arXiv subjects

Sibylle Günter

Publications and source records attributed to Sibylle Günter.

11 recordsLinked to original sources

arXiv2025

Quantitative Magnetohydrodynamic Modelling of Flux Pumping in ASDEX Upgrade

The sawtooth-free hybrid scenario has been achieved recently in ASDEX Upgrade (AUG) with applied non-inductive current sources and auxiliary heating [A. Burckhart et al 2023 Nucl. Fusion 63 126056]. Control experiments in AUG suggest that the self-regulating magnetic flux pumping mechanism, characterized by anomalous current redistribution, is responsible for clamping the central safety factor (q_0) close to unity, thereby preventing the sawtooth onset. This work presents a numerical and theoretical investigation of flux pumping in the AUG hybrid scenario based on the two-temperature, visco-resistive, full magnetohydrodynamic (MHD) model with the JOREK code. To quantitatively model the flux pumping, we choose realistic parameters, plasma configurations, and source terms based on AUG experiments. During the initial saturation stage of the unstable 1/1 quasi-interchange mode (on millisecond timescales), q_0 exhibits fast under-damped oscillation and reaches a value closer to unity, which is attributed to the self-regulation of core plasma and the fast dynamo effect on the order of V/m. On the longer resistive diffusion timescale of seconds, the slow negative dynamo effect on the order of mV/m induced by the 1/1 MHD instability plays an effective role in flux pumping, which provides quantitative agreement with experimental observations for the first time. The final saturated 1/1 MHD instability exhibits features of the quasi-interchange mode and tearing mode, and the associated convective plasma flow velocity is a few m/s. The toroidal negative electric field from the slow dynamo dominantly offsets the positive current drive and continuously redistributes the current density and pressure. As a result, q_0 is maintained close to unity due to the low-shear profiles of current density and pressure in the plasma core, and the system enters a sawtooth-free and quasi-stationary helical state.

physics.plasm-ph↗

arXiv2023

MHD simulations of formation, sustainment and loss of Quiescent H-mode in the all-tungsten ASDEX Upgrade

Periodic edge localized modes (ELMs) are the non-linear consequences of pressure-gradient-driven ballooning modes and current-driven peeling modes becoming unstable in the pedestal region of high confinement fusion plasmas. In future tokamaks like ITER, large ELMs are foreseen to severely affect the lifetime of wall components as they transiently deposit large amounts of heat onto a narrow region at the divertor targets. Several strategies exist for avoidance, suppression, or mitigation of these instabilities, such as the naturally ELM-free quiescent H-mode (QH-mode). In the present article, an ASDEX Upgrade equilibrium that features a QH-mode is investigated through non-linear extended MHD simulations covering the dynamics over tens of milliseconds. The equilibrium is close to the ideal peeling limit and non-linearly develops saturated modes at the edge of the plasma. A dominant toroidal mode number of $n=1$ is found, for which the characteristic features of the edge harmonic oscillation are recovered. The saturated modes contribute to heat and particle transport preventing pedestal build-up to the ELM triggering threshold. The non-linear dynamics of the mode, in particular its interaction with the evolution of the edge safety factor is studied, which suggest a possible new saturation mechanism for the QH-mode. The simulations show good qualitative and quantitative agreement to experiments in AUG. In particular, the processes leading to the termination of QH-mode above a density threshold is studied, which results in the transition into an ELM regime. In the vicinity of this threshold, limit cycle oscillations are observed.

physics.plasm-ph↗

arXiv2023

How well can VMEC predict the initial saturation of external kink modes in near circular tokamaks and $l=2$ stellarators?

The equilibrium code, VMEC, is used to study external kinks in low $β$ tokamaks and $l=2$ stellarators. The applicability of the code when modelling nonlinear MHD effects is explored in an attempt to understand and predict how the initial saturation of the MHD mode depends on the external rotational transform. It is shown that helicity preserving, free boundary VMEC computations do not converge to a single perturbed solution with increasing spectral resolution. Additional constraints are therefore applied to narrow down the numerical resolution parameters appropriate for physical scans. The dependence of the modelled (4, 1) kink mode on the external rotational transform and field periodicity is then studied. While saturated states can be identified which decrease in amplitude with increasing external rotational transform, bifurcated states are found that contradict this trend. It was therefore not possible to use VMEC alone to identify the physical dependency of the nonlinear mode amplitude on the magnetic geometry. The accuracy of the VMEC solutions is nevertheless demonstrated by showing that the expected toroidal mode coupling is captured in the magnetic energy spectrum for stellarator cases. Comparing with the initial value code, JOREK, the predicted redistribution of poloidal magnetic energy from the vacuum to plasma region in VMEC is shown to be physical. This work is a first step towards using VMEC to study MHD modes in stellarator geometry.

