Boboc, A.

Bonfiglio, D.

Carvalho, P.

Hender, T.

Hoelzl, M.

Hu, D.

Jachmich, S.

Kong, M.

Lawson, K.

Nardon, E.

Sheikh, U.

Silburn, S.

Sweeney, R.

Szepesi, G.

Štancar, Ž.

English

MPG.PuRe

Interpretative 3D MHD modelling of deuterium shattered pellet injectioninto a JET H-mode plasmaM. Kong1, E. Nardon2, M. Hoelzl3, D. Bonfiglio4, D. Hu5, U. Sheikh6,A. Boboc1, P. Carvalho1, T.C. Hender1, S. Jachmich7, K.D. Lawson1, S. Silburn1,Ž. Štancar1, R. Sweeney8, G. Szepesi1, the JOREK team∗ and JET contributors†1 UKAEA-CCFE, Culham Science Centre, Abingdon, Oxon, OX14 3DB, UK2 CEA, IRFM, F-13108 Saint-Paul-lez-Durance, France3 Max Planck Institute for Plasma Physics, Boltzmannstr. 2, 85748 Garching b. M., Germany4 Consorzio RFX, Corso Stati Uniti 4, 35127 Padova, Italy5 School of Physics, Beihang University, Beijing, 100191, China6 École Polytechnique Fédérale de Lausanne (EPFL), Swiss Plasma Center (SPC), CH-1015Lausanne, Switzerland7 ITER Organization, Route de Vinon sur Verdon, CS 90 046, 13067 Saint Paul-lez-Durance,Cedex, France8 Massachusetts Institute of Technology, Cambridge, MA 02139, USAIntroductionShattered pellet injection (SPI) is the current solution for the ITER disruption mitigationsystem (DMS) to prevent disruption-related damage. Compared with impurity SPI, deuterium(D2) SPI could contribute to runaway electron (RE) avoidance via strong dilution cooling beforethermal quench (TQ) [1,2]. However, the drifts of ablation plasmoids towards the tokamak lowfield side (LFS) [3,4] and the existence of background impurities [2] could put this strategy intoquestion. In this work, we have performed detailed modelling of a JET D2 SPI discharge withJOREK [5], focusing on these two aspects. The JET H-mode plasma considered (#96874) has aplasma current Ip ≈ 3MA, thermal energy Wth ≈ 7MJ, central electron temperature Te0 ≈ 7keVand central electron density ne0 ≈ 8.5×1019m−3 before the SPI [6, 7]. A D2 pellet with about1.6× 1023 atoms was launched and broke into two pieces before shattering, leading to twogroups of shards arriving at the plasma about 3.5ms apart (25% atoms contained in the 1stgroup). The pre-TQ duration, defined here as the time elapsed from the time when the 1st groupof shards reach the plasma edge (t = 0 in this paper) to the Ip spike, is about 9.5ms.Numerical model and simulation setupThe basic model used consists of reduced MHD equations, diffusive neutrals and an extensionfor SPI [1]. The ablation rate is estimated by N′ ∝ r1.33s n0.33e T1.64e , where rs is the shard radius, nethe electron density and Te the electron temperature. The ablated neutrals are deposited aroundeach shard with a Gaussian shape in the toroidal, poloidal and minor radius directions, the halfe−1 width of which are set to 0.5rad, 15cm and 2cm in this paper. Radiative cooling rates of∗See the author list of M. Hoelzl et al Nucl. Fusion 61 065001 (2021)†See the author list of J. Mailloux et al Nucl. Fusion 62 042026 (2022)48th EPS Conference on Plasma Physics O3.102background impurities are estimated using ADAS data and assuming coronal equilibrium. Weare limited by spatial resolution of 3D simulations to directly resolve ablation plasmoid drifts.Instead, we propose a “teleportation” model to account for the particle and energy transfersresulting from drifts. The general idea is as follows: shifting the ablation neutral source along theoutward R direction by a certain distance (∆drift) from the shard’s location; transferring energyfrom the shard location to the deposited neutral location. The energy transfer rate correspondsto the ablation neutral source times a few tens of electron volts (∆E) to consider the overalleffects of dissociation, ionization, radiation and early heating before plasmoid drifts.The JOREK grid used comprises about 22000 finite elements on the poloidal plane and upto n = 10 Fourier components toroidally. Ti = Te is