arXiv subjects

Jordi De Jonghe

Publications and source records attributed to Jordi De Jonghe.

13 recordsLinked to original sources

arXiv2026

GIMLI: a toolkit connecting linear and non-linear magnetohydrodynamic regimes

In this work, we present the General Interface for MPI-AMRVAC / Legolas Interconnection (or GIMLI, for short) as a toolkit for in-depth (magneto)hydrodynamic studies combining linear and non-linear methods. Acting as a bridge between the linear (M)HD spectroscopy code Legolas and the non-linear simulation code MPI-AMRVAC, GIMLI facilitates the initialization of non-linear MPI-AMRVAC simulations with linear solutions. We showcase this functionality on both Cartesian and cylindrical setups, covering representative plasma physical and astrophysical scenarios: Parker unstable magnetized atmospheres, interchange modes in a straight tokamak setup, resistive Harris sheet evolutions and thermally modified discrete Alfvén waves in coronal loops. We offer suggestions on how to combine linear and non-linear methods, and demonstrate how to leverage GIMLI in the process.

astro-ph.IM↗

arXiv2026

Streamer slab eigenmode analysis with the Legolas code

Context. Helmet streamers are large ray-like structures extending from the solar corona that thin further away from the solar surface, forming an extended current sheet. These structures are quasi-stable, and are observed to support kink waves travelling outward from the Sun, called helmet streamer waves. Aims. Limited analytical models identify streamer waves as fast body kink eigenmodes of the streamer slab. To bridge the gap between analytical models and numerical simulations, we investigate the eigenmode spectrum of more realistic streamer slab configurations, obtained from simulations, to retrieve the kink profiles and firmly establish that streamer waves are eigenmodes of the streamer. Methods. Using a streamer slab model extracted from numerical simulations, the Legolas code is applied to compute the eigenmode spectrum, for wavelengths observed in the simulation. In the spectrum we identify the mode matching the behaviour in the non-linear simulations by comparing to analytical and numerical results for the established Epstein profile. The identified modes's phase speeds are then compared to analytical, simulation, and observational results. Results. For each case, the spectrum is found to contain a mode matching the properties of a streamer wave. The phase speeds of the identified modes are compatible with those measured in observations, strongly suggesting that the observed streamer waves are fast body kink modes. Comparison to the analytical slab model is difficult due to the sensitivity of the analytical dispersion relation to the internal values.

astro-ph.SR↗

arXiv2026

Thermal instability in coronal loops: linking eigenvalue spectra to time-dependent evolution

Cool, dense condensations such as coronal rain and prominences suggest that coronal plasma can undergo runaway radiative cooling. Connecting this behaviour to linear thermal modes requires us to fully understand the deeper connection between eigenvalue spectra and actual time-dependent evolution. We aim to clarify this intricate link for a simplified, coronal-only model of a stratified coronal loop by combining spectral, linear initial-value, and nonlinear simulations of the same loop setup. We study waves and instabilities, as well as temporal evolutions for a 1D hydrostatic, thermally balanced loop with optically thin radiation and prescribed heating. The non-adiabatic spectrum is computed with our open-source Legolas code. We demonstrate our newly developed boundary value-initial value solver Legolas-IVP, where linear evolutions are performed for controlled perturbations, and fully equivalent nonlinear runs are carried out with MPI-AMRVAC. The spectrum contains discrete acoustic modes and a thermally unstable branch including a thermal continuum. Linear initial-value experiments with isochoric, isobaric, and isentropic pulses highlight how the polarisation of the eigenmodes demonstrates physically consistent behaviour expected from the eigenspectrum. Even in the linear stage, thermal imbalance drives siphon-like flows toward the cooling region. Growth rates from Legolas-IVP agree with spectral predictions and are reproduced in MPI-AMRVAC, which follows the condensation through runaway cooling to chromospheric temperatures, with the cool dense blob sliding under gravity toward the loop footpoint. The spectral-linear-nonlinear investigation demonstrates a direct link between thermal eigenmodes and condensation dynamics, providing a basis for extending to fully 3D MHD models.

