Control of non-axisymmetric magnetic fields for plasma enhanced performances: the RFX contribution

1. Control of non-axisymmetric magnetic fields for plasma enhanced performances:the RFX contribution P. Sonato, R.Piovan, A.Luchetta and the RFX team

2. Outline • Introduction to MHD instabilities in tokamaks & RFPs • Error field control in tokamaks • RWM stabilization in tokamaks • Error field reduction in RFX • Control of m=1 modes in RFX • The new experiments on the modified RFX • The machine modification and the saddle coil system • Power supply • Magnetic measurements • Control system • Control strategies • Conclusions

3. Introduction: MHD plasma instabilities • The MHD instabilities limit the operational space of the plasma in any magnetically confined plasma operating at the highest performances • MHD instability sources: • current gradients • pressure gradients • MHD instability types: • Ideal instabilities • Resistive instabilities

4. m=1, n=3 Introduction: MHD description • 2-D Fourier decomposition of the magnetic field: • Poloidal spectrum: m • Toroidal spectrum: n Resonant surfaces in toroidal geometry

5. Introduction: MHD resonance • Tokamak: • Internally resonant modes • Externally resonant modes Resonance for rational q

6. MHD instabilities in the Tokamak – error fields • The non-axisymmetric magnetic error fields are sources of instabilities: • coils misalignments • coil feed connections • inhomogeneity of conductive passive structures • ferromagnetic structures • ripple • …….. The error fields exert a braking torque against the plasma rotation • Problems of present error field studies: • Many sources of error fields are not completely evidenced • Sidebands of correction coils

7. Error field control in DIII-D • Static error field compensation to attain low density regimes • Recent multi error field compensation with both N=1 coil and C-coils • b limit vs. Br(2,1) Multi-mode Error field compensation Reference discharge

8. MHD instabilities in the Tokamak – RWMs • Advanced scenarios require: • sufficiently high b : • high boostrap current fraction • flat or reversed shear • Consequence: Resistive Wall Modes (RWMs) appearance • external kink modes: n=1,2 and various m • stabilized only by an infinitely conductive wall close to the plasma surface • severe limit in b

9. Feedback Pre-programmed No feedback RWMs stabilization and control in DIII-D • C-coil feedback control of RWMs and pre-programmed similar correction obtain similar improvement • RWMs avoidance strategies: • Stabilisation by rotation through tangential NBI • Careful error field control • Feedback stabilisation with additional coils

10. Error fields & RWM extrapolation to ITER • The RWMs can be stabilized by feedback control acting on the outer correction coils

11. MHD instabilities in the RFP experiments:mode classification

12. internally nonresonant on-axis RWM, m=1, n=-10 Internally resonant tearing mode m=1, n=-12 RWMs in the RFP experiments HBTX-1C EXTRAP-T2R

13. Error fields in RFX - ’92-’99 • The broad spectrum of internally resonant MHD m=1 tearing modes on rational surfaces can easily couple with harmonics of an error field • Two main sources of error fields in the passive Aluminium stabilizing shell: • 2 poloidal insulating gaps • 2 toroidal insulating gaps m=1,n=0 Equilibrium feedback with m=0 Pre-programmed Equilibrium Axisymmetric equilibrium coils local control coils short circuited gap local field error minimization poloidal gap

14. Tearing modes in RFX - ’92-’99 • RFX always exhibited high amplitude m=1 tearing modes: • phase locked with respect to each other • locked with respect to the wall

15. 1,7 1,8 Toroidal position 1,9 1,10 1,11 1,12 m=1 mode control through m=0 mode coupling in RFX • Controlling the currents on the toroidal winding sectors (0,1 mode) the control the m=1 tearing mode position has been obtained • Also a slight reduction of mode amplitude has been evidenced

16. The modified RFX • It has been conceived to extend the non-axisymmetric control of the MHD modes by introducing a direct action of external harmonic m=1 magnetic fields • The capability to produce m=0 modes has been improved by the new toroidal system power supply to control the toroidal field independently on each of the 12 winding sectors • Further significant improvements: • Axisymmetric equilibrium control • Poloidal gap field error minimized • Toroidal gap field error minimized • First wall power handling capability • Vessel wall protection • Plasma breakdown

17. new toroidal support structure toroidal coil new vacuum vessel ports for ISIS feedthroughs saddle coil system shell clamping bands vessel-shell insulated spacers shell equatorial gap shortcircuits vacuum vessel 3 mm copper shell The modified RFX

