Calculating magnetohydrodynamic flow spectra

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

doi:10.1016/s0010-4655(97)00082-9

Cited by 19 publications

(22 citation statements)

References 9 publications

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“…For these, we used a finite-element code called LEDAFLOW, which is an extension with flow equilibria of the code LEDA (large-scale eigenvalue solver for the dissipative Alfvén spectrum) (Kerner et al 1985). We shall give a full description of the code in another paper (Nijboer et al 1997).…”

Section: Spectrum Of the Compressible Plasma: Numerical Resultsmentioning

confidence: 99%

Spectrum and stability of a rigidly rotating compressible plasma

1997

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We consider the spectrum and stability of a compressible, rigidly rotating plasma column with constant magnetic pitch. It is found that when the pressure on axis is zero, a continuous spectrum arises, which may become unstable. When the pressure on axis is finite or a conducting core is included, the spectrum is discrete, but may still be unstable. The instability is due to the poloidal magnetic field and/or the rotation of the cylinder in combination with the density profile. It is found numerically that the pressure stabilizes both types of instabilities.

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Section: Spectrum Of the Compressible Plasma: Numerical Resultsmentioning

confidence: 99%

Spectrum and stability of a rigidly rotating compressible plasma

1997

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“…We used two independent ideal MHD stability codes, described in detail elsewhere (Appl & Camenzind 1992;Appl 1996;Appl et al 2000;Nijboer et al 1997). In both codes, an eigenvalue problem for an infinitely long cylindrical jet is solved using a normal mode expansion for the perturbed quantities of the form f ðrÞ exp½iðm þ kz À !tÞ .…”

Section: Stability Studymentioning

confidence: 99%

“…The linear growth rate C of a mode specified by the wavenumbers m and k is then obtained. In the LEDAFLOW program (Nijboer et al 1997), one similarly fixes the wavenumbers m and k, but one can solve for all eigenvalues ! simultaneously (including both overstable and damped eigenmodes) by solving the eigenvalue problem using the QR algorithm.…”

Section: Stability Studymentioning

confidence: 99%

Interplay between Kelvin‐Helmholtz and Current‐driven Instabilities in Jets

Baty

Keppens

2002

ApJ

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We investigate, by means of three-dimensional compressible magnetohydrodynamic numerical simulations, the interaction of Kelvin-Helmholtz (KH) and current-driven (CD) instabilities in a magnetized cylindrical jet configuration. The jet has a supersonic axial flow, sheared in the radial direction, and is embedded in a helical magnetic field. The strength of the axial magnetic field component is chosen to be weak, in accord with the '' weak field regime '' previously defined by Ryu, Jones, & Frank for uniformly magnetized configurations. We follow the time evolution of a periodic section where the jet surface is perturbed at m ¼ AE1 azimuthal mode numbers. A m ¼ À1 KH surface mode linearly develops dominating the m ¼ þ1 KH one, in agreement with results obtained using an independent ideal stability code. This lifted degeneracy, because of the presence of the helical field, leads nonlinearly to clear morphological differences in the jet deformation as compared to uniformly magnetized configurations. As predicted by stability results, a m ¼ À1 CD instability also develops linearly inside the jet core for configurations having a small enough magnetic pitch length. As time proceeds, this magnetic mode interacts with the KH vortical structures and significantly affects the further nonlinear evolution. The magnetic field deformation induced by the CD instability provides a stabilizing effect through its azimuthal component B . This helps to saturate the KH vortices in the vicinity of the jet surface. Beyond saturation, the subsequent disruptive effect on the flow is weaker than in cases having similar uniform and helical magnetic field configurations without the CD mode. We discuss the implications of this stabilizing mechanism for the stability of astrophysical jets.

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“…The Galerkin method in combination with a mixed finite-element-Fourier discretization applied to (3.2)-(3.6) leads to a very large matrix eigenvalue problem. The analogous problem for one-dimensional geometries is solved using a QR solver and an inverse vector iteration method as described by Nijboer et al (1997b). However, for two-dimensional problems, these solvers are quite limiting.…”

Section: The In2fles Codementioning

confidence: 99%

“…5, the complete spectrum for one poloidal harmonic in a circular cylinder (c = 1) is shown. This spectrum was calculated using the LEDAFLOW code (Nijboer et al 1997b) for a circular geometry as a check on the IN2FLES code. Since the equilibrium is one-dimensional, no mode coupling occurs.…”

Section: The Two-dimensional Discrete Spectrummentioning

confidence: 99%

Mode coupling in two-dimensional magnetohydrodynamic flows

Nijboer

Goedbloed

1999

J. Plasma Phys.

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The spectrum of incompressible waves and instabilities of two-dimensional plasma geometries with background flow is calculated. The equilibrium is solved numerically by the recently developed program FLow Equilibrium Solver (FLES). The spectra of the equilibria are computed by means of another new program, the INcompressible 2-dimensional FLow Eigenvalue Solver (IN2FLES). Magnetic instabilities and instabilities driven by the two-dimensionality and the flow are found. For linear equilibria, the eigenvalues for elliptical geometries remain close to the curves on which the eigenvalues for circular geometries lie. These curves may be found for unbounded domains by a calculation in Fourier space [see Lifschitz, A. In: Proceedings of 1995 International Workshop on Operator Theory and Applications (ed. R. Mennicken and C. Tretter), pp. 97-117, Birkhäuser, Boston, 1998]. Here the relation between a new continuous spectrum of unbounded domains and the discrete spectrum of bounded domains is investigated. Finally, it is found that the two-dimensionality and the background flow may lead to an overstable clusterpoint.

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Calculating magnetohydrodynamic flow spectra

Cited by 19 publications

References 9 publications

Spectrum and stability of a rigidly rotating compressible plasma

Spectrum and stability of a rigidly rotating compressible plasma

Interplay between Kelvin‐Helmholtz and Current‐driven Instabilities in Jets

Mode coupling in two-dimensional magnetohydrodynamic flows

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