astro-ph.SR↗

arXiv2026

Eigenmode initialisation of 2D (magneto)hydrodynamic simulations

The early evolution of unstable hydrodynamic and magnetohydrodynamic equilibria is often governed by a few dominant linear eigenmodes. We investigate whether initialising a simulation with a superposition of linear eigenmodes that contains the most unstable mode saves computation time, and how the selection of the included modes affects the non-linear evolution. Using the non-linear (magneto)hydrodynamic simulation code MPI-AMRVAC, the evolutions of a flow-sheared fluid interface, a Harris current sheet, and a flow-sheared plasma interface were simulated for various initial perturbations. The novel initial perturbations were linear eigenmodes of the equilibrium, or superpositions thereof, and calculated with the Legolas code. We benchmarked to initialisation with velocity noise and, in the case of the Harris sheet, initialisation with an analytic magnetic field perturbation. By perturbing an unstable equilibrium with a superposition of linear eigenmodes that contains the most unstable mode, significantly less computation time is spent on the linear stage of the evolution compared to traditional perturbation methods. In the best case, the simulation time needed to reach the non-linear stage is reduced by an order of magnitude. The inclusion or omission of certain modes in the initial perturbation is observed to affect the non-linear evolution to various degrees. The perturbation of equilibria with a superposition of linear eigenmodes that contains the most unstable mode allows simulations to reach a late-evolution stage faster, thus saving computation time. Additional eigenmodes can be included alongside the fastest growing mode to obtain further benefits, for example, to accelerate symmetry breaking in the non-linear stage, or to delay their effect on the non-linear evolution. Coupling spectroscopic codes with (magneto)hydrodynamic codes therefore offers significant advantages.

astro-ph.IM↗

arXiv2025

The hydrodynamic thermal continuum, with applications to stratified atmospheres and 1D coronal loop models

Using both analytical and numerical means, we demonstrate that linear stability analysis of a hydrodynamic stratified atmosphere or a 1D coronal loop model in non-adiabatic settings features a thermal continuum corresponding to highly localized eigenfunctions. This thermal continuum can be precomputed, involving the net heat-loss function and its partial derivatives, and is the generalization of the thermal instability introduced by~\citet{Parker1953}. We account for a thermal imbalance, directly affecting thermal instability growthrates. We present completely general equations that govern all eigenmodes, including non-adiabatically affected p- and g-modes of the stratified settings. We intend to clarify how linear thermal instability is relevant for solar loops that show spontaneous in-situ condensations, and eliminate recent confusion on specific isochoric routes to linear instability alongside other thermal instability channels. The thermal continuum, previously identified as a crucial ingredient in magnetohydrodynamic eigenmode spectra for coronal loops and atmospheres, drives multithermal aspects across our universe, such as forming solar coronal rain and prominences, or cold cloud creation in intracluster to interstellar medium environments.

astro-ph.SR↗

arXiv2024

The coupled tearing-thermal instability in coronal current sheets from the linear to the non-linear stage

In the solar corona, magnetically sheared structures are unstable to both tearing and thermal instabilities in a coupled fashion. However, how the choice of linear perturbation modes influences the time-scale to achieve the thermal runaway in a coupled tearing-thermal coronal current sheet is not well understood to date. Here, we model a force-free Harris current sheet under solar coronal conditions to investigate this coupling in the linear and non-linear regimes. In the linear regime, we adopt the magnetohydrodynamic spectroscopy code Legolas to compare the current sheet under thermal and thermoresistive conditions, after which we initialise non-linear simulations (with MPI-AMRVAC) with the unstable, linear tearing and thermal perturbations obtained with Legolas. It is shown that part of the unstable thermal quasi-continuum adopts tearing properties in the linear stage, but that it is not until the non-linear stage is reached that a true thermal 'runaway' effect leads to condensations inside tearing-induced flux ropes. Hence, the linear stage is governed by the dominant tearing instability whilst condensations form due to tearing-thermal coupling in the non-linear stage. Our results imply that perturbing an equilibrium current sheet with the fastest growing linear mode skips the mode mixing phase in which the dominant instability traditionally emerges, and significantly reduces the time-scale to enter into the non-linear stage and thermal runaway process from its equilibrium configuration.