assumed. Spitzer resistivity ηsp is kept forTe up to 1.7keV, above which the resistivity is uniform. Central resistivity η0 ≈ 5ηsp. Spitzer-Härm parallel heat diffusivity is used, while perpendicular heat diffusivity κ⊥≈ 2m2/s. Parallelparticle transport is purely convective except at the entry of post-drift plasmoids for numericalreasons, while D⊥ ≈ 2m2/s. The bulk velocity of the two groups of shards is 300 and 260m/s,respectively, and each with a±40% velocity spread. The shard radii are distributed according toa fragmentation model [8], with 280 and 32 shards in the two groups, respectively. Only smallshards are present in the front and rear of the shard plume based on lab measurements [9].Effects of ablation plasmoid drifts on SPI shard ablation and penetrationDrifts of high-β plasmoids formed by the ablated material of frozen pellets have been ob-served in hydrogen isotope pellet fuelling experiments, e.g., plasmoids have shown to traverse20% of the minor radius in about 10 µs in AUG experiments [10]. In JET #96874, evidentoutward motion of shards was observed by the fast camera, possibly due to a rocket effect as-sociated with plasmoid drifts [10]. In fact, as shown by the red curve in Fig. 1 (a), the JOREKsimulation without plasmoid drifts clearly overestimates the central line-integrated density.0 2 4 6Time [ms]0.20.40.60.811.21.41.61.8210 21(a)JET polarimetry015cm20cm30cm0123410 25(b) Total ablation rate015cm20cm30cm0 2 4 6Time [ms]0246810 22(c) Total number of ablated particlesFigure 1: Scan of drift distance with 1×1017m−3 background neon and 4.5×1015m−3 tungsten.48th EPS Conference on Plasma Physics O3.1020 1 2 3 4 5Time [ms]00.20.40.60.811.2q=1q=2q=3030cmFigure 2: Average normalized Ψ location of theremaining shards from the 1st group at each timeslice for the red and green cases shown in Fig. 1.The effects of drifts are studied with the pro-posed teleportation model and fixed ∆E = 50eV:scans within its theoretical range do not showmuch difference. As for ∆drift, a scaling law ex-ists for fuelling hydrogen pellets [11], but maynot be directly applied to SPI cases consider-ing the modification of plasma profiles and in-teractions among plasmoids that were not in-cluded in the scaling law. Given the uncertain-ties, we have assumed the same ∆drift for all ab-lation plasmoids at this stage. Simulations with∆drift = 15,20 and 30cm are depicted in Fig. 1. 30cm matches best the measured density evo-lution. The total ablation rate N′ of all the shards, as shown in Fig. 1 (b), is much higher for thecases with drifts (before the entry of the post-drift ablation plasmoids indicated by the spikes).This is due to lower dilution cooling and higher local Te with drifts. After the arrival of post-driftplasmoids, N′ drops sharply and remains lower than in the case without drifts due to smallershard radii remaining. The 1st group of shards are fully ablated at t ≈ 4ms, as observed bythe fast camera. Simulations suggest a shallower penetration when considering plasmoid driftsgiven the strong ablation, as illustrated in Fig. 2.Effects of background impurities on radiative cooling during D2 SPIBackground impurities could dominate radiative cooling during D2 SPI due to their abil-ity to radiate more strongly [2]. In JET #96874, neon and carbon densities are nNE ≈ nC ≈1× 1017m−3 based on charge exchange measurements before the SPI; tungsten density nW ≈4.5× 1015m−3 is predicted with the 1.5D transport code JINTRAC, neglecting other (highcharge number) impurities that were present. We have performed scans of nNE and nC assum-ing spatially uniform distributions and fixed ∆drift = 30cm (that matches the measured density).As shown in Fig. 3 (a), background neon plays a key role in the radiative cooling during SPI,especially in the sharp Prad increase at t ≈ 6ms. This can be explained by the Te-dependence ofthe radiative cooling rates of different