Advanced Magnetohydrodynamics

Goedbloed, J. P.; Keppens, Rony; Poedts, Stefaan

doi:10.1017/cbo9781139195560

Cited by 248 publications

(203 citation statements)

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“…The threshold is not modified by compressibility. This can be easily demonstrated by recalling that in ideal MHD the frequency of the modes is either real or pure imaginary (Goedbloed & Poedts 2004;Goedbloed et al 2010), so the transition from a stable to an unstable situation is necessarily at the points in which ω = 0 is satisfied. Inserting this condition in Eq.…”

Section: Fully Ionized Plasmamentioning

confidence: 99%

Rayleigh-Taylor instability in partially ionized compressible plasmas: One fluid approach

Díaz

Khomenko

Collados

2014

A&A

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Aims. We study the modification of the classical criterion for the linear onset and growth rate of the Rayleigh-Taylor instability (RTI) in a partially ionized (PI) plasma in the one-fluid description by considering a generalized induction equation. Methods. The governing linear equations and appropriate boundary conditions, including gravitational terms, are derived and applied to the case of the RTI in a single interface between two partially ionized plasmas. The boundary conditions lead to an equation for the frequencies in which some have positive complex parts, marking the appearance of the RTI. We study the ambipolar term alone first, extending the result to the full induction equation later. Results. The configuration is always unstable because of the presence of a neutral species. In the classical stability regime, the growth rate is small, since the collisions prevent the neutral fluid to fully develop the RTI. For parameters in the classical instability regime, the growth rate is lowered, but the differences with the compressible MHD case are small for the considered theoretical values of the collision frequencies and diffusion coefficients for solar prominences. Conclusions. The PI modifies some aspects of the linear RTI instability, since it takes into account that neutrals do not feel the stabilizing effect of the magnetic field. For the set of parameters representative for solar prominences, our model gives the resulting timescale comparable to observed lifetimes of RTI plumes.

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Section: Fully Ionized Plasmamentioning

confidence: 99%

Rayleigh-Taylor instability in partially ionized compressible plasmas: One fluid approach

Díaz

Khomenko

Collados

2014

A&A

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“…We here attempt to demonstrate the same ability to chart out all eigenmodes for realistically structured prominences, starting with the determination of the continuous parts of the MHD eigenspectrum. These MHD continua form the basic organizing structure of the entire collection of MHD eigenmodes (Goedbloed & Poedts 2004;Goedbloed et al 2010), and because of the multi-dimensional nature of the prominence-containing flux rope, will contain avoided crossings and frequency gaps (Poedts & Goossens 1991). To quantify these mode couplings, and to subsequently take the next step towards full diagnosis of all global discrete eigenmodes, we must ensure that our equilibrium solution is amenable to such an analysis.…”

Section: Prominence Seismology and Equilibrium Configurationsmentioning

confidence: 99%

Toward detailed prominence seismology

Blokland

Keppens

2011

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Context. Prominence seismology exploits our knowledge of the linear eigenoscillations for representative magnetohydrodynamic models of filaments. To date, highly idealized models for prominences have been used, especially with respect to the overall magnetic configurations. Aims. We initiate a more systematic survey of filament wave modes, where we consider full multi-dimensional models with twisted magnetic fields representative of the surrounding magnetic flux rope. This requires the ability to compute accurate 2.5 dimensional magnetohydrodynamic equilibria that balance Lorentz forces, gravity, and pressure gradients, while containing density enhancements (static or in motion). Methods. The governing extended Grad-Shafranov equation is discussed, along with an analytic prediction for circular flux ropes for the Shafranov shift of the central magnetic axis due to gravity. Numerical equilibria are computed with a finite element-based code, demonstrating fourth order accuracy on an explicitly known, non-trivial test case. Results. The code is then used to construct more realistic prominence equilibria, for all three possible choices of a free flux-function. We quantify the influence of gravity, and generate cool condensations in hot cavities, as well as multi-layered prominences. Conclusions. The internal flux rope equilibria computed here have the prerequisite numerical accuracy to allow a yet more advanced analysis of the complete spectrum of linear magnetohydrodynamic perturbations, as will be demonstrated in the companion paper. Key words. Sun: filaments, prominences -instabilities -magnetohydrodynamics (MHD) -plasmas Prominence seismology and equilibrium configurationsOne of the most fascinating phenomena embedded in the million degree solar coronal plasma is the presence of so-called filaments, which are plasma concentrations suspended magnetically against the downward pull of the solar gravitational field. They are up to 100 times colder and denser than their immediate surroundings, and in Hα observations of the solar disk appear as dark features extending over huge distances. High resolution observations indicate that the filament is actually composed of many individual threads, down to the resolution limit of modern observations (about 100 km in width, see Lin et al. 2005), while their length can reach several tens of megameters. When viewed at the solar limb, the filaments can be identified as prominences, and the surrounding magnetic geometry introduces a classification supported by early analytical magnetohydrostatic models (see e.g. Priest 1988): normal and inverse polarity prominences differ in the relative orientation of the filament-carrying flux rope with respect to the underlying (and overarching arcade) magnetic orientation. Comparing their locations to photospheric magnetograms, the filament threads appear primarily suspended above a magnetic neutral line. The study of solar filaments still poses many contemporary challenges to theoretical solar physicists, in terms of their sudden for...

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“…Among them, the family of specific equilibria found by Solov'ev is well known [2]. Even these analytic examples become impossibly complex when applied to equation (43) with full generality of parameters.…”

Section: Static Equilibriamentioning

confidence: 99%

“…Among the many references we may select the classical review [1], and the excellent modern exposition [2]. One of the aims of this theory is to identify perturbation frequencies which lead to exponential growth and therefore show the instability of the equilibrium.…”

Section: Introductionmentioning

confidence: 99%