astro-ph.SR↗

arXiv2024

Collisional damping of wave modes in ion-electron plasmas

To expand on recent work, we introduce collisional terms in the analysis of the warm ion-electron, two-fluid equations for a homogeneous plasma at rest. Consequently, the plasma is now described by six variables: the magnetisation, the ratio of masses over charges, the electron and ion sound speeds, the angle between the wave vector and the magnetic field, and a new parameter describing the electron-ion collision frequency. This additional parameter does not introduce new wave modes compared to the collisionless case, but does result in complex mode frequencies. Both for the backward and forward propagating modes the imaginary components are negative and thus quantify collisional damping. We provide convenient (polynomial) expressions to quantify frequencies and damping rates in all short and long wavelength limits, including the cut-off and resonance limits, whilst the one-fluid magnetohydrodynamic limit is retained with the familiar undamped slow, Alfvén and fast (SAF) waves. As collisions only introduce a damping, the previously introduced labelling of the wave modes S, A, F, M, O and X can be kept and assigned based on their long and short wavelength behaviour. The obtained damping at cut-off and resonance limits is parametrised with the collision frequency, and can be tailored to match known kinetic damping expressions. It is demonstrated that varying the angle can introduce crossings between the wave modes, as was already present in the ideal ion-electron case, but also a collision frequency exceeding a critical collision frequency can lead to crossings at angles where previously only avoided crossings were found.

physics.plasm-ph↗

arXiv2024

Modification of the resistive tearing instability with Joule heating by shear flow

We investigate the influence of background shear flow on linear resistive tearing instabilities with Joule heating for two compressible plasma slab configurations: a Harris current sheet and a force-free, shearing magnetic field that varies its direction periodically throughout the slab, possibly resulting in multiple magnetic nullplanes. To do so, we exploit the latest version of the open-source, magnetohydrodynamic spectroscopy tool Legolas. Shear flow is shown to dramatically alter tearing behaviour in the presence of multiple magnetic nullplanes, where the modes become propagating due to the flow. Finally, the tearing growth rate is studied as a function of resistivity, showing where it deviates from analytic scaling laws, as well as the Alfvén speed, the plasma-beta, and the velocity parameters, revealing surprising nuance in whether the velocity acts stabilising or destabilising. We show how both slab setups can produce growth rate regimes which deviate from analytic scaling laws, such that systematic numerical spectroscopic studies are truly necessary, for a complete understanding of linear tearing behaviour in flowing plasmas.

physics.plasm-ph↗

arXiv2023

Neural network classification of eigenmodes in the magnetohydrodynamic spectroscopy code Legolas

To predict the immediate evolution of a plasma system, one needs to identify the nature of the dominant instability. In this work, a neural network is employed to address a non-binary classification problem of instabilities in astrophysical jets, whose natural oscillations and instabilities are quantified with the magnetohydrodynamic spectroscopy code Legolas. The trained models exhibit reliable performance in the identification of the two instability types supported by these jets. To improve the neural network aided classification process, techniques for training data augmentation and refinement of predictions for general eigenproblems are discussed.

physics.plasm-ph↗

arXiv2022

Legolas: magnetohydrodynamic spectroscopy with viscosity and Hall current

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 setup 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 to 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.

