de Vries, P.

Havlicek, J.

Klevarová, Veronika

Komm, M.

Lehnen, M.

Markovic, T.

Pautasso, G.

Verdoolaege, Geert

Zohm, H.

Klevarova, V.

Zohm, H. 

Vries, P.

MPG.PuRe

Multi-device study of MHD modes locking in tokamaks

Ghent University Academic Bibliography

This work was supported by the European Commission and carried out within the frameworks of the Erasmus Mundus International Doctoral College in Fusion Science and Engineering (FUSION-DC) and of the EUROfusion Consortium and has received funding from the Euratom research and training programme 2014-2018 under grant agreement No 633053. The views and opinions expressed herein do not necessarily reflect those of the ITER Organization or the European Commission.  * See the author list of “X. Litaudon et al Nucl. Fusion 57 102001 (2017)” + See the author list of “H. Meyer et al Nucl. Fusion 57 102014 (2017)” • Tearing modes are observed to cause disruptions in tokamaks, prior to the disruption   onset, modes are either locked or rotating:                          ROT – rotating until disruption             ROT->LM – initially rotating mode,             locked at the disruption onset            BLM – born-locked mode                  • Multi-device database of disruptive            discharges assembled, suitable for            study of disruption precursors (Tab.1)                 • Fraction of  ROT/ROT->LM/BLM           scales with device size                 • In disruption prediction schemes,           it might be desirable to implement           amplitude of rotating modes, else           risk of missing ROT (Fig.1)        • Different disruption avoidance techniques may be applied for ROT and LM   → At what mode amplitude is locking initiated?    → What determines the ROT/ROT->LM/BLM fraction in particular device?  • Answering RQs with the ROT/ROT->LM devices databases (> 150 COMPASS, > 220 AUG, > 40 JET cases) might help to estimate conditions for mode locking in ITER MULTI-DEVICE STUDY OF MHD MODES LOCKING IN TOKAMAKS V. Klevarová1, G. Pautasso2, H. Zohm2, P.C. de Vries3, M. Lehnen3, T. Markovič4,5, M. Komm4, J. Havlíček4,  G. Verdoolaege1,6, JET contributors*, the EUROfusion MST1 team+ and the ASDEX Upgrade team  1Department of Applied Physics, Ghent University, Sint-Pietersnieuwstraat 41, B-9000 Ghent, Belgium 2Max-Planck-Institut für Plasmaphysik, 85748 Garching, Germany  3ITER Organization, Route de Vinon sur Verdon, CS 90 046, 13067 St Paul Lez Durance, Cedex, France 4Institute of Plasma Physics of the CAS, Za Slovankou 1782/3, 182 00, Prague, Czech Republic 5Faculty of Mathematics and Physics, Charles University, Prague, Czech Republic 6Laboratory for Plasma Physics, Royal Military Academy (LPP-ERM/KMS), B-1000 Brussels, Belgium  • Equation of mode motion comprises sum of all torques exerted on the island mass   • Motion restoring viscous force FVS and braking resistive wall force FRW considered [2]       • Search for points of balanced forces, i.e. solutions of           , for increasing {w/a}                 → multiple solutions ∃ for {w/a} ∈ [{w/a}crit,min {w/a}crit,max], at {w/a}  = {w/a}crit,max last stable  solution is met and for further {w/a}    , mode decays from                   to low-    solution • Condition of {w/a}crit,max ∃:                For further {w/a}   ,                                      and    • Example of integration of (2) for an AUG-like set of input parameters (Tab.2) is in Fig.4            • AUG ROT/ROT->LM database is populated with various instabilities (explosively growing, immediately locking radiation-driven modes near the density limit (Fig.5a), quasi-stable NTMs (Fig.5b)..)           • Median of rotation phase duration is ~ 23 ms, median growth rate (exponential or linear) ~ 6.0 ms-1 , 95 % of  w/acrit,max evaluated with Eq.4 are within interval w/acrit,max ~ [7 28] %  • Median of braking resistive wall torque at the initiation of the mode slowing down phase ~ 0.06 Nm → torque too low to cause mode locking in any of the database entries, an            example is shown in Fig.6                   APPLICATION OF MODEL TO THE AUG EXPERIMENT MODE LOCKING MODEL SUMMARY & OUTLOOK • Simple model for mode locking incorporating restoring viscous force and braking      resistive wall force was used to characterize mode locking in AUG  • Model allows to define critical condition for mode locking exactly (Eq.4), calculated     critical island sizes are in reasonable correspondence with experimental data