physics.plasm-ph↗

arXiv2022

Modelling of saturated external MHD instabilities in tokamaks: a comparison of 3D free boundary equilibria and nonlinear stability calculations

3D free boundary equilibrium computations have recently been used to model external kinks and edge harmonic oscillations (EHOs), comparing with linear MHD stability codes, and nonlinear analytic theory [Kleiner et al, PPCF 61 084005 (2019)]. In this study, results of the VMEC equilibrium code are compared further with nonlinear reduced MHD simulations, using the JOREK code. The purpose of this investigation is to understand the extent to which the modelling approaches agree, and identify the important physical effects which can modify the dynamics. For the simulated external kink, which is dominated by a single toroidal harmonic, good agreement is found when a large Lundquist number is used in the JOREK simulation, such that resistive effects are sub-dominant. Modelling EHOs where multiple toroidal harmonics are linearly unstable, the saturated perturbation observed can differ in the dominant toroidal harmonic. On the ideal timescale, a n=2 EHO is observed in JOREK, while the saturated perturbation predicted by VMEC is a n=1 mode. Extending simulations into timescales where resistive effects can play a role, similar n=1 perturbations can be found. The coupling of different linearly unstable toroidal harmonics in the JOREK simulation broadens the magnetic energy spectrum and ergodises the plasma edge region, resulting in a more localised pressure perturbation. These effects are not observed in VMEC, because closed magnetic flux surfaces are enforced. Despite the sensitivity of JOREK results on the assumed resistivity, saturated states can be found using both approaches that are in reasonable agreement, even for this more advanced case.

physics.plasm-ph↗

arXiv2022

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

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. This recent success has revived interest in the nonlinear 3D MHD modelling of stellarators in order to better understand their performance and operational limits. 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.

physics.plasm-ph↗

arXiv2021

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

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 stabilising 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 stabilised.

physics.plasm-ph↗

arXiv2019

A three-dimensional reduced MHD model consistent with full MHD

Within the context of a viscoresistive magnetohydrodynamic (MHD) model with anisotropic heat transport and cross-field mass diffusion, we introduce novel three-term representations for the magnetic field (background vacuum field, field line bending and field compression) and velocity ($\vec E\times\vec B$ flow, field-aligned flow and fluid compression), which are amenable to three-dimensional treatment. Once the representations are inserted into the MHD equations, appropriate projection operators are applied to Faraday's law and the Navier-Stokes equation to obtain a system of scalar equations that is closed by the continuity and energy equations. If the background vacuum field is sufficiently strong and the $β$ is low, MHD waves are approximately separated by the three terms in the velocity representation, with each term containing a specific wave. Thus, by setting the appropriate term to zero, we eliminate fast magnetosonic waves, obtaining a reduced MHD model. We also show that the other two velocity terms do not compress the magnetic field, which allows us to set the field compression term to zero within the same reduced model. Dropping also the field-aligned flow, a further simplified model is obtained, leading to a fully consistent hierarchy of reduced and full MHD models for 3D plasma configurations. Finally, we discuss the conservation properties and derive the conditions under which the reduction approximation is valid. We also show that by using an ordering approach, reduced MHD equations similar to what we got from the ansatz approach can be obtained by means of a physics-based asymptotic expansion.

physics.plasm-ph↗

arXiv2013

Multi-mode Alfvénic Fast Particle Transport and Losses: Numerical vs. Experimental Observation

