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
MAST plaatje gebruiken? Kleuren? Pixels? , welke auteurs? Deze style? Abstract naar FOM sturen!!
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)
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3. Introduction: Sawtooth crash
Periodic instability in magnetic field
Sawtooth crash->temperature crash: relaxation oscillation
The sawtooth period can be measured by change in temperature. Why is the sawtooth so important? It can create a lot of instabilities and misery! Control of the period is essential for multiple reason
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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
Resultaten als teazer presenteren. Sawtooth period is the time between two consecutive sawtooth crashes. We need a pacemaker for the plasma.
TCV in Lausanne, Switzerland.
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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)
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6. q-profile evolution (CRONOS)
r(q=1)
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7. ECCD launchers on TCV
Courtesy of F.Felici
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8. q-profile influence (CRONOS)
s(q=1)
ECCD
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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)
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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
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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
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12. Locking (and pacing)
Courtesy of F.Felici
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13. Simulink simulations (G.Witvoet)
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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
Plaatje?
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15. Sawtooth period locking (TCV)
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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.
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17. Sawtooth period locking
Locking range: locking depends on duty cycle, modulation period and power level. Green area is locking area.
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18. Open loop control
Open loop control is without using real-time processing of measurements.
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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)
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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
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21. EC17 Deurne 2012

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