Abstract
Astrophysical jets are widely believed to be self-collimated by the hoop-stress due to the azimuthal component of their magnetic field. However this implies that the magnetic field is largely dominated by its azimuthal component in the outer jet region. In the fusion context, it is well-known that such configurations are highly unstable in static columns, leading to plasma disruption. It has long been pointed out that a similar outcome may follow for MHD jets, and the reasons preventing disruption are still not elucidated, although some progress has been accomplished in the recent years.
In these notes, I review the present status of this open problem for pressure-driven instabilities, one of the two major sources of ideal MHD instability in static columns (the other one being current-driven instabilities).
I first discuss in a heuristic way the origin of these instabilities. Magnetic resonances and magnetic shear are introduced, and their role in pressure-driven instabilities discussed in relation to Suydam’s criterion. A dispersion relation is derived for pressure-driven modes in the limit of large azimuthal magnetic fields, which gives back the two criteria derived by Kadomtsev for this instability. The growth rates of these instabilities are expected to be short in comparison with the jet propagation time.
What is known about the potential stabilizing role of the axial velocity of jets is then reviewed. In particular, a nonlinear stabilization mechanism recently identified in the fusion literature is discussed.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Begelman, M.C.: Instability of toroidal magnetic field in jets and plerions. 493, 291 (1998)
Bernstein, I.B., Frieman, E.A., Kruskal, M.D., Kulsrud, R.M.: Proc. Roy. Soc. London A 244, 17 (1958)
Blandford, R.D., Rees, M.J.: A ‘twin-exhaust’ model for double radio sources. Monthly Not. Royal Astron. Soc. 169, 395 (1974)
Bodo, G., Massaglia, S., Rossi, P., Rosner, R., Malagoli, A., Ferrari, A.: The long-term evolution and mixing properties of high Mach number hydrodynamic jets. Astron. Astrophys. 303, 281 (1995)
Bodo, G., Rossi, P., Massaglia, S., Ferrari, A., Malagoli, A., Rosner, R.: Three-dimensional simulations of jets. Astron. Astrophys. 333, 1117 (1998)
Bondeson, A., Iacono, R., Bhattacharjee, A.: Local magnetohydrodynamic instabilities of cylindrical plasma with sheared equilibrium flows. Phys. Fluids 30, 2167 (1987)
Chiueh, T.: Suppression of the edge interchange instability in a straight tokamak. Phys. Rev. E 54, 5632–5635 (1996)
Desouza-Machado, S., Hassam, A.B., Sina, R.: Stabilization of Z pinch by velocity shear. Phys. Plasmas 7, 4632–4643 (2000)
Dewar, R.L., Glasser, A.H.: Ballooning mode spectrum in general toroidal systems. Phys. Fluids 26, 3038–3052 (1983)
Dewar, R.L., Tatsuno, T., Yoshida, Z., Nührenberg, C., McMillan, B.F.: Statistical characterization of the interchange-instability spectrum of a separable ideal-magnetohydrodynamic model system. Phys. Rev. E 70, 066409 (2004)
Ferreira, J.: Magnetically-driven jets from Keplerian accretion discs. Astron. Astrophys. 319, 340–359 (1997)
Freidberg, J.P.: Ideal Magnetohydrodynamics. Plenum Press, New York (1987)
Goedbloed, J.P.: Stabilization of magnetohydrodynamic instabilities by force-free magnetic fields. II. Linear pinch. Physica 53, 501–534 (1971)
Goedbloed, J.P., Sakanaka, P.H.: Phys. Fluids 17, 908 (1974)
Hain, K., Lüst, R.: Z. Naturforsch. Teil A 13, 936 (1958)
Hassam, A.B.: Nonlinear stabilization of the Rayleigh-Taylor instability by external velocity shear. Phys. Fluids B 4, 485–487 (1992)
Kersalé, E., Longaretti, P.Y., Pelletier, G.: Pressure- and magnetic shear-driven instabilities in rotating MHD jets. Astron. Astrophys. 363, 1166–1176 (2000)
Krall, N.A., Trievelpiece, A.W.: Principles of Plasma Physics. San Francisco Press, San Francisco (1986)
Li, Z.: Magnetohydrodynamic disk-wind connection: magnetocentrifugal winds from ambipolar diffusion-dominated accretion disks. Astrophys. J. 465, 855–+ (1996)
Ryu, D., Jones, T.W., Frank, A.: The magnetohydrodynamic Kelvin-Helmholtz instability: a three-dimensional study of nonlinear evolution. Astrophys. J. 545, 475–493 (2000)
Sharma, P., Hammett, G.W., Quataert, E., Stone, J.M.: Shearing box simulations of the MRI in a collisionless plasma. Ap637, 952 (2006)
Shu, F.H.: Physics of Astrophysics, Vol. II. University Science Books, Mill Valley (1992)
Shumlak, U., Hartman, C.W.: Sheared flow stabilization of the m = 1 Kink Mode in Z Pinches. Phy. Rev. Lett. 75, 3285–3288 (1995)
Waelbroeck, F.L., Chen, L.: Ballooning instabilities in tokamaks with sheared toroidal flows. Phys. Fluids B 3, 601–610 (1991)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2008 Springer-Verlag Berlin Heidelberg
About this chapter
Cite this chapter
Longaretti, PY. (2008). Pressure-Driven Instabilities in Astrophysical Jets. In: Massaglia, S., Bodo, G., Mignone, A., Rossi, P. (eds) Jets From Young Stars III. Lecture Notes in Physics, vol 754. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-76967-5_4
Download citation
DOI: https://doi.org/10.1007/978-3-540-76967-5_4
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-76966-8
Online ISBN: 978-3-540-76967-5
eBook Packages: Physics and AstronomyPhysics and Astronomy (R0)