Legolas 2.0: Improvements and extensions to an MHD spectroscopic framework

Claes, Niels; Keppens, Rony

doi:10.1016/j.cpc.2023.108856

Cited by 6 publications

(4 citation statements)

References 25 publications

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“…We calculate all MHD eigenspectra in this work using the Legolas 3 code developed by Claes et al (2020) andDe Jonghe et al (2022) and recently upgraded in terms of solver and memory performance (Claes & Keppens 2023). It uses a finite-element approach to solve the following generalized matrix eigenvalue problem obtained from the linearized MHD equations, where the Fourier coefficients become eigenfunctions:…”

Section: Eigenvalue Problemmentioning

confidence: 99%

“…The matrix system is then solved using various available solvers depending on the requirements. In this work, we use the QR-invert algorithm to produce complete eigenspectra, and the Arnoldi shift-invert method to search for eigenvalues in the neighborhood of some complex number (Claes & Keppens 2023). The mathematical formulation of the eigenvalue problem is closed by fixing the boundary conditions at radius 1 and 1 + δ.…”

Section: Eigenvalue Problemmentioning

confidence: 99%

“…We define a grid of target shift frequencies that sample the 2D region of interest, where we use the quasi-continuum edges found by the QR algorithm. Thanks to the recent upgrades to the Legolas code (Claes & Keppens 2023), this can now easily be done at high radial resolutions: we choose a resolution of n = 1000 gridpoints for the equilibria and look for 100 eigenvalues in the neighborhood of each shift. depending on the location, resolution, and number of eigenvalues.…”

Section: Quasi-continuum Modesmentioning

confidence: 99%

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Parametric Survey of Nonaxisymmetric Accretion Disk Instabilities: Magnetorotational Instability to Super-Alfvénic Rotational Instability

Brughmans,

Keppens,

Goedbloed

2024

ApJ

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Accretion disks are highly unstable to magnetic instabilities driven by shear flow, where classically, the axisymmetric, weak-field magnetorotational instability (MRI) has received much attention through local WKB approximations. In contrast, discrete nonaxisymmetric counterparts require a more involved analysis through a full global approach to deal with the influence of the nearby magnetohydrodynamic (MHD) continua. Recently, rigorous MHD spectroscopy identified a new type of ultralocalized, nonaxisymmetric instability in global disks with super-Alfvénic flow. These super-Alfvénic rotational instabilities (SARIs) fill vast unstable regions in the complex eigenfrequency plane with (near eigen)modes that corotate at the local Doppler velocity and are radially localized between Alfvénic resonances. Unlike discrete modes, they are utterly insensitive to the radial disk boundaries. In this work, we independently confirm the existence of these unprecedented modes using our novel spectral MHD code Legolas, reproducing and extending our earlier study with detailed eigenspectra and eigenfunctions. We calculate the growth rates of SARIs and MRI in a variety of disk equilibria, highlighting the impact of field strength and orientation, and find correspondence with analytical predictions for thin, weakly magnetized disks. We show that nonaxisymmetric modes can significantly extend instability regimes at high mode numbers, with maximal growth rates comparable to those of the MRI. Furthermore, we explicitly show a region filled with quasi-modes whose eigenfunctions are extremely localized in all directions. These modes must be ubiquitous in accretion disks, and play a role in local shearing box simulations. Finally, we revisit recent dispersion relations in the appendix, highlighting their relation to our global framework.

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Section: Eigenvalue Problemmentioning

confidence: 99%

Section: Eigenvalue Problemmentioning

confidence: 99%

Section: Quasi-continuum Modesmentioning

confidence: 99%

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Parametric Survey of Nonaxisymmetric Accretion Disk Instabilities: Magnetorotational Instability to Super-Alfvénic Rotational Instability

Brughmans,

Keppens,

Goedbloed

2024

ApJ

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“…Before introducing the neural network based algorithm, we briefly describe the data generated with the Legolas code. The MHD spectroscopic code Legolas (Claes et al, 2020;De Jonghe et al, 2022;Claes and Keppens, 2023) is a finite element method (FEM) code that solves the generalised eigenproblem…”

Section: Astrophysical Jets In the Legolas Codementioning

confidence: 99%

Legolas: magnetohydrodynamic spectroscopy with viscosity and Hall current

2022

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Many linear stability aspects in plasmas are heavily influenced by non-ideal effects beyond the basic ideal magnetohydrodynamics (MHD) description. Here, the extension of the modern open-source MHD spectroscopy code Legolas with viscosity and the Hall current is highlighted and benchmarked on a stringent set of historic and recent findings. The viscosity extension is demonstrated in a cylindrical set-up featuring Taylor–Couette flow and in a viscoresistive plasma slab with a tearing mode. For the Hall extension, we show how the full eigenmode spectrum relates to the analytic dispersion relation in an infinite homogeneous medium. We quantify the Hall term influence on the resistive tearing mode in a Harris current sheet, including the effect of compressibility, which is absent in earlier studies. Furthermore, we illustrate how Legolas mimics the incompressible limit easily to compare with literature results. Going beyond published findings, we emphasise the importance of computing the full eigenmode spectrum, and how elements of the spectrum are modified by compressibility. These extensions allow for future stability studies with Legolas that are relevant to ongoing dynamo experiments, protoplanetary disks or magnetic reconnection.

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Neural network classification of eigenmodes in the magnetohydrodynamic spectroscopy code Legolas

De Jonghe,

Kuczyński

2024

Neural Comput & Applic

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A neural network is employed to address a non-binary classification problem of plasma instabilities in astrophysical jets, calculated with the code. The trained models exhibit reliable performance in the identification of the two instability types supported by these jets. We also discuss the generation of artificial data and refinement of predictions in general eigenfunction classification problems.

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Legolas 2.0: Improvements and extensions to an MHD spectroscopic framework

Cited by 6 publications

References 25 publications

Parametric Survey of Nonaxisymmetric Accretion Disk Instabilities: Magnetorotational Instability to Super-Alfvénic Rotational Instability

Parametric Survey of Nonaxisymmetric Accretion Disk Instabilities: Magnetorotational Instability to Super-Alfvénic Rotational Instability

Legolas: magnetohydrodynamic spectroscopy with viscosity and Hall current

Neural network classification of eigenmodes in the magnetohydrodynamic spectroscopy code Legolas

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