In many discharges at ASDEX Upgrade fast particle losses can be observed due to Alfvénic gap modes, Reversed Shear Alfvén Eigenmodes or core-localized Beta Alfvén Eigenmodes. For the first time, simulations of experimental conditions in the ASDEX Upgrade fusion device are performed for different plasma equilibria (particularly for different, also non-monotonic q profiles). The numerical tool is the extended version of the HAGIS code [Pinches'98, Brüdgam PhD Thesis, 2010], which also computes the particle motion in the vacuum region between vessel wall in addition to the internal plasma volume. For this work, a consistent fast particle distribution function was implemented to represent the strongly anisotropic fast particle population as generated by ICRH minority heating. Furthermore, HAGIS was extended to use more realistic eigenfunctions, calculated by the gyrokinetic eigenvalue solver LIGKA [Lauber'07]. The main aim of these simulations is to allow fast ion loss measurements to be interpreted with a theoretical basis. Fast particle losses are modeled and directly compared with experimental measurements [García-Muñoz'10]. The phase space distribution and the mode-correlation signature of the fast particle losses allows them to be characterized as prompt, resonant or diffusive (non-resonant). The experimental findings are reproduced numerically. It is found that a large number of diffuse losses occur in the lower energy range (at around 1/3 of the birth energy) particularly in multiple mode scenarios (with different mode frequencies), due to a phase space overlap of resonances leading to a so-called domino [Berk'95] transport process. In inverted q profile equilibria, the combination of radially extended global modes and large particle orbits leads to losses with energies down to 1/10th of the birth energy.

physics.plasm-ph↗

arXiv2012

Nonlinear alfvénic fast particle transport and losses

Magnetohydrodynamic instabilities like Toroidal Alfvén Eigenmodes or core-localized modes such as Beta Induced Alfvén Eigenmodes and Reversed Shear Alfvén Eigenmodes driven by fast particles can lead to significant redistribution and losses in fusion devices. This is observed in many ASDEX Upgrade discharges. The present work aims to understand the underlying resonance mechanisms, especially in the presence of multiple modes with different frequencies. Resonant mode coupling mechanisms are investigated using the drift kinetic HAGIS code [Pinches 1998]. Simulations were performed for different plasma equilibria, in particular for different q profiles, employing the availability of improved experimental data. A study was carried out, investigating double-resonant mode coupling with respect to various overlapping scenarios. It was found that, depending on the radial mode distance, double-resonance is able to enhance growth rates as well as mode amplitudes significantly. Small radial mode distances, however can also lead to strong nonlinear mode stabilization of a linear dominant mode. With the extended version of HAGIS, losses were simulated and directly compared with experimental loss measurements. The losses' phase space distribution as well as their ejection signal is consistent with experimental data. Furthermore, it allowed to characterize them as prompt, resonant or stochastic. It was found that especially in multiple mode scenarios (with different mode frequencies), abundant incoherent losses occur in the lower energy range, due to a broad phase-space stochastization. The incoherent higher energetic losses are "prompt", i.e. their initial energy is too large for confined orbits.

physics.plasm-ph↗

arXiv2012

Double-resonant fast particle-wave interaction

In future fusion devices fast particles must be well confined in order to transfer their energy to the background plasma. Magnetohydrodynamic instabilities like Toroidal Alfvén Eigenmodes or core-localized modes such as Beta Induced Alfvén Eigenmodes and Reversed Shear Alfvén Eigenmodes, both driven by fast particles, can lead to significant losses. This is observed in many ASDEX Upgrade discharges. The present study applies the drift-kinetic HAGIS code with the aim of understanding the underlying resonance mechanisms, especially in the presence of multiple modes with different frequencies. Of particular interest is the resonant interaction of particles simultaneously with two different modes, referred to as 'double-resonance'. Various mode overlapping scenarios with different q profiles are considered. It is found that, depending on the radial mode distance, double-resonance is able to enhance growth rates as well as mode amplitudes significantly. Surprisingly, no radial mode overlap is necessary for this effect. Quite the contrary is found: small radial mode distances can lead to strong nonlinear mode stabilization of a linearly dominant mode.

physics.plasm-ph↗

arXiv2007

Large-mode-number magnetohydrodynamic instability driven by sheared flows in a tokamak plasma with reversed central shear

The effect of a narrow sub-Alfvenic shear flow layer near the minimum q_min of the tokamak safety factor profile in a configuration with reversed central shear is analyzed. Sufficiently strong velocity shear gives rise to a broad spectrum of fast growing Kelvin-Helmholtz (KH)-like ideal magnetohydrodynamic (MHD) modes with dominant mode numbers m,n ~ 10. Nonlinear simulations with finite resistivity show magnetic reconnection near ripples caused by KH-like vortices, the formation of turbulent structures, and a flattening of the flow profile. The KH modes are compared to double tearing modes (DTM) which dominate at lower shearing rates. The possible application of these results in tokamaks with internal transport barrier is discussed.

physics.plasm-ph↗