Plasma and Fusion Research
Volume 2, 016 (2007)
Regular Articles
- Graduate School of Frontier Sciences, The University of Tokyo
- 1)
- Faculty of Mathematics, Kyushu University
- 2)
- Indian Institute of Astrophysics
Abstract
Axisymmetric magneto-rotational instability (MRI) is studied in comparison with interchange instability (IntI) in a rotating cylindrical plasma. MRI is driven by the shear of plasma rotation, and the IntI by the density gradient with effective gravity due to the plasma rotation. The eigenmode equation for the MRI has the same form as that for the IntI. The local stability criterion is also summarized in a similar statement as “the spatial gradient of centrifugal force greater than the square of Alfvén frequency causes instability.” However, the MRI is essentially different from the IntI because of the non-Hermitian property. The Keplerian rotation generates irregular singularity at the center of the disk, which yields a continuum of eigenvalues with non-orthogonal and square-integrable eigenfunctions.
Keywords
flowing plasma, magneto-rotational instability, interchange instability, Alfvén wave, irregular singularity
Full Text
References
- [1] J.W. Connor, R.J. Hastie and J.B. Taylor, Proc. R. Soc. London Ser. A 365, 1 (1979).
- [2] R.L. Dewar and A.H. Glasser, Phys. Fluids 26, 3038 (1983).
- [3] W.A. Cooper, Plasma Phys. Control. Fusion 30, 1805 (1988).
- [4] R.L. Miller, F.L. Waelbroeck, A.B. Hassam and R.E. Waltz, Phys. Plasmas 2, 3676 (1995).
- [5] M. Furukawa, Y. Nakamura et al., Phys. Plasmas 8, 4889 (2001).
- [6] M. Furukawa and S. Tokuda, Phys. Rev. Lett. 94, 175001 (2005).
- [7] M. Furukawa, Z. Yoshida and S. Tokuda, Phys. Plasmas 12, 072517 (2005).
- [8] D. Pfirsch and H. Tasso, Nucl. Fusion 11, 259 (1971).
- [9] A. Bondeson and D.J. Ward, Phys. Rev. Lett. 72, 2709 (1994).
- [10] D.J. Ward and A. Bondeson, Phys. Plasmas 2, 1570 (1995).
- [11] E.J. Strait et al., Phys. Rev. Lett. 74, 2483 (1995).
- [12] W. Horton, Rev. Mod. Phys. 71, 735 (1999).
- [13] S. Chandrasekhar, Hydrodynamic and Hydromagnetic Stability (Dover Publications, Inc., New York, 1981).
- [14] T. Tatsuno, J. Plasma Fusion Res. 79, 1169 (2003).
- [15] T. Tajima and K. Shibata, Plasma Astrophysics (Perseus Publishing, Cambridge, Massachusetts, 2002).
- [16] S.A. Balbus and J.F. Hawley, Rev. Mod. Phys. 70, 1 (1998).
- [17] E.P. Velikhov, Sov. Phys. JETP 36(9), 995 (1959).
- [18] S. Chandrasekhar, Proc. Nat. Acad. Sci. 46, 253 (1