points • However, experimental time traces were not reproduced due to too weak a wall drag • Model requires modification, in terms of adding braking force and/or modification of the already considered terms • Formulas (2,4) incorporate device&discharge dependent parameters enabling direct         comparison of experimental time traces with that predicted by the model • First, model applicability tested on AUG ROT/ROT->LM database entries     necessary input for model test collected and validated:                COLLECTION AND VALIDATION OF EXPERIMENTAL DATA   [1] P.C. de Vries et al., Nucl. Fusion 56 (2016) 56026007, [2] R.J. La Haye et al., Nucl. Fusion 46 (2006) 451, [3] Chang, Z. et al., Nucl. Fusion 36 (1996) 219, [4] M.F.F. Nave, J.A. Wesson, Nucl. Fusion 30 (1990) 2575, [5] D.A. Gates et al., Nucl. Fusion 36 (1996) 273, [6] N.C. Logan et al., Plasma Phys. Control. Fusion 52 (2010) 045013 veronika.klevarova@ipp.mpg.de INTRODUCTION DEVICE # of database entries a [m] R0 [m] ROT/ROT->LM/BLM [%] COMPASS 283 0.18 0.56 55/40/5 AUG full-W wall 457 0.50 1.65 21/56/23 JET-ILW 281 1.0 2.96 5/52/43 Tab.1 Parameters concerning the full multi-device database of disruptive discharges RQs Fig.1 (a) Spectrogram showing the presence of disruptive ROT  (b) mode amplitude measured by sensors sensitive to ROT/LM  and the predicted LM disruptive amplitude  [1] a) b) ~ ~ ~ only toroidal motion assumed (1) (2) In [2],                                   is proposed, adopting model for             degradation [3]                    as presented in [4], assuming the  whole plasma decelerating with the mode+  REFERENCES {w/a}1 {w/a}2 {w/a}3 = {w/a}crit,min  {w/a}5 = {w/a}crit,max  {w/a}4 {w/a}6 Fig.2 FVS – FRW plotted for increasing {w/a}, shown as a function of dimensionless ωτw Fig.3 Trajectories of single&multiple solutions of (2) = 0 presented in Fig.2 shown for increasing {w/a} mode initial rotational frequency ‘forbidden’ frequency range [5] last stable solution low-ω solution (3) B = 0 → (4) Fig.4 Evolution of the mode rotational frequency prescribed by (2) for the AUG-like standard set, B = 0; island width growth was prescribed by  w/a = w/as(t/τ) τw [ms] q95 R0 [m] ω0/2π [kHz] τM0 [ms] m/n 1.0 3.6 1.65 3.5 50 2/1 B Ip [MA] BT [T] ne [m-3] rs/a 1.0 1.0 2.5 5.0e19 1.0 Tab.2 AUG-like set of parameters submitted to (2) integration *plasma modeled as a rigid body, +derived for cylindrical plasma Mode frequency and amplitude → tracked with help of spectrograms  retrieved by set of Mirnov coils  Mode m/n structure → retrieved with the help of phase fitting m/n 2/1 3/1 4/1 other % of cases 42 50 6 <2 MHD equilibrium reconstruction → for modes evolving in flat-top phase q0 = 1 set,    rs compared with phase jump in ECE records Resistive wall time → set to inverse of typical growth rates of RWMs, i.e. τ𝑤 = 10 ms Momentum confinement time → retrieved for ~ 140 shots with TRANSP code, If unavailable, calibration τ𝑀0 = 1.8 · τ𝐸0 used Island width → cylindrical formula for w calculation used, calibrated with ECE records Plasma density → retrieved preferentially with HRTS records, if unavailable, with interferometer core LoS data  Fig.5 (a,b) Examples of ROT/ROT->LM AUG database entries, encircled are points of initiation of mode deceleration a) b) Fig.6 Experimental ω and w/a times traces, shown together with the result of integration of Eq.(2) for the respective input parameters. Note that the resulting ω = f(t) does not lock within the designated temporal window. Integration result approaches experimental points when a trial integration is performed, multiplying A by a factor ~ 100 • Force balance (2) is       incomplete and does not       describe mode locking in AUG  resistive wall force is weak  by a factor ~ 100  other braking terms (e.g.   interaction with the intrinsic   error fields) should be  considered or  existing to  be modified  * similar problem encountered in [6], addressing mode locking in DIII-D → authors proposed to include in FRW a 2nd resistive wall, mimicked by in-vessel tiles, of  τ𝑤  ≫ τ𝑡𝑖𝑙𝑒𝑠   * First author would like to thank ASDEX Upgrade team  members that contributed to the here presented work, especially to M. Maraschek, A. Gude, G. Tardini , T. Odstrčil (former AUG team member) and R. McDermott. 

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Multi-device study of MHD modes locking in tokamaks

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Ghent University Academic Bibliography