Performance limiting MHD phenomena in fusion devices: physics and active control M. Baruzzo

Performance limiting MHD phenomena in fusion devices: physics and active control M. Baruzzo Consorzio RFX, Associazione Euratom-ENEA sulla fusione, Padova Università di Padova

Outline • Introduction to MHD limiting phenomena • Short description of RFX-mod experiment and of its MHD active control system • RWM in RFX-mod, phenomenology and statistical analysis • NTMs, physics and a method for radial localization • Examples of NTMs localization at JET • Conclusion and future developments

Introduction to MHD limiting phenomena Reactorial high beta (tokamak) steady state operation (tokamak, RFP) RWM understanding and control In tomamaks and RFPs NTM localization and control in Tokamaks Prevention of beta collapses and disruptions Determination of q profile's evolution

RFP equilibrium RFP equilibrium is characterized by the two field components of the same order of magnitude, and the reversal of Bfat the edge The equilibrium parameters are The goodness of confinement is identified by poloidal beta

Experimentoverview: RFX-mod • Large RFP, major radius 2m, minor radius 0.459m. • Vacuum toroidal field up to 0.7T, maximum plasma current of 2MA. • Conductive shell with vertical field penetration time of 50ms, discharge length 500ms • Control of MHD instabilities by mean of an extensive set of active saddle coils (2005)‏ • The shell's external surface is covered by 48(toroidal)x4(poloidal) active coils, each independently fed, each able to produce a radial magnetic field up to 50mT • Each active coil corresponds to a radial magnetic sensor that covers the same solid angle, placed on the internal surface of the shell

MHD active control in RFX-mod Digital controller (PID)‏ Possibility to let predefined modes free of control Acquisition of 192x3 signals from sensors Creation of 192 references to feed active coils Action of control algorithm inverse FFT FFT 500μs ALGORITHMS FOR MHD ACTIVE CONTROL Virtual Shell Mode Control Control applied to each active coil with different control parameters (PID), freezing to zero the radial magnetic flux in each sensor, real space control Control applied to each MHD mode with different control parameters (PID), Fourier space control More information in L. Piron’s talk

Time (s) MHD active control in RFX-mod

Resistive Wall Modes • In absence of conductive structures near the plasma they grow as ideal kink modes (helical deformation of field lines, radial displacement) • These modes are stabilized by a perfectly conductive wall very close to the plasma edge • If the wall is a resistive shell their growth rate is related to the timescale of the magnetic field penetration time in the wall (First discovery in a RFP experiment, B. Alper, PPCF 31 no. 2, 205-212, 1989) their control is compulsory for long time operation Control strategies Fluid rotation of bulk plasma (partially effective in tokamaks)‏ Active feedback control (effective in RFPs and tokamaks)‏

Resistive Wall Modes Drake J., Bolzonella T. IAEA 2008, Bolzonella T. et. al. Phys.Rew.Lett, acceptedtopublication Villone F. et. al. Phys.Rew.Lett 100 255055 (2008) All important for tokamaks as well!!

MHD instability description The displacement of magnetic field lines from their equilibrium position is: gm,nis called mode's growth rate, if it is positive the mode is unstable, if it is negative or null the mode is stable m and n are the mode wave numbers, they point out the periodicity of the mode in toroidal geometry Example of kink perturbation m=1, n=8 (x10)

RWM behaviour in RFX-mod

RWM behaviour, discharge 17304 Flat plasma currentprofile

RWM behaviour, discharge 17327 Peaked plasma currentprofile

RWM growth rates predictions Linear MHD calculation of RWM growth rates normalized to the shell's time costant for two equilibria: Θ=1.55 (solid) e Θ=1.78 (dashed) in T2R RFP P.R. Brunsell et all. Phys. Rev. Lett. 93 (2004)

Statistical analysis of RWM growth rates • Statistical study of growth rates as a function of plasma parameters (I, F, n, βθ) • Selected parameters are considered independent among theirselves, dependencies in F and βθ are known from the theory; I, n are considered to complete the variables set • In the picture are shown the variation ranges of the considered plasma parameters • An overall number of 234 pulses were analyzed

Growth rates calculation For each free mode the logarithm of the signal was linearly interpoled in the range in which a single exponential growth was found

Statistical study for an internal mode, n=-5 Negative trend with IFI in agreement with theory

