October 2008, MPI fϋr Plasmaphysik, Garching 1 Performance limiting MHD phenomena in fusion devices: physics and active control M. Baruzzo Consorzio RFX, Associazione Euratom-ENEA sulla fusione, Padova Università di Padova

October 2008, MPI fϋr Plasmaphysik, Garching 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 2

October 2008, MPI fϋr Plasmaphysik, Garching 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 3

October 2008, MPI fϋr Plasmaphysik, Garching 4 Introduction to MHD limiting phenomena Reactorial high beta (tokamak) steady state operation (tokamak, RFP) Reactorial high beta (tokamak) steady state operation (tokamak, RFP) Determination of q profile's evolution Determination of q profile's evolution Prevention of beta collapses and disruptions Prevention of beta collapses and disruptions

October 2008, MPI fϋr Plasmaphysik, Garching 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 5

October 2008, MPI fϋr Plasmaphysik, Garching RFP equilibrium 6 The goodness of confinement is identified by poloidal beta RFP equilibrium is characterized by the two field components of the same order of magnitude, and the reversal of B  at the edge The equilibrium parameters are

October 2008, MPI fϋr Plasmaphysik, Garching 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 7 Experiment overview: RFX-mod

October 2008, MPI fϋr Plasmaphysik, Garching MHD active control in RFX-mod Possibility to let predefined modes free of control 8 ALGORITHMS FOR MHD ACTIVE 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 Mode Control Control applied to each MHD mode with different control parameters (PID), Fourier space control Virtual Shell Acquisition of 192x3 signals from sensors FFT Action of control algorithm inverse FFT Creation of 192 references to feed active coils 500μs Digital controller (PID)‏ More information in L. Piron’s talk

October 2008, MPI fϋr Plasmaphysik, Garching 9 Time (s) MHD active control in RFX-mod The MHD control compulsory to reach high performance!

October 2008, MPI fϋr Plasmaphysik, Garching 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 10

October 2008, MPI fϋr Plasmaphysik, Garching 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, , 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)‏

October 2008, MPI fϋr Plasmaphysik, Garching 12 Resistive Wall Modes Why RWM studies in RFPs Optimization of active control strategies Comparison with theory and code benchmarking Interaction of RWM with rotating plasmas All important for tokamaks as well!! Drake J., Bolzonella T. IAEA 2008, Bolzonella T. et. al. Phys.Rew.Lett, accepted to publication Villone F. et. al. Phys.Rew.Lett (2008)

October 2008, MPI fϋr Plasmaphysik, Garching MHD instability description 13 The displacement of magnetic field lines from their equilibrium position is:  m,n is 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)

October 2008, MPI fϋr Plasmaphysik, Garching RWM behaviour in RFX-mod 14 Modes m=1 n=-6,-5,-4,-3 are called internal RWM (same helicity sign of magnetic field inside the toroidal field's reversal surface) ‏ Modes m=1 n=+3,+4,+5,+6 are called external RWM (same helicity sign of magnetic field outside the toroidal field's reversal surface) ‏ Non resonant modes (no magnetic surface inside the plasma in which the mode has the same toroidal and poloidal periodicity (m,n) of magnetic field's lines) ‏

October 2008, MPI fϋr Plasmaphysik, Garching RWM behaviour, discharge Flat plasma current profile

October 2008, MPI fϋr Plasmaphysik, Garching RWM behaviour, discharge Peaked plasma current profile

October 2008, MPI fϋr Plasmaphysik, Garching RWM growth rates predictions 17 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 Phys. Rev. Lett. P.R. Brunsell et all. Phys. Rev. Lett. 93 (2004)

October 2008, MPI fϋr Plasmaphysik, Garching Statistical analysis of RWM growth rates 18 Statistical study of growth rates as a function of plasma parameters (I, F, n, β θ ) Selected parameters are considered independent among theirselves, dependencies in F and β θ are known from the theory; I, n are considered to complete the variables set Statistical study of growth rates as a function of plasma parameters (I, F, n, β θ ) Selected parameters are considered independent among theirselves, dependencies in F and β θ 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 In the picture are shown the variation ranges of the considered plasma parameters An overall number of 234 pulses were analyzed

October 2008, MPI fϋr Plasmaphysik, Garching 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 19

