Zanca et al, NF, v47 p 1425 (2007)
Ongoing investigations on TM control Can we further improve with a different feedback law[1]? - Simulations with independent gains on b r and b t Improving persistence of SHAx states (m=1,n=-7) - helical boundary control: experiments and simulations with b edge 1,-7 = b 1 sin(ωt) - Simultaneous control of m=0,n=7 with and without Dynamic Decoupler good for possible divertor operation [2] [1] J.Finn et al. Phys. Plasmas 17, 112511 (2010) [2] Martines E. et al., Nucl.Fusion, 50, 035014 (2010)
Independent gains on b r and b t A first set of simulations have been performed with a single mode and with different weights of the b t component
Multi-mode simulations Multi-mode simulations are on-going in order to maximize the difference in rotation frequency of different modes and therefore improve wall-unlocking λ =0,1,3,5,6 The more promising gain sets will then be experimentally tested
Helical Boundary Experiments In order to improve SHAx persistence, the feedback law is modified in order to prescribe a given helical field at the edge. plasma current (MA) m=1, n=-7 mode rotates at 30Hz #28218 1/-7 B r (a) ampl. (%) 1/-7 phase (rad) time (s)
Helical Boundary Experiments In order to improve SHAx persistence, the feedback law is modified in order to prescribe a given helical field at the edge. plasma current (MA) m=1, n=-7 mode maintained static #28218 1/-7 B r ampl. (%) 1/-7 phase (rad) time (s) Time selected for VMEC/V3FIT equilibrium reconstruction
The helical boundary increases the magnetic persistence. High density Low density
Real-time Dynamic Decoupler Helical boundary on m=1,n=7 produces poloidal harmonics - Partly due to plasma toroidicity partly due to passive structures Control of poloidal harmonics requires a more complex feedback law: a real-time dynamic decoupler [1] has been implemented and is under test dynamic decoupler ON current ampl. (A) 1/-7 #27085 B r ampl. (mt) 1/-7 0/7, 1/7, 2/7 time (s) [1] A.Soppelsa talk, this workshop [2] P.Piovesan, oral, EPS 2011
Effect on n=7 eigenfunctions Dynamic decoupling allow changing edge values of the poloidal harmonics: analysis of the possible effect on m=0,n=7 islands is ongoing r 1,-7 s p s c m = 1, n = -7 vacuum field only dominant harmonic of the helical equilibrium with plasma (#28784) with plasma + dynamic decoupling (#28765) perturbed flux (mwb) r s 0,7 m = 0, n = 7 edge resonant, partly due to toroidal coupling m = 1, n = 7 non resonant radius (m)
Tokamak experiments Tokamak discharges can be produced in RFX-mod up to 1.2s: much longer than the shell time (50ms vert field penetration time) - B t =0.55T - Ohmic heating only / circular geometry - Graphite wall act as a limiter - Feedback controlled plasma current and plasma position - b/a=1.12 (vacuum vessel may also play an important role) This configuration allows studying current driven RWMs in a reproducible way similarly to RFX-mod RFP discharges. The (2,1) current driven Resistive Wall Mode is observed when operating below q(a)=2
q(a) < 2 tokamak discharge Sawtooth activity is very often observed in tokamak discharges - On axis q oscillates around 1 As long as q(a) is below 2 an exponentially growing (2,1) mode appear which terminate the discharge with a disruption - Mode is wall locked - Mode amplitude is small compared to pickups in magnetic signals VMEC reconstruction confims q(a)<2 - Experimental pressure profile - Parametric current density j (1-Ψ t ) α
Feedback controlled discharges Activating Clean Mode Control on the (2,1) harmonic only, discharges with q(a) as low as 1.6 can be obtained. - Low q(a) limit not explored yet Gain change @600ms FB stops @800ms
(2,1) mode locking In some discharges without FB, an initially rotating (2,1) mode may lock to the wall when q(a) >2. Once the mode locks, br field grows on the shell time scale and the discharge eventually disrupts The same occur in RFP discharges without control CMC mitigates wall locking in the tokamak as in the RFP
Role of the feedback variable A key element of successful stabilization is the use of Clean Mode Control and not Virtual Shell (i.e. Raw Mode Control) No control Raw Mode Control Clean Mode Control A gain scan was performed in Raw Mode control, but mode growth was only delayed.
Simple model of Clean and Raw control Newcomb equation (for a zero β cylindrical tokamak) is used to determine the dynamics of the unstable mode and of all the sidebands. Unstable mode eigenfunction Dominant sideband eigenfunction In CMC the feedback variable correspond to the mode amplitude and stabilization is obtained trivially for K p > γ (2,1)
Raw Mode Control In Raw Mode control the feedback variable includes the dynamics of all sidebands. A qualitative model considers only the most significant sideband The solution of the closed loop is easily obtained by considering the locus of the roots of the laplace transform of the open loop equation Sidebands Aliasing zero Stable sideband Unstable mode
More complete simulations Taking into account all the sidebands and the delays of the real RFX-mod control circuit Simulation predicts that if b p is used, cleaning is not necessary for stabilisation. The same applies for b t
Discussion/Outlook RFX-mod tokamak RWMs require cleaning while RFP RWM doesn t. - The number of coils was designed in order to stabilize m=1 RFP RWMs with raw radial field sensors [1] Sideband cleaning is not considered at present in tokamak feedback experiments: - The plasma response is a similar concept - The poloidal field sensors are less affected by sidebands aliasing RFX-mod tokamak discharges at q(a)<2 will allow experimental verification of the feedback laws for RWM control. - Use of poloidal sensors (raw) - Implementation of the plasma response Can we apply these results to shaped (X-point) tokamak discharges? [1] Paccagnella et al 2002 Nucl. Fusion 42 1102
Summary Work is in progress for optimizing TM control - Independent feedback on br and bt SHAx states - Helical boundary - Dynamic decoupler acting on the n=7 mode structure RFX-mod as a tokamak: - Clean Mode Control is necessary for (2,1) RWM stabilization - (2,1) wall locking is mitigated and disruption avoided - q(a) as low as 1.6 can be obtained - Different feedback schemes on tokamak RWM control can be tested and compared to models