A 3D numerical model for the ablation of pellets and shattered pellet injection (SPI) fragments in tokamaks in the plasma disruption mitigation and fueling parameter space has been developed based on the Lagrangian particle code [R. Samulyak, X. Wang, H.-S. Chen, Lagrangian Particle Method for Compressible Fluid Dynamics, J. Comput. Phys., 362 (2018), 1-19]. The pellet code implements the low magnetic Reynolds number MHD equations, kinetic models for the electronic heating, a pellet surface ablation model, an equation of state that supports multiple ionization states, radiation, and a model for grad-B drift of the ablated material across the magnetic field. The Lagrangian particle algorithm is highly adaptive, capable of simulating a large number of fragments in 3D while eliminating numerical difficulties of dealing with the tokamak background plasma. The code has achieved good agreement with theory for spherically symmetric ablation flows. Axisymmetric simulations of neon and deuterium pellets in magnetic fields ranging from 1 to 6 Tesla have been compared with previous simulations using the FronTier code, and very good agreement has also been obtained. The main physics contribution of the paper is a detailed study of the influence of 3D effects, in particular grad-B drift, on pellet ablation rates and properties of ablation clouds. Smaller reductions of ablation rates in magnetic fields compared to axially symmetric simulations have been demonstrated because the ablated material is not confined to narrowing channels in the presence of grad-B drift. Contribution of various factors in the grad-B drift model has also been quantified.
For the first time the pellet cycle of a multiple-isotope plasma is successfully reproduced with reduced turbulent transport modelling, within an integrated simulation framework. Future nuclear fusion reactors are likely to be fuelled by cryogenic pellet injection, due to higher penetration and faster response times. Accurate pellet cycle modelling is crucial to assess fuelling efficiency and burn control. In recent JET tokamak experiments, deuterium pellets with reactor-relevant deposition characteristics were injected into a pure hydrogen plasma. Measurements of the isotope ratio profile inf…
The complete refuelling of the plasma density loss (pump-out) caused by mitigation of Edge Localised Modes (ELMs) is demonstrated on the ASDEX Upgrade tokamak. The plasma is refuelled by injection of frozen deuterium pellets and ELMs are mitigated by external resonant magnetic perturbations (RMPs). In this experiment relevant dimensionless parameters, such as relative pellet size, relative RMP amplitude and pedestal collisionality are kept at the ITER like values. Refuelling of density pump out requires a factor of two increase of nominal fuelling rate. Energy confinement and pedestal temperat…
An effective disruption mitigation system in a tokamak reactor should limit the exposure of the wall to localized heat losses and to the impact of high current runaway electron beams, and avoid excessive forces on the structure. We evaluate with respect to these aspects a two-stage deuterium-neon shattered pellet injection in an ITER-like plasma, using simulations with the DREAM framework [M. Hoppe et al (2021) Comp. Phys. Commun. 268, 108098]. To minimize the obtained runaway currents an optimal range of injected deuterium quantities is found. This range is sensitive to the opacity of the pla…
In this letter, we report results of numerical studies of the ablation of argon and neon pellets in tokamaks and compare them with theoretical predictions and studies of deuterium pellets. Results demonstrate the influence of atomic physics processes on the pellet ablation process.
The fuelling of plasmas by shallow frozen pellets with simultaneous mitigation of edge localised modes (ELM) by external magnetic perturbation is demonstrated on the MAST tokamak. Post-pellet particle loss is dominated by ELMs and inter-ELM gas fuelling. It is shown that the size of post-pellet ELMs can be controlled by external magnetic perturbations. Post-pellet ELMs remove particles from the large part of pellet deposition zone including the area with positive density gradient. The mechanism explaining this peculiarity of particle loss is suggested.
Integrated full pulse modeling for pellet injection in tokamaks: HPI2 model improvement and validation in WEST
DIFFER – Dutch Institute for Fundamental Energy Research（荷兰基础能源研究所）；Eindhoven University of Technology（埃因霍温理工大学）；ITER Organization（国际热核聚变实验堆组织）；CEA Cadarache, IRFM（法国原子能和替代能源委员会卡达拉舍校区，核聚变研究集成设施）
本文改进了 HPI2 模型，通过自洽的等离子体释放空间步长计算，提高了数值稳定性，并在 WEST 实验中验证了其预测能力，支持其在集成建模中的应用。
The lifetime and utilization of a nuclear fusion reactor like ITER depends strongly on its capabilities to mitigate damage during disruptions. While shattered pellet injection (SPI) was chosen as the baseline mitigation method for ITER, the exact relation of pellet injection parameters and the resulting fragment distributions is not yet clear. This knowledge is of paramount importance for optimizing the impurity deposition and disruption mitigation efficiency. In this thesis, I present fragmentation analysis of 170 SPI pellets, with the focus on the produced fragment sizes as a function of nor…
Spacecraft heat shield study in the DIII-D tokamak
University of California San Diego（加州大学圣迭戈分校）；Auburn University（奥本大学）；General Atomics（通用原子能公司）；Princeton Plasma Physics Laboratory（普林斯顿等离子体物理实验室）；Baylor University（贝勒大学）；University of Stuttgart（斯图加特大学）；Oak Ridge National Laboratory（橡树岭国家实验室）；Lawrence Livermore National Laboratory（劳伦斯利弗莫尔国家实验室）
Results from the last FTU campaigns on the deuterium large (wrt FTU volume) pellet REs suppression capability, mainly due to the induced burst MHD activity expelling REs seed are presented for discharges with 0.5 MA and 5.3T. Clear indications of avalanche multiplication of REs following single pellet injection on 0.36 MA flat-top discharges is shown together with quantitative indications of dissipative effects in terms of critical electrical field increase due to fan-like instabilities. Analysis of large fan-like instabilities on post-disruption RE beams, that seem to be correlated with low e…