October 2008, MPI fϋr Plasmaphysik, Garching 20 Statistical study for an internal mode, n=-5 Negative trend with IFI in agreement with theory

October 2008, MPI fϋr Plasmaphysik, Garching 21 Statistical study for an internal mode, n=-6 Negative trend with IFI in agreement with theory

October 2008, MPI fϋr Plasmaphysik, Garching Code Benchmarking on RWM statistical data 22 Linear cylindrical resistive incompressible MHD equations Boundary with up to two resistive thin walls ETAW Toroidal 2D single fluid MHD equations Boundary with vacuum region, thin conductive shells MARS-F Single fluid MHD equations solved inside a coupling surface Coupling to a 3D volumetric integral formulation of the eddy currents problem, conductive structures as a tridimensional finite element mesh CARMA Villone F. et. al. 35° EPS Conference, Crete, July 2008 Equilibr. A: F= Equilibr. B: F=-0.136

October 2008, MPI fϋr Plasmaphysik, Garching 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 23

October 2008, MPI fϋr Plasmaphysik, Garching Neoclassical Tearing Modes 24 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, (2006) 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, (2006)

October 2008, MPI fϋr Plasmaphysik, Garching Radial localization of modes using coherence 25 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)

October 2008, MPI fϋr Plasmaphysik, Garching Radial localization of NTM in JET tokamak With the help of B. Alper

October 2008, MPI fϋr Plasmaphysik, Garching Radial localization of NTM in JET: used diagnostics 27 High resolution magnetic coils (H302..) (up to 500kHz)‏ Off axis high resolution ECE radiometer KK3 KK3F signals (250kHz-1MHz)‏

October 2008, MPI fϋr Plasmaphysik, Garching Radial localization of NTM in JET: Analysis procedure Spectrogram and n number analysisTracking of the biggest modes in the fourier space Loading of 48 KK3F signals, smoothing and downsampling (250kHz), with checks on signal's saturation, and density cut off. Calculation of coherence for each ECE channel and for each mode, in a narrow frequency band (~0.5-1 kHz) around the frequency of the mode, for the whole KK3F window. The sub-windows in which an ELM is present are discarded (H-alpha). 28

October 2008, MPI fϋr Plasmaphysik, Garching Coherence and phase radial profiles The phase jump radii are recognized automatically. 29 n=2 n=3

October 2008, MPI fϋr Plasmaphysik, Garching Coherence and phase radial profiles The phase jump radii are recognized automatically. 30 n=2 n=3

October 2008, MPI fϋr Plasmaphysik, Garching 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 31

October 2008, MPI fϋr Plasmaphysik, Garching Detailed analysis for JET pulse TFS1 High current, high triangularity, 2.5MA, 2.7T Move inner strike point of 14 cm from 18.8 to 19.8s

October 2008, MPI fϋr Plasmaphysik, Garching Absolute amplitude and frequency 33

October 2008, MPI fϋr Plasmaphysik, Garching Radial localization of tearing modes (tracked) ‏ 34

October 2008, MPI fϋr Plasmaphysik, Garching Checked consistency with EFIT 35

October 2008, MPI fϋr Plasmaphysik, Garching 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 36

October 2008, MPI fϋr Plasmaphysik, Garching Conclusions and (near) future developments 37 RWM statistical study For internal RWM a negative trend of growth rates in respect to I F I 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 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

October 2008, MPI fϋr Plasmaphysik, Garching Thanks for your attention! The end 38

October 2008, MPI fϋr Plasmaphysik, Garching Multi-parameter fit Growth rates fitted using the trial function: Negative trend of gro wth rates in IFI for external modes, positive trend for external modes (according to theory) Strange behaviour of n=6 mode (error fields?) β θ and n trend negligible High uncertainty and poor statistic for external modes (new experiments planned) 39

October 2008, MPI fϋr Plasmaphysik, Garching Average RWM growth rates IFI < < IFI < < IFI <

October 2008, MPI fϋr Plasmaphysik, Garching 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 41

October 2008, MPI fϋr Plasmaphysik, Garching ECE density cut off 42 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

October 2008, MPI fϋr Plasmaphysik, Garching Mode analysis for JET pulse

October 2008, MPI fϋr Plasmaphysik, Garching Radial localization of tearing modes 44

October 2008, MPI fϋr Plasmaphysik, Garching Checked consistency with EFIT 45