Testing of the new JOREK stellarator-capable model in the tokamak limit

Nikulsin, N.; Hoelzl, M.; Zocco, A.; Lackner, K.; Günter, S.; Team, Jorek

doi:10.1017/s0022377821000477

Cited by 7 publications

(11 citation statements)

References 19 publications

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“…One can also ensure global conservation of the x and y components of linear momentum by excluding the n = 1 term from the Fourier series, which forces the x and y components of the integrated total momentum to zero due to symmetry. This topic is considered in more detail in reference [70]. The full MHD model is conserving momentum exactly on the equation level, comparisons presented in section 4 between both models provide confidence to some degree that the introduced error does not affect linear and non-linear dynamics significantly.…”

Section: Boundary Conditionsmentioning

confidence: 92%

The JOREK non-linear extended MHD code and applications to large-scale instabilities and their control in magnetically confined fusion plasmas

et al. 2021

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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.

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Section: Boundary Conditionsmentioning

confidence: 92%

The JOREK non-linear extended MHD code and applications to large-scale instabilities and their control in magnetically confined fusion plasmas

et al. 2021

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“…Continuing the work of previous papers 15,16 , we implement a stellarator-capable reduced MHD model in JOREK and run several test cases based on the simple geometry of the Wendelstein 7-A stellarator. This paper presents the results, starting with section II, which shows that the reduced model introduces an error into equilibrium force balance, but the error is negligible.…”

Section: Discussionmentioning

confidence: 99%

“…The work consists of two parts: first, a reduced MHD model compatible with three-dimensional geometries was derived by generalizing the ideas of Breslau et al, Izzo et al and Strauss [12][13][14] , then this model is implemented in the JOREK code and tested on a simple stellarator. The first part of the work has already been published in previous papers 15,16 , and so this paper will present the results of the second part of this effort.…”

Section: Introductionmentioning

confidence: 99%

“…As discussed in our previous papers 15,16 , the magnetic field ansatz and equations in stellarator-capable reduced MHD involve a magnetic scalar potential χ, which represents the part of the magnetic field that is generated by the coils. In the tokamak limit, this potential reduces to χ = F 0 φ, where φ is the toroidal angle, however a stellarator-capable code using this model will need to allow arbitrary scalar potentials.…”

Section: Introductionmentioning

confidence: 99%

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JOREK3D: An extension of the JOREK nonlinear MHD code to stellarators

Nikulsin,

Ramasamy,

Hoelzl

et al. 2022

Preprint

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Although the basic concept of a stellarator was known since the early days of fusion research, advances in computational technology have enabled the modelling of increasingly complicated devices, leading up to the construction of Wendelstein 7-X, which has recently shown promising results. However, there has been surprisingly little activity in nonlinear 3D MHD modelling of stellarators. This paper reports on the extension of the JOREK code to 3D geometries and on the first stellarator simulations carried out with it. The first simple simulations shown here address the classic Wendelstein 7-A stellarator using a reduced MHD model previously derived by us. The results demonstrate that stable full MHD equilibria are preserved in the reduced model: the flux surfaces do not move throughout the simulation, and closely match the flux surfaces of the full MHD equilibrium. Further, both tearing and ballooning modes were simulated, and the linear growth rates measured in JOREK are in reasonable agreement with the growth rates from the CASTOR3D linear MHD code.

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“…The nonlinear MHD code, JOREK [13], is currently being extended to model stellarators. A hierarchy of stellarator capable models have been derived [14,15], and are currently being validated. Assessments of the nonlinear dynamics of global current driven instabilities require an evolution of the magnetic field in time.…”

Section: Introductionmentioning

confidence: 99%

Nonlinear MHD simulations of external kinks in quasi-axisymmetric stellarators using an axisymmetric external rotational transform approximation

et al. 2021

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Reduced magnetohydrodynamic (MHD) equations are used to study the nonlinear dynamics of external kinks in a quasi-axisymmetric (QA) stellarator with varying fractions of external rotational transform. The large bootstrap currents associated with high beta plasmas may make QA configurations susceptible to low n external modes, limiting their operational space. The violence of the nonlinear dynamics, and, in particular, when these modes lead to a disruption, is not yet understood. In this paper, the nonlinear phase of external kinks in an unstable QA configuration with an edge safety factor below two is simulated. An axisymmetric approximation of this stellarator is constructed in the nonlinear MHD code, JOREK, capturing the influence of the external rotational transform. The use of this approximation for the considered stellarator is validated by comparing the linear dynamics against the linear viscoresistive MHD code, CASTOR3D. The nonlinear dynamics of this stellarator approximation are compared with an equivalent tokamak to understand the influence of a relatively small external rotational transform. While the external rotational transform does have a stabilizing influence on the MHD activity, it remains violent. To explore the first order influence of a larger external rotational transform, this equilibrium parameter is artificially increased for the considered stellarator, reducing the effective plasma current. The violence of the kink instability is quantified, and shown to reduce with the increasing external rotational transform. At the same time, the external kink triggers internal modes that exacerbate the loss in confinement during the nonlinear phase, such that it remains large over much of the parameter space. It is only with a significant fraction of external rotational transform that these subsequent modes are stabilized.

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Testing of the new JOREK stellarator-capable model in the tokamak limit

Cited by 7 publications

References 19 publications

The JOREK non-linear extended MHD code and applications to large-scale instabilities and their control in magnetically confined fusion plasmas

The JOREK non-linear extended MHD code and applications to large-scale instabilities and their control in magnetically confined fusion plasmas

JOREK3D: An extension of the JOREK nonlinear MHD code to stellarators

Nonlinear MHD simulations of external kinks in quasi-axisymmetric stellarators using an axisymmetric external rotational transform approximation

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