Measurements of the parameter dependencies of the bootstrap current in the W7-X stellarator

Neuner, U.; Beidler, C. D.; Dinklage, A.; Turkin, Y.; Stange, T.; Andreeva, T.; Schilling, J.; Thomsen, H.; Beurskens, M.; Bozhenkov, S.; Brunner, K. J.; Damm, H.; Fuchert, G.; Geiger, J.; Hergenhahn, U.; Höfel, U.; Knauer, J.; Krychowiak, M.; Kwak, S.; Langenberg, A.; Pablant, N.; Pasch, E.; Pavone, A.; Scott, E. R.; Svensson, J.; Mora, H. Trimiño; team, the Wendelstein 7-X

doi:10.1088/1741-4326/abd61a

Cited by 18 publications

(19 citation statements)

References 76 publications

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“…The behavior for λ e > 1 is incorrect and motivates the need for an asymptotic expression for λ e → ∞. Plasma parameters for this plot are B = 2.2 T, T e = 112 eV and n e = 2 × 10 19 m −3 , which can be realized in a device like Wendelstein 7-X [32] and will be used for the analysis of fully kinetic simulations in later sections.…”

Section: Small Wavenumber Approximation For Uh Wavesmentioning

confidence: 99%

Trapped upper hybrid waves as eigenmodes of non-monotonic background density profiles

Senstius

Nielsen

Vann

2021

Plasma Phys. Control. Fusion

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Non-monotonic plasma density structures such as blobs and magnetic islands give rise to trapped upper hybrid (UH) waves. Trapped UH waves which satisfy Bohr–Sommerfeld quantization can be thought of as eigenmodes of a cavity. Using fully kinetic particle-in-cell simulations, we verify the existence of these UH eigenmodes and demonstrate their significance as only eigenfrequencies become unstable to three-wave interactions. The eigenmodes can be excited through parametric decay instabilities (PDIs) of an X-mode pump wave at approximately twice the UH frequency, as could be the case for a gyrotron beam traversing a blob in a magnetically confined fusion plasma. We derive a closed expression for the wavenumber of UH waves, which is accurate both close to the UH layer and to the electron cyclotron resonance. This allows for fast analysis of eigenmodes in a non-monotonic structure. An expression for the amplification of PDI daughter waves in an inhomogeneous plasma is extended to a decay region where the first several derivatives vanish. From the amplification in a convective PDI, we estimate the growth rate of the absolute PDI involving the trapped waves. We show that the excitation of eigenmodes through PDIs in our simulations are indeed absolute rather than convective due to the trapping of the daughter waves. Additionally, we show that only eigenmodes get excited through the PDIs, and that we are able to predict the growth rates of the daughter waves and how they scale with the pump wave intensity. This is evidence supporting a fundamental assumption of analytical theory describing low threshold strong scattering observed in magnetically confined fusion experiments during second harmonic electron cyclotron resonance heating (ECRH). Such low threshold instabilities can degrade ECRH performance but also offer novel uses for ion heating or as diagnostics.

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Section: Small Wavenumber Approximation For Uh Wavesmentioning

confidence: 99%

Trapped upper hybrid waves as eigenmodes of non-monotonic background density profiles

Senstius

Nielsen

Vann

2021

Plasma Phys. Control. Fusion

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“…For one channel (ECE13, which views the plasma centre), the resonance is located at r/a = 0.05, whereas the second one, ECE24, views the plasma at r/a = 0.7, where r is the effective radius and a its value at the plasma boundary. (Right plot) Evolution of the total toroidal current measured by a Rogowski coil [17].…”

