Artola, F.

Hoelzl, M.

Lehnen, M.

Loarte, A.

Pitts, R.

Schwarz, N.

English

MPG.PuRe

3D MHD simulations of unmitigated Vertical Displacements Events inITERF.J. Artola1, A. Loarte1, M. Hoelzl2, N. Schwarz2, M. Lehnen1, R.A. Pitts1 and the JOREK team31 ITER Organization, St. Paul Lez Durance, France2 Max Planck Institute for Plasmaphysics, Garching, Munich3 please refer to [M Hoelzl, G T A Huijsmans, S J P Pamela, M Becoulet, E Nardon, F J Artola,B Nkonga et al, Nuclear Fusion 61, 065001 (2021)]One of the high priority research needs for the ITER project is the development of a solidphysics basis for plasma disruptions and their mitigation. Present predictions for the thermaland electromagnetic loads caused by unmitigated Vertical Displacement Events (VDEs) rely onexperimental observations and axisymmetric simulations [1]. 3D effects, such as the sidewaysvacuum vessel (VV) force produced by toroidally asymmetric VDEs, must be understood to pro-vide the basis for load validation in support of the ITER Research Plan and to make predictionsfor full current operation. Previous 3D simulations of ITER unmitigated VDEs reported a max-imum sideways force of Fh ∼ 30 MN [2], but the plasma current evolution Ip(t), as well as theThermal Quench (TQ) were artificially imposed. In this paper, we provide simulations of the TQphase as well as the initial Current Quench (CQ) phase for an ITER 15 MA unmitigated VDE.The novelty of this work is that the TQ occurs naturally and the evolution of Ip and the edgesafety factor (q95) is calculated self-consistently. Special attention is paid to the TQ onset, TQduration and the heat-flux decay length λq during the TQ. The initial phase of the CQ is alsoanalysed, with particular interest in the evolution of q95. It is thought that the cause of the side-ways force is the growth of a 1/1 MHD mode which occurs once q95 drops to a value of 1, andthus, a key question is how q95 reaches unity considering that the disruptive kink limit occursalready at q95 ∼ 2.2 4 6 8 10T/ T (cm)2.55.07.510.012.515.017.520.0/ne0 (m2 /s)ReferenceSet 2Figure 1: Perpendicular thermal conductivitycoefficients with ne0 = 5.4×1019 m−3.To address these issues, the MHD code JOREK[3, 4] is employed together with the STARWALLcode [6] that includes the effect of coils andpassive conductors. The included ITER relevantpassive conductors are taken as in [7]. The ini-tial condition for the presented simulations is anITER 15 MA L-mode reference equilibrium mod-elled with CORSICA [5]. The following Dirichletboundary conditions were chosen at the plasma-48th EPS Conference on Plasma Physics P5a.111wall interface Te = 1 eV, ne = 1.1× 1019 m−3 and no normal-flow conditions [7]. AlthoughJOREK has different model extensions, here we use the single temperature model without impu-rities employed in [7] but including the Ohmic heating term. Validation activities for this modelwith unmitigated ASDEX-Upgrade VDE experiments can be found in [8].TQa)b)c)d)e)Figure 2: Reference upward VDE evolu-tion with fscale = 20 and κmin∥ = κ∥(30eV ).(a) Vertical position and poloidal halocurrent. (b) Integral VV forces. (c) Ther-mal energy and total plasma current. (d)Edge safety factor. (e) Poloidal magneticenergy for different toroidal mode num-bers. The dashed lines represent an ax-isymmetric run without a TQ.Since unmitigated VDEs in ITER are expected to oc-cur on time-scales given by the wall time ∼ 500 ms,complete 3D JOREK simulations with present capabil-ities imply years of runtime. To make the simulationscomputationally feasible, we choose a set of expectedparameters for an ITER L-mode plasma (see Table 1and Figure 1) and rescale them by a common factorfscale. The rescaled parameters are (η , ηw, D, κ⊥, κ∥)so that the characteristic diffusion times of current, par-ticles and energy become fscale times shorter. This re-duces the computational cost since the simulation timestep is typically determined by the Alfvén time. Therescaling procedure gives an identical evolution (butwith the time axis scaled) to axisymmetric (2D) sim-ulations with realistic parameters.For the VDE initiation and direction, a current per-turbation of ±20 kA is applied in the in-vessel verti-cal stability coils (VS3). Next, the plasma moves verti-cally on a time-scale given by the wall time at roughlyconstant Ip (see Figure 2 a, c) since the plasma tem-perature remains sufficiently high. The shrinkage of theplasma volume caused by the VDE and the constancyof Ip causes a drop in q95 (since q95 ∝ a2/Ip). Once q95approaches a value of 2, low−n external kink modesbecome unstable at the plasma edge, which lead to theTQ onset (see Figure 2 c, d, e). In addition, a 1/1 core mode develops due to the presence of aq = 1 surface inside the plasma. The growth of the external kink modes causes a stochastic fieldline front that propagates from the plasma edge to the core. The temperature decreases in theopen field line region until parallel conduction becomes no longer effective.48th EPS Conference on Plasma Physics P5a.111Parameter Value DescriptionD 2 m2/s Isotropic particle diffusionκ⊥ ∇T -dependent (see Figure 1) Perp. thermal conductivitySpitzer-Haerm ∝ T 5/2eκ∥ κmax∥ = κ∥(0.3/1keV) Parallel thermal conductivityκmin∥ = κ∥(1/30eV)Spitzer ∝ T−3/2e with Ze f f = 1.12η ηmax = η(1eV) Parallel resistivityηmin = η(300/∞eV)ηw/dw 13.3 µΩ Wall resistivity over thickness(ν⊥,ν∥) (2,297) m2/s Perp./Parallel viscosityTable 1: Unscaled simulation parameters. Redvalues correspond to the cases labelled as "Set 2".The values for ν are evaluated for a density ofne0 = 5.4×1019 m−3.The latter can be observed in Figure 3, wherethe transition to closed field lines is correlatedwith a change in the Te gradient. The stochas-tic front does not penetrate all the way to themagnetic axis and stops approximately at half-radius. The final core temperature collapse iscaused by the 1/1 mode which enhances thecore transport.The dependence of the TQ duration on fscaleis studied in order to extrapolate to ITER pa-rameters. We define the TQ duration τWthT Q by us-ing the times where the thermal energy decaysfrom 90% to 20% of the pre-TQ value as it was defined in [9].Figure 3: (Upper) Electron temperatureprofile at the Zaxis midplane. (Lower)Traced field line length before intersect-ing the first wall for different points inthe midplane. The line colors correspondto time instances with different fractionsof the pre-TQ thermal energy. The dashedlines indicate the transition between openand closed field lines.The results shown in Figure 4 a) suggest that τT Q ∝f−1scale and that predicted values for ITER parameters willbe larger than 10 ms (up to 60 ms). However impu-rity radiation is not included in this work, and there-fore these values represent upper limits. The maxi-mum n = 1 growth rate in the linear phase is foundto scale with fscale, which is consistent with τT Q ∝f−1scale if the stochastic front propagation is given bythe n = 1 growth. Such growth rate scaling is similarto the RWTM scaling proposed by [10], which givesγ ∝ f 0.8scale.When using the drop of the core temperature to char-acterize the TQ duration, a big scatter in τWthT Q/τTe,coreT Qis found in the simulations (0.8-6.5) as well as in JETVDE experiments (1-4) [9].To characterize the heat flux decay length during theTQ (λq), we use the following definition to define atoroidally averaged decay length < λq >< λq >=PSOL4πROMPLCFS (Bθ/Bφ )OMP max(< qOMP∥ >)(1)where "OMP" denotes that quantities are evaluated at the outer midplane, PSOL is the total48th EPS Conference on Plasma Physics P5a.111a) b)Figure 4: (a) TQ duration as a function of fscale for different parameter variations. (b) Time traces of thethermal energy and < λq > for different fscale values for the "Set 2" parameters.thermal power reaching the first wall, ROMPLCFS is the major radius at the plasma boundary and< qOMP∥ > is the toroidal average of the parallel heat flux mapped from the first wall to the OMP.The chosen diffusion parameters lead to a pre-TQ < λq >∼ 1 cm for the set of parameters "Set2" (which has less restricting thresholds) as indicated in Figure 4 b). During the TQ, < λq >expands to 2-3 cm without a clear dependence on fscale.Finally we note that the MHD activity during the TQ is able to pause the decay of q95 byinducing halo currents (Figure 2 a,d). After the TQ, q95 continues to decay at a similar rate as inthe axisymmetric simulation despite the continued growth of the n = 1 mode. This points to thepossibility of attaining q95 = 1 in ITER leading to large horizontal VV forces. The simulationsmust continue to assess this issue, but the strong non-linearities pose a challenging convergenceto the JOREK solver.Acknowledgements ITER is the Nuclear Facility INB No. 174. This work explores the physics processes during plasma operation of the tokamak when disruptions take place; neverthelessthe nuclear operator is not constrained by the results presented here. The views and opinions expressed herein do not necessarily reflect those of the ITER Organization. The simulationspresented here have been performed using the JFRS-1 and the ITER HPC clusters. This work has been carried out within the framework of the EUROfusion Consortium, funded by the EuropeanUnion via the Euratom Research and Training Programme (Grant Agreement No 101052200 — EUROfusion). Views and opinions expressed are however those of the author(s) only and do notnecessarily reflect those of the European Union or the European Commission. Neither the European Union nor the European Commission can be held responsible for them.References[1] M. Lehnen, et al., Journal of Nuclear Materials 463, 39-48 (2015)[2] H. Strauss, Physics of Plasmas 25, 2 (2018)[3] G. T. A. Huysmans, and O. Czarny, Nuclear fusion 47, 7 (2007)[4] M. Hoelzl, et al., Nuclear Fusion 61, 6 (2021)[5] S.H. Kim, et al, Nuclear Fusion 57, 8 (2017)[6] P. Merkel, and E. Strumberger, arXiv preprint arXiv:1508.04911 (2015).[7] F.J. Artola, et al, Nuclear Fusion 62, 5 (2022)[8] N. Schwarz, et al, 48th EPS Conference on Plasma Physics I3.101 (2022)[9] G. Arnoux, et al, Nuclear Fusion 49, 8 (2009)[10] H. Strauss, Physics of Plasmas 28, 7 (2021)48th EPS Conference on Plasma Physics P5a.111

3D MHD simulations of unmitigated Vertical Displacements Events in ITER

http://hdl.handle.net/21.11116/0000-000B-F488-8

3D MHD simulations of unmitigated Vertical Displacements Events in ITER

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