Magnetohydrodynamic spectrum of 
gravitating plane plasmas with flow

Holst, B. van der; Nijboer, R. J.; Goedbloed, J. P.

doi:10.1017/s0022377898007454

Cited by 12 publications

(7 citation statements)

References 23 publications

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“…Bondeson, Iacono, & Bhattacharjee (1987) and Hameiri (1976) derived this system for cylindrical equilibria with flow but without gravity. An analysis for gravitating, flowing magnetized equilibria in planar geometry is found in van der Holst, Nijboer, & Goedbloed (1999).…”

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confidence: 99%

Waves and Instabilities in Accretion Disks: Magnetohydrodynamic Spectroscopic Analysis

Keppens¹,

Casse²,

Goedbloed³

2002

The Astrophysical Journal

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A complete analytical and numerical treatment of all magnetohydrodynamic waves and instabilities for radially stratified, magnetized accretion disks is presented. The instabilities are a possible source of anomalous transport. While recovering results on known hydrodynamic and both weak-and strong-field magnetohydrodynamic perturbations, the full magnetohydrodynamic spectra for a realistic accretion disk model demonstrate a much richer variety of instabilities accessible to the plasma than previously realized. We show that both weakly and strongly magnetized accretion disks are prone to strong nonaxisymmetric instabilities. The ability to characterize all waves arising in accretion disks holds great promise for magnetohydrodynamic spectroscopic analysis. Subject headings: accretion, accretion disks -instabilities -MHD -waves 1. HYDROMAGNETIC STABILITY FOR STATIONARY EQUILIBRIAMagnetohydrodynamic (MHD) spectroscopy (Goedbloed et al. 1994) entails the ability to calculate all MHD perturbations accessible to a particular magnetized plasma configuration (the forward spectral problem) and holds the promise to use the MHD spectrum to diagnose the internal plasma state (the backward spectral problem). In this Letter we predict all MHD waves and instabilities for magnetized accretion disks.To analyze the entire MHD spectrum of gravitationally and thermally stratified, rotating magnetized equilibrium configurations, we use the formalism of Frieman & Rotenberg (1960). The equation of motion for the Lagrangian displacement of a fluid y element is2 Ѩt Ѩt where measures the Eulerian perturbation of total pressure, is the Eulerian P p Ϫy · ١p Ϫ g p١ · y ϩ B · Q Q p ١ ؋ (y ؋ B) perturbation of the magnetic field B, and g is the gravitational acceleration. Equation (1) describes all waves supported by a timeinvariant equilibrium with density r, pressure p, flow field , gravity g, and magnetic field B; g is the ratio of specific heats. We v specify our analysis to one-dimensional axisymmetric stationary equilibria satisfying 2 2 2 2

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confidence: 99%

Waves and Instabilities in Accretion Disks: Magnetohydrodynamic Spectroscopic Analysis

Keppens¹,

Casse²,

Goedbloed³

2002

The Astrophysical Journal

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“…This is evident by comparing the cylindrical expressions of Bondeson et al 5 with the corresponding gravitating slab expressions of van der Holst et al 6 Both Refs. Note that the density perturbation appears in the momentum equation (4) as a downward acceleration −ge x [when moved to the right-hand side (RHS)], somewhat similar to the way in which the outward centrifugal acceleration −v · ٌ v = ͑v 2 / r͒e r would appear for a cylindrical equilibrium.…”

Section: ͑2͒mentioning

confidence: 89%

No additional flow continua in magnetohydrodynamics

et al. 2004

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The classical continuous spectrum of fluid flow found by C.M. Case [Phys. Fluids 3, 143 (1960)] is contained in the Alfvén and slow continua of magnetohydrodynamics (MHD). Contrary to several statements in the literature, most recently by S.N. Bhattacharyya and A. Bhattacharjee [Phys. Plasmas 4, 3744 (1997)], there are no additional flow continua in MHD. Additional Eulerian continuum modes do exist in both fluids and plasmas, but they only involve non-Lagrangian perturbations of the density or the entropy, not of the pressure and the magnetic field.

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“…The ODE ͑59͒ was first derived by Goedbloed 54 for static plasmas, and generalized to stationary plasmas by van der Holst et al 55 by means of the replacement 2 → 2 ͑x͒. For the sake of reference, we briefly summarize some of the central properties of the ODEs ͑59͒ and ͑63͒, and of their cylindrical counterparts derived much earlier by Hain and Lüst 56 for static plasmas, and generalized to stationary plasmas by Hameiri 25,27 and Bondeson et al 57 It should be noticed that the latter modification for cylindrical plasmas is much more substantial than just replacing 2 by 2 because of the additional effects of the Coriolis and centrifugal terms.…”

Section: ͑58͒mentioning

confidence: 99%

Magnetohydrodynamic spectrum of gravitating plane plasmas with flow

Cited by 12 publications

References 23 publications

Waves and Instabilities in Accretion Disks: Magnetohydrodynamic Spectroscopic Analysis

Waves and Instabilities in Accretion Disks: Magnetohydrodynamic Spectroscopic Analysis

No additional flow continua in magnetohydrodynamics

New construction of the magnetohydrodynamic spectrum of stationary plasma flows. I. Solution path and alternator

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