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Control of a Fusion Plasma Instability: Period Locking of the Sawtooth Period

This study explores a new method for controlling the period of sawtooth instabilities in fusion plasma. Experimental and simulation results show that modulation of the electron cyclotron current drive (ECCD) power can effectively lock the sawtooth period. The locking range is influenced by parameters such as power modulation period, duty cycle, and power level. This research has potential applications in controlling other periodic instabilities and relaxation oscillations in plasma.

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Control of a Fusion Plasma Instability: Period Locking of the Sawtooth Period

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  1. Control of a Fusion Plasma Instability:Period Locking of the Sawtooth Period Menno Lauret Lauret, Felici, Witvoet, Goodman, Vandersteen, de Baar, Sauter, TCV team FOM, TU/e, TCV, VUB EC17 Deurne 2012

  2. Result • A new way to use ECCD for sawtooth period control • Succesful in experiments (TCV) and simulations • Concept works for period control in general • Related to talk by F.Felici on sawtooth pacing this morning but without real-time measurements (no feedback) EC17 Deurne 2012

  3. Introduction: Sawtooth crash • Periodic instability in magnetic field • Sawtooth crash->temperature crash: relaxation oscillation EC17 Deurne 2012

  4. Motivation • Sawtooth crash = destructive periodic magnetic instability • Sawtooth period influences plasma (NTM, ELM, disruption) • Sawtooth period has to be controlled • Crash physics less relevant here EC17 Deurne 2012

  5. Sawtooth physics (Porcelli et al.) • q (safety factor) profile evolution • Current diffusion relaxes profile • Shear (derivative) at q=1 surface > c then: Reconnection in centre (crash) EC17 Deurne 2012

  6. q-profile evolution (CRONOS) r(q=1) EC17 Deurne 2012

  7. ECCD launchers on TCV Courtesy of F.Felici EC17 Deurne 2012

  8. q-profile influence (CRONOS) s(q=1) ECCD EC17 Deurne 2012

  9. Sawtooth control • Change shear near r(q=1) with ECCD • Deposition location of ECCD power influences period • Feedback: measure period then change deposition • Problem: slow and uncertain due to mechanics mirror • Other degree of freedom: ECCD power • E.g. sawtooth pacing by F.Felici this morning (feedback) EC17 Deurne 2012

  10. Intermezzo: Period locking • Nonlinear oscillator + periodic input • Period of system : input = 1:1 or 2:1 or 3:2 etc. • Classical example: van der Pol (relaxation) oscillator • Chose f `close’ to natural frequency -> System frequency = f • Note 3d relaxation o.d.e. for sawtooth and ELM period: A low-dimensional model system for quasi-periodic plasma perturbations. Constantinescu et al. Phys.Plasma 2011 EC17 Deurne 2012

  11. ECCD power modulation • ECCD power outside r(q=1) -> crash delayed • Modulate power signal with a period close to the requested sawtooth period • 3 Degrees of freedom: • Power modulation period • Duty cycle • Power level EC17 Deurne 2012

  12. Locking (and pacing) Courtesy of F.Felici EC17 Deurne 2012

  13. Simulink simulations (G.Witvoet) EC17 Deurne 2012

  14. Simulations • Simulink simulations [1] : 1:1 locking between power modulation and sawtooth period (For certain range of power periods, duty cycle, power level) • [1] Witvoet, Lauret, de Baar, Westerhof, Steinbuch. Numerical demonstration of injection locking of the sawtooth period by means of modulated EC current drive. Nucl.Fusion 51 EC17 Deurne 2012

  15. Sawtooth period locking (TCV) EC17 Deurne 2012

  16. Sawtooth period locking Period 15 ms power modulation results in 15 ms sawtooth period. Modulation with 25 ms and 35 ms does not work. Difference: duty cycle. EC17 Deurne 2012

  17. Sawtooth period locking Locking range: locking depends on duty cycle, modulation period and power level. Green area is locking area. EC17 Deurne 2012

  18. Open loop control EC17 Deurne 2012

  19. Conclusions • Sawtooth locking experiments carried out (in TCV) • Power, duty cycle and frequency of input systematically varied • The sawtooth period robustly locks with power modulation in locking range [2]. Confirms simulations [1] • Locking range identified and applied for control • Locking is dynamic process, not instanteneous • [1] Witvoet et al. Nucl. Fusion 51 (2011) • [2] Lauret et al. Nucl. Fusion 52 (2012) EC17 Deurne 2012

  20. Suggestions for future work • Extendable to other periodic instabilities/relaxation oscillations? • Use feedback to adapt modulation (measure sawtooth period real-time) and improve locking and pacing control • Derive 1D o.d.e. for sawtooth period from data EC17 Deurne 2012

  21. EC17 Deurne 2012

  22. Simulink model: reset model (G.Witvoet) 31th Benelux meeting 2012, Heijen

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