Abstract:Non-linear magnetohydrodynamic (MHD) simulations play an essential role in active research and understanding of tokamak plasmas for the realization of a fusion power plant. The development of MHD codes such as JOREK is a key aspect of this research effort. In this paper, we present an operational version of the full-MHD model implemented in JOREK, a significant advancement from the reduced-MHD model used for previous studies, where assumptions were made on the perpendicular dynamics and the toroidal magnetic f… Show more
“…The full MHD model has recently been extended for sheath boundary conditions and numerical stabilization terms were implemented [114]. The full-MHD physics model implemented in reference [65] includes plasma flows like the reduced-MHD model, with diamagnetic terms, neoclassical poloidal friction, and toroidal rotation. The bootstrap current source has also been included.…”
Section: Full Mhd Modelmentioning
confidence: 99%
“…A benchmark of peeling-ballooning modes (PBMs) is done using an X-point JET-like plasma. Refer to reference [65] for details regarding the benchmark configuration. Figure 22 shows the growth rate with and without diamagnetic effects, as a function of toroidal mode number, for both reduced-and full-MHD.…”
JOREK is a massively parallel fully implicit non-linear extended magneto-hydrodynamic (MHD) code for realistic tokamak X-point plasmas. It has become a widely used versatile simulation code for studying large-scale plasma instabilities and their control and is continuously developed in an international community with strong involvements in the European fusion research programme and ITER organization. This article gives a comprehensive overview of the physics models implemented, numerical methods applied for solving the equations and physics studies performed with the code. A dedicated section highlights some of the verification work done for the code. A hierarchy of different physics models is available including a free boundary and resistive wall extension and hybrid kinetic-fluid models. The code allows for flux-surface aligned iso-parametric finite element grids in single and double X-point plasmas which can be extended to the true physical walls and uses a robust fully implicit time stepping. Particular focus is laid on plasma edge and scrape-off layer (SOL) physics as well as disruption related phenomena. Among the key results obtained with JOREK regarding plasma edge and SOL, are deep insights into the dynamics of edge localized modes (ELMs), ELM cycles, and ELM control by resonant magnetic perturbations, pellet injection, as well as by vertical magnetic kicks. Also ELM free regimes, detachment physics, the generation and transport of impurities during an ELM, and electrostatic turbulence in the pedestal region are investigated. Regarding disruptions, the focus is on the dynamics of the thermal quench (TQ) and current quench triggered by massive gas injection and shattered pellet injection, runaway electron (RE) dynamics as well as the RE interaction with MHD modes, and vertical displacement events. Also the seeding and suppression of tearing modes (TMs), the dynamics of naturally occurring TQs triggered by locked modes, and radiative collapses are being studied.
“…The full MHD model has recently been extended for sheath boundary conditions and numerical stabilization terms were implemented [114]. The full-MHD physics model implemented in reference [65] includes plasma flows like the reduced-MHD model, with diamagnetic terms, neoclassical poloidal friction, and toroidal rotation. The bootstrap current source has also been included.…”
Section: Full Mhd Modelmentioning
confidence: 99%
“…A benchmark of peeling-ballooning modes (PBMs) is done using an X-point JET-like plasma. Refer to reference [65] for details regarding the benchmark configuration. Figure 22 shows the growth rate with and without diamagnetic effects, as a function of toroidal mode number, for both reduced-and full-MHD.…”
JOREK is a massively parallel fully implicit non-linear extended magneto-hydrodynamic (MHD) code for realistic tokamak X-point plasmas. It has become a widely used versatile simulation code for studying large-scale plasma instabilities and their control and is continuously developed in an international community with strong involvements in the European fusion research programme and ITER organization. This article gives a comprehensive overview of the physics models implemented, numerical methods applied for solving the equations and physics studies performed with the code. A dedicated section highlights some of the verification work done for the code. A hierarchy of different physics models is available including a free boundary and resistive wall extension and hybrid kinetic-fluid models. The code allows for flux-surface aligned iso-parametric finite element grids in single and double X-point plasmas which can be extended to the true physical walls and uses a robust fully implicit time stepping. Particular focus is laid on plasma edge and scrape-off layer (SOL) physics as well as disruption related phenomena. Among the key results obtained with JOREK regarding plasma edge and SOL, are deep insights into the dynamics of edge localized modes (ELMs), ELM cycles, and ELM control by resonant magnetic perturbations, pellet injection, as well as by vertical magnetic kicks. Also ELM free regimes, detachment physics, the generation and transport of impurities during an ELM, and electrostatic turbulence in the pedestal region are investigated. Regarding disruptions, the focus is on the dynamics of the thermal quench (TQ) and current quench triggered by massive gas injection and shattered pellet injection, runaway electron (RE) dynamics as well as the RE interaction with MHD modes, and vertical displacement events. Also the seeding and suppression of tearing modes (TMs), the dynamics of naturally occurring TQs triggered by locked modes, and radiative collapses are being studied.
“…Note that in the tokamak limit χ = F 0 φ, the latter is equivalent to the the model without parallel flow from the set of new stellarator-capable models, as introduced in § 2. In addition, we point out that the standard tokamak reduced MHD model in JOREK is known to accurately reproduce tearing modes when compared with full MHD (Haverkort et al 2016;Pamela et al 2020), thus comparing with the standard tokamak model is sufficient.…”
In preparation for extending the JOREK nonlinear magnetohydrodynamics (MHD) code to stellarators, a hierarchy of stellarator-capable reduced and full MHD models has been derived and tested. The derivation was presented at the EFTC 2019 conference. Continuing this line of work, we have implemented the reduced MHD model (Nikulsin et al., Phys. Plasmas, vol. 26, 2019, 102109) as well as an alternative model which was newly derived using a different set of projection operators for obtaining the scalar momentum equations from the full MHD vector momentum equation. With the new operators, the reduced model matches the standard JOREK reduced models for tokamaks in the tokamak limit and conserves energy exactly, while momentum conservation is less accurate than in the original model whenever field-aligned flow is present.
“…The variation along the toroidal direction is represented by Fourier harmonics and for the time advance typically the Crank-Nicolson or the BDF5 Gears scheme is used. Although a full MHD model is available in JOREK [19,20], the extension for resistive walls has not been implemented yet for that physics model. The base MHD model used for this benchmark is…”
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 wall forces and energy decay. This benchmark does not only bring confidence regarding the use of the mentioned codes for disruption studies, but also shows differences with respect to the used models (e.g. reduced versus full MHD models). The simulations show important 3D features for a NSTX plasma such as the self-consistent evolution of the halo current and the origin of the wall forces. In contrast to other reduced MHD models based on an ordering in the aspect ratio, the ansatz based JOREK reduced MHD model allows capturing the 3D dynamics even in the spherical tokamak limit considered here.
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