physics.plasm-ph↗

arXiv2021

Legolas: a modern tool for magnetohydrodynamic spectroscopy

Magnetohydrodynamic (MHD) spectroscopy is central to many astrophysical disciplines, ranging from helio- to asteroseismology, over solar coronal (loop) seismology, to the study of waves and instabilities in jets, accretion disks, or solar/stellar atmospheres. MHD spectroscopy quantifies all linear (standing or travelling) wave modes, including overstable (i.e. growing) or damped modes, for a given configuration that achieves force and thermodynamic balance. Here, we present Legolas, a novel, open-source numerical code to calculate the full MHD spectrum of one-dimensional equilibria with flow, that balance pressure gradients, Lorentz forces, centrifugal effects and gravity, enriched with non-adiabatic aspects like radiative losses, thermal conduction and resistivity. The governing equations use Fourier representations in the ignorable coordinates, and the set of linearised equations are discretised using Finite Elements in the important height or radial variation, handling Cartesian and cylindrical geometries using the same implementation. A weak Galerkin formulation results in a generalised (non-Hermitian) matrix eigenvalue problem, and linear algebraic algorithms calculate all eigenvalues and corresponding eigenvectors. We showcase a plethora of well-established results, ranging from p- and g-modes in magnetised, stratified atmospheres, over modes relevant for coronal loop seismology, thermal instabilities and discrete overstable Alfvén modes related to solar prominences, to stability studies for astrophysical jet flows. We encounter (quasi-)Parker, (quasi-)interchange, current-driven and Kelvin-Helmholtz instabilities, as well as non-ideal quasi-modes, resistive tearing modes, up to magneto-thermal instabilities. The use of high resolution sheds new light on previously calculated spectra, revealing interesting spectral regions that have yet to be investigated.

astro-ph.SR↗

arXiv2021

Two-fluid treatment of whistling behaviour and the warm Appleton-Hartree extension

As an application of the completely general, ideal two-fluid analysis of waves in a warm ion-electron plasma, where six unique wave pair labels (S, A, F, M, O, and X) were identified, we here connect to the vast body of literature on whistler waves. We show that all six mode pairs can demonstrate whistling behaviour, when we allow for whistling of both descending and ascending frequency types, and when we study the more general case of oblique propagation to the background magnetic field. We show how the general theory recovers all known approximate group speed expressions for both classical whistlers and ion cyclotron whistlers, which we here extend to include ion contributions and deviations from parallel propagation. At oblique angles and at perpendicular propagation, whistlers are investigated using exact numerical evaluations of the two-fluid dispersion relation and their group speeds under Earth's magnetosphere conditions. This approach allows for a complete overview of all whistling behaviour and we quantify the typical frequency ranges where they must be observable. We use the generality of the theory to show that pair plasmas in pulsar magnetospheres also feature whistling behaviour, although not of the classical type at parallel propagation. Whistling of the high frequency modes is discussed as well, and we give the extension of the Appleton-Hartree relation for cold plasmas, to include the effect of a non-zero thermal electron velocity. We use it to quantify the Faraday rotation effect at all angles, and compare its predictions between the cold and warm Appleton-Hartree equation.

physics.plasm-ph↗

arXiv2020

A two-fluid analysis of waves in a warm ion-electron plasma

Following recent work, we discuss waves in a warm ideal two-fluid plasma consisting of electrons and ions starting from a completely general, ideal two-fluid dispersion relation. The plasma is characterised by five variables: the electron and ion magnetisations, the squared electron and ion sound speeds, and a parameter describing the angle between the propagation vector and the magnetic field. The dispersion relation describes 6 pairs of waves which we label S, A, F, M, O, and X. Varying the angle, it is argued that parallel and perpendicular propagation (with respect to the magnetic field) exhibit unique behaviour. This behaviour is characterised by the crossing of wave modes which is prohibited at oblique angles. We identify up to 6 different parameter regimes where a varying number of exact mode crossings in the special parallel or perpendicular orientations can occur. We point out how any ion-electron plasma has a critical magnetisation (or electron cyclotron frequency) at which the cutoff ordering changes, leading to different crossing behaviour. These are relevant for exotic plasma conditions found in pulsar and magnetar environments. Our discussion is fully consistent with ideal relativistic MHD and contains light waves. Additionally, exploiting the general nature of the dispersion relation, phase and group speed diagrams can be computed at arbitrary wavelengths for any parameter regime. Finally, we recover earlier approximate dispersion relations that focus on low-frequency limits and make direct correspondences with some selected kinetic theory results.

physics.plasm-ph↗