Statistical study for an internal mode, n=-6 Negative trend with IFI in agreement with theory Negative trend with IFI in agreement with theory

Code Benchmarking on RWM statistical data Equilibr. A: F=-0.073 Equilibr. B: F=-0.136 Villone F. et. al. 35° EPS Conference, Crete, July 2008

Neoclassical Tearing Modes TM are modes that cause tearing and reconnection of magnetic field lines, creating magnetic islands at the singular layer q=m/n (resonant modes) because of finite plasma resistivity. TM linear stability is determined by the plasma current profile (minimum magnetic energy principle) Bootstrap current is a toroidal effect induced by momentum unbalance between passing and trapped particles, this unbalance is determined by the radial gradient of plasma pressure, therefore bootstrap current depends on the beta parameter NTMs are TM destabilized by an helical perturbation of bootstrap current, caused by the flattening of the pressure profile inside the island, which can change the local bootstrap profile and affect the non linear stability of the TM NTMs appearance leads to a strong degradation of confinement and beta, and also may lead to disruptions NTM radial location can flag the position of a resonant surface, giving the possibility to reconstruct the radial magnetic q profile, for this reason NTMs are also called MHD markers H. Zohm et. Al, Nucl. Fus. 41, No. 2 (2001) R.J. La Haye, PoP 13, 055501 (2006)

Radial localization of modes using coherence Magnetic fluctuation Diagnostic fluctuation Study of the average cross-coherence in Fourier space • Chance to inspect the radial structure of the magnetic perturbation by studying profiles of • Chance to radially locate magnetic islands localized at phase inversion radius (flattening of internal temperature of the island, P. De Vries PPCF 39 (1997) 439-451

Radial localization of NTM in JET tokamak With the help of B. Alper

Radial localization of NTM in JET: used diagnostics • Off axis high resolution ECE radiometer KK3 • KK3F signals (250kHz-1MHz)‏ • High resolution magnetic coils (H302..) (up to 500kHz)‏

Radial localization of NTM in JET: Analysis procedure

Coherence and phase radial profiles The phase jump radii are recognized automatically. n=2 n=2 n=3 n=3 n=2 n=2

Detailed analysis for JET pulse 73519 TFS1 High current, high triangularity, 2.5MA, 2.7TMove inner strike point of 14 cm from 18.8 to 19.8s

Absolute amplitude and frequency

Radial localization of tearing modes (tracked)‏

Checked consistency with EFIT

RWM statistical study For internal RWM a negative trend of growth rates in respect to IFI was found. Other dependencies are negligible For external RWM the trend in IFI is not totally clear in the present database, more experimental time is needed to better understand n=6 behaviour All of the modes have negligible rotation speed, and grow locked to the wall The statistical analysis may be extended to plasma rotation speed (important in tokamaks) Future work will aim at enlarging the statistical database, comparing experimental results with modelling, and investigating Resonant Field Amplification phenomena, with emphasis on issues common to tokamaks and RFPs Conclusions and (near) future developments NTM radial localization Same analysis method of Central Acquisition Trigger System, but totally automatic and independent Same diagnostic as CATS with a window of 12 seconds (six times larger)‏ Rather large number of points and high temporal resolution Under development an algorithm to track mode’s position temporal evolution, the ultimate goal is unattended batch implementation and PPF writing

The end Thanks for your attention!

Multi-parameter fit Growth rates fitted using the trial function: • Negative trend of growth rates in IFI for external modes, positive trend for external modes (according to theory) • Strange behaviour of n=6 mode (error fields?) • βθ and n trend negligible • High uncertainty and poor statistic for external modes (new experiments planned)

Average RWM growth rates IFI < 0.1 0.1< IFI < 0.2 0.2< IFI < 0.3

Radial localization of NTM in JET: Analysis procedure • Calculation of |M|2, |D|2, MD* for each sub-block • Average of this quantities on (16) sublocks • Calculation of amplitude and phase • All the calculation is performed in a narrow frequency band

ECE density cut off Two plasma mode: O-mode, linear polarization with E//B X-mode, elliptically polarized with E┴B O-mode cutoff at X-mode cutoff at And at

Mode analysis for JET pulse 72669

Radial localization of tearing modes

Checked consistency with EFIT

Performance limiting MHD phenomena in fusion devices: physics and active control M. Baruzzo