18. The stabilizing shell • The first basic choice has been to install a passive stabilising shell as close as possible to the plasma having a t(1,0) = 40-50 ms: • to allow a passive stabilisation for instabilities acting on a time scale faster than the operational frequency of the power supplies/winding systems (~20 ms) • corresponding to a passive stabilization of the characteristic internal resonant modes of ~10-20 ms for m=1, n=7 to n=18 • the shell will be nearly completely penetrated for the m=1,n=1,5 RWMs during the shot Welded gap

19. The stabilizing shell:passive error field minimization Field error through the poloidal gap overlapped poloidal gap 23°overlapped poloidal gap short-circuited equatorial gap Butt joint gap

20. The saddle coils • The second design choice regards the shape and the discretization of the radial field control coils: • the presence of an equatorial gap used also as an opening surface to have access to the vessel -> only saddle coils are compatible • the saddle coils must be designed without any gap in between, to avoid undesired sources of high spectrum error fields and source of sidebands

21. nsb= n1,8 ± k.Nt k = ±1, ±2, …. Nt = 48 The saddle coils: sidebands • Toroidal and poloidal sidebands at the plasma edge for a single m=1, n=8 harmonic produced

22. Current (480 A/div) Voltage (750 V/div) Reference (480 A/div) Saddle coil power supply • Each saddle coil is fed with its own switching dc/dc power supply, which performs independent control of the current • H-bridge converter topology with standard voltage components (IGBT ) • Total power: 50 MW Time: 20 ms/div

23. Toroidal field power supply • The system is foreseen to be used also to generate rotating m=0, n=1-5 modes superimposed to the bias reversed Bj

24. 10 Hz 5 Hz 20 Hz Old RFX Rotation frequency limit 50 Hz * old RFX * Vessel braking torque and driving m=0, n=1 torque m=1, n=8 braking torque Normalized to 1 mT of mode amplitude lower amplitude is expected in the modified RFX The new PS will allow an increased m=0, n=1

25. Magnetic measurements: out-vessel probes • “Ad hoc” designed for non-axisymmetric control • The system comprises 192 (4x48) measures of <Br> , Bt , Bp • Bandwidth few kHz (vessel shielding effect) • Btor-Bpol biaxial pick up coils • saddle probes <Br>

26. Magnetic measurements: In-vessel probes • Designed to measure high frequency, high n components of Bt • 96 (48 x 2) measures of Bt • Bandwidth close to 1 MHz

27. Control system:computer based, distributed system • The system includes seven VMEbus stations equipped with single board computers, all connected through one real-time network: • Three stations (processors) dedicated to the real time data acquisition • Four stations (controllers) drive the control power amplifiers. • The performance was measured: • latency time worst case 300 ms

28. Actuator: SC Field harmonics Generated by SC X’= Fx + Gu y = Hx + Pu X’= Ax + Bu y = Cx + Du Measured field harmonics Plasma dynamic model Coil currents Dynamic & FFT - 0 K + Applied voltages Reference Control system: MHD mode control scheme • It consists of a lumped parameter electromagnetic model of the Saddle Coil (SC) system integrated with a linear model of the evolution of RWMs in a RFP plasma

29. Control system: MHD mode control scheme applied to T2R • Recently in T2R a saddle coils system has been installed: • Total SC = 64 • Poloidal = 4 • Toroidal = 16 • Not covering completely the plasma surface • The RFX MHD mode control system has been tested • The RWMs multi mode control has been demonstrated • NO FEEDBACK • Feedback on n=+5,+6 • Feedback on n=+5,+6,+7,+8

30. Control strategies • MHD mode control • stabilisation of RWMs having m=1, n=2-5 • interaction with internally resonant tearing modes, to either mitigate or excite their amplitudes or control their phases • “Virtual ideal shell” close to the plasma. • “Wise virtual shell” is similar to the “virtual ideal shell”, but the components of the radial magnetic field are minimised, except for the equilibrium m=1,n=0 component • Phase control of m=0, n=1-5 modes. Action on the dynamic current unbalance on the toroidal winding sectors to produce m=0, n=1-5 rotating modes able to drag the m=1 phase & wall locked modes

31. Conclusions • The new RFX device is the most versatile experiment to test the interaction of external harmonic fields with MHD modes • The experiments will allow to investigate: • the RWMs stabilization and tearing mode interaction • the error field control, including the effect of the sidebands • All of these features are of common interest for: • Present tokamak and RFP experiments • For the implementation of similar systems in ITER