A change of the particle density (by gas puff, pellets or impurity seeding) during the plasma discharge in tokamak produces a radial current and implicitly a torque and rotation that can modify the state of confinement. After ionization the newly born ions will evolve toward the periodic neoclassical orbits (trapped or circulating) but the first part of their excursion, which precedes the periodicity, is an effective radial current. It is short, spatially finite and unique for each new ion, but multiplied by the rate of ionization and it can produce a substantial total radial current. The asso…
Quantitative 3D non-linear simulations of shattered pellet injection in ASDEX Upgrade using JOREK
Max Planck Institute for Plasma Physics（马克斯·普朗克等离子体物理研究所）；Beihang University（北京航空航天大学）；ITER Organization（国际热核聚变实验堆组织）；Institute of Plasma Physics of the CAS（捷克科学院等离子体物理研究所）；CEA/IRFM（法国原子能和替代能源委员会/核聚变研究集成设施）；École Polytechnique Fédérale de Lausanne (EPFL)（洛桑联邦理工学院）
The Tore Supra tokamak is the largest superconducting magnetic fusion facility, has been devoted to long-duration high-performance discharge research. With a steady-state magnetic field and water cooled plasma facing components, discharges up to 6 minutes 24 seconds duration with injected / extracted energy up to 1 GJ have been performed. The Tore Supra real time measurements and control (RTMC) system has been upgraded to address schemes dedicated to long pulse operation with simultaneous control of an increasing number of plasma parameters. This includes plasma equilibrium control with possib…
The fragment ablation rate plays significant roles in the mitigation efficiency of Shattered Pellet Injection (SPI) as a Disruption Mitigation System (DMS). Current mainstream 3D MHD codes modelling SPIs mostly assume instantaneous thermalization between the previously hot ambient electrons and the newly released cold electrons, which results in underestimation of the ablation rate if the hot electron thermalization time is comparable or even longer than the fragment flying time. To resolve this doubt, we hereby investigate the thermalization dynamics and the overall hot-electron impact. The f…
The radiation response and the MHD destabilization during the thermal quench after a mixed species Shattered Pellet Injection (SPI) with impurity species neon and argon are investigated via 3D non-linear MHD simulation using the JOREK code. Both the $n=0$ global current profile contraction and the local helical cooling at each rational surface caused by the pellet fragments are found to be responsible for MHD destabilization after the injection. Significant current driven mode growth is observed as the fragments cross low order rational surfaces, resulting in rapidly inward propagating stochas…
The interaction of passing-ion drift orbits with spatially-inhomogeneous but purely diffusive radial transport is demonstrated to cause spontaneous toroidal spin-up to experimentally-relevant values in the tokamak edge. Physically, major-radial orbit shifts cause orbit-averaged diffusivities to depend on parallel velocity, including its sign, leading to residual stress. The resulting intrinsic rotation scales with ion temperature over poloidal magnetic field strength, resembling typical experimental scalings. Additionally, an inboard (outboard) X-point is expected to enhance co- (counter-) cur…
First simulations of deuterium shattered pellet injection (SPI) into an ASDEX Upgrade H-Mode plasma with the JOREK MHD code are presented. Resistivity is increased by one order of magnitude in most simulations to reduce computational costs and allow for extensive parameter scans. The effect of various physical parameters onto MHD activity and thermal quench (TQ) dynamics is studied and the influence of MHD onto ablation is shown. TQs are obtained quickly after injection in most simulations with a typical duration of 100 microseconds, which slows down at lower resistivity. Although the n=1 magn…
AXUV synthetic diagnostic for ASDEX Upgrade and its application for SPI simulations
Budapest University of Technology and Economics（布达佩斯技术与经济大学）；Institute for Atomic Energy Research, HUN-REN Centre for Energy Research（原子能研究所，匈牙利研究网络能源研究中心）；Max Planck Institute for Plasma Physics（马克斯·普朗克等离子体物理研究所）；Chalmers University of Technology（查尔姆斯理工大学）；Institute of Plasma Physics, Czech Academy of Sciences（捷克科学院等离子体物理研究所）；ITER Organization（国际热核聚变实验堆组织）；Ecole Polytechnique Fédérale de Lausanne（洛桑联邦理工学院）
In recent years, the nonlinear 3D magnetohydrodynamic codes JOREK, M3D-C$^1$ and NIMROD developed the capability of modelling realistic 3D vertical displacement events (VDEs) including resistive walls. In this paper, a comprehensive 3D VDE benchmark is presented between these state of the art codes. The simulated case is based on an experimental NSTX plasma but with a simplified rectangular wall. In spite of pronounced differences between physics models and numerical methods, the comparison shows very good agreement in the relevant quantities used to characterize disruptions such as the 3D wal…
During tokamak disruptions the profile of the net parallel current is observed to flatten on a time scale that is so fast that it must be due to a fast magnetic reconnection. After a fast magnetic reconnection has broken magnetic surfaces, a single magnetic field line covers an entire volume and not just a magnetic surface. The current profile, given by $K\equivμ_0j_{||}/B$, relaxes to a constant within that volume by Alfvén waves propagating along the chaotic magnetic field lines. The time scale for this relaxation determines the commonly observed disruption phenomena of a current spike and a…
In order to contribute to the understanding of runaway electron generation mechanisms during tokamak disruptions, a test particle tracker is introduced in the JOREK 3D non-linear MHD code, able to compute both full and guiding center relativistic orbits. Tests of the module show good conservation of the invariants of motion and consistency between full orbit and guiding center solutions. A first application is presented where test electron confinement properties in a JET massive gas injection-triggered disruption simulation are investigated. It is found that electron populations initialised be…