species, among which the radiative cooling rate of neonincreases by two orders of magnitude from 150 to 30eV. As shown in Fig. 4, neon radiationpeaks at Te = 30eV. We also note the effect of plasmoid drifts on Prad in Fig. 3 (a): the sharpincrease of Prad is missing for the case without drifts (red curve). This could be explained by thehigher ablation rate during the 2nd group of shards for cases with ∆drift = 30cm (green versusred traces in Fig. 1 (b)), which could lead to higher local pressure gradient and stronger MHD48th EPS Conference on Plasma Physics O3.102activity. As shown in Fig. 3 (b), high-n modes are excited and eventually lead to a fast growth ofall harmonics. These high-n modes are probably resistive interchange modes enabled by edgecooling (Fig. 4), similar to those evoked in relation to the Greenwald limit [12].0 2 4 6 8Time [ms]050100150200250300Prad [MW](a)JET bolometryNE1e17, w/o driftNE1e17NE1e18NE5e17+C5e172 3 4 5 6Time [ms]10 -1210 -1010 -810 -610 -4Magnetic energies [a.u.]5 10 1510 -1210 -1010 -810 -610 -4Magnetic energies [a.u.](b)12345678910Arrival of post-drift plasmoids (2nd group)Arrival of post-driftplasmoids (1st group)(b)5.6 5.8Ti e [ms]10 -4Figure 3: (a) Scan of nNE and nC with ∆drift = 30cm (except for the red curve) and nW = 4.5×1015m−3.(b) Magnetic energy evolution of the purple case in Fig. 3 (a).0.0e+00 5.0e+06Imp_bg_Ne_Wm150 eVTe=30 eVq=3q=2q=3/2q=1Activeshards-3Figure 4: Neon radia-tion for the purple casein Fig. 3 (a) at t ≈ 6ms.Conclusions and outlookThe pre-TQ dynamics of a JET D2 SPI discharge have been studiedin detail with JOREK. With a new teleporation model, ablation plas-moid drifts are shown to limit the penetration of LFS D2 SPI and affectMHD activity. Background impurities, especially neon in the consid-ered JET discharge, are shown to dominate radiative cooling during D2SPI by comparing with measurements. These could affect the effective-ness of D2 SPI in RE avoidance and need to be considered in ITER pre-dictions. In future studies, we will explore the effects of non-uniformdrift distance and finite mixture of neon in the pellet on plasmoid drifts.Further validation of D2 SPI against additional experiments on JET andAUG are also envisaged.This work has been carried out within the framework of the EUROfusion Consortium, funded by theEuropean Union via the Euratom Research and Training Programme (Grant Agreement No 101052200— EUROfusion) and from the EPSRC [grant number EP/T012250/1]. To obtain further information onthe data and models underlying this paper please contact PublicationsManager@ukaea.uk. Views andopinions expressed are however those of the author(s) only and do not necessarily reflect those of theEuropean Union or the European Commission or the ITER organization. Neither the European Unionnor the European Commission can be held responsible for them.References[1] D. Hu et al, Nucl. Fusion 58, 126025 (2018)[2] E. Nardon et al, Nucl. Fusion 60, 126025 (2020)[3] B. Pégourié, Plasma Phys. Control. Fusion 49,R87 (2007)[4] A. Matsuyama, Phys. Plasmas 29, 042501 (2022)[5] M. Hoelzl et al, Nucl. Fusion 61, 065001 (2021)[6] S. Jachmich et al, Nucl. Fusion 62, 026012 (2022)[7] U.A. Sheikh et al, Nucl. Fusion 61, 126043 (2021)[8] T.E. Gebhart et al, IEEE Trans. Plasma Sci. 48, 1598 (2020)[9] T.E. Gebhart et al, Fusion Sci. Tech. 77, 33 (2021)[10] H.W. Müller, et al, Nucl. Fusion 42, 301 (2002)[11] F. Köchl et al, 35th EPS Conference, P4.099 (2008)[12] M. Giacomin et al, Phys. Rev. Lett. 128, 185003 (2022)48th EPS Conference on Plasma Physics O3.102

Interpretative 3D MHD modelling of deuterium shattered pellet injection into a JET H-mode plasma

https://pure.mpg.de/pubman/item/item_3482704_1/component/file_3482705/O3.102.pdf

Interpretative 3D MHD modelling of deuterium shattered pellet injection into a JET H-mode plasma

Abstract

Similar works

Full text

Available Versions

MPG.PuRe