Section: Introductionmentioning

confidence: 99%

Model for current drive induced crash cycles in W7-X

et al. 2021

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In the Wendelstein 7-X (W7-X) stellarator, the vacuum rotational transform, ι, has a flat radial profile and does not cross any major rational resonance. Nevertheless, during plasma operation the ι‐profile can be strongly modified by electron cyclotron current drive in such a way that the resulting ι-profile passes through low-order rational values, and this can trigger magnetohydrodynamic (MHD) events. Indeed, W7-X plasmas are sometimes subject to repetitive collapses of core confinement, which can be observed regardless of the direction in which the EC current is driven. Even though the origin of these MHD instabilities is under investigation, the crashes may be connected to the formation of magnetic islands and magnetic reconnection. In the present work, we try to shed light on the dynamics of different events happening during the course of sawtooth cycles in W7-X by proposing a model that combines a slow current diffusion with a recipe for fast relaxation that conserves the corresponding helical flux (Kadomtsev 1975 Fiz. Plazmy 1 710–15). We also propose a simple model based on Taylor relaxation (Taylor 1974 Phys. Rev. Lett. 33 1139), (Taylor 1986 Rev. Mod. Phys. 58 741) to predict the nonlinear redistribution of plasma current caused by the largest of the observed events.

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“…The changes in D β , induced by finite-beta effects, are then small compared to those in D config , induced by coil currents (i. e., finite-beta effects span a space that only slightly expands the vacuum solution). Therefore, the spread of the output data in the finite-beta cases is smaller than in the vacuum scenarios: the coil system of W7-X has been designed to allow a large flexibility in the vacuum magnetic configuration space [74,75], while the W7-X optimization explicitly targeted robustness against changes in plasma profiles, in particular pressure profiles [54,76]. These features are expected to make the output data in the finiteβ tasks more difficult to resolve because of the smaller spread.…”

Section: Resultsmentioning

confidence: 99%

Proof of concept of a fast surrogate model of the VMEC code via neural networks in Wendelstein 7-X scenarios

Merlo,

Böckenhoff,

Schilling

et al. 2021

Preprint

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In magnetic confinement fusion research, the achievement of high plasma pressure is key to reaching the goal of net energy production. The magnetohydrodynamic (MHD) model is used to self-consistently calculate the effects the plasma pressure induces on the magnetic field used to confine the plasma. Such MHD calculations -usually done computationally -serve as input for the assessment of a number of important physics questions. The variational moments equilibrium code (VMEC) is the most widely used to evaluate 3D ideal-MHD equilibria, as prominently present in stellarators. However, considering the computational cost, it is rarely used in large-scale or online applications (e. g., Bayesian scientific modeling, real-time plasma control). Access to fast MHD equilbria is a challenging problem in fusion research, one which machine learning could effectively address. In this paper, we present artificial neural network (NN) models able to quickly compute the equilibrium magnetic field of Wendelstein 7-X. Magnetic configurations that extensively cover the device operational space, and plasma profiles with volumeaveraged normalized plasma pressure β (β = 2µ0p /B 2 ) up to 5 % and non-zero net toroidal current are included in the data set. By using convolutional layers, the spectral representation of the magnetic flux surfaces can be efficiently computed with a single network. To discover better models, a Bayesian hyper-parameter search is carried out, and 3D convolutional neural networks are found to outperform feed-forward fully-connected neural networks. The achieved normalized root-mean-squared error, the ratio between the regression error and the spread of the data, ranges from 1 % to 20 % across the different scenarios. The model inference time for a single equilibrium is on the order of milliseconds. Finally, this work shows the feasibility of a fast NN drop-in surrogate model for VMEC, and it opens up new operational scenarios where target applications could make use of magnetic equilibria at unprecedented scales.I Run time on the Max Planck computing and data facility (MPCDF)cluster "DRACO", using the small partition and 16 cores.

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Measurements of the parameter dependencies of the bootstrap current in the W7-X stellarator

Cited by 18 publications

References 76 publications

Trapped upper hybrid waves as eigenmodes of non-monotonic background density profiles

Trapped upper hybrid waves as eigenmodes of non-monotonic background density profiles

Model for current drive induced crash cycles in W7-X

Proof of concept of a fast surrogate model of the VMEC code via neural networks in Wendelstein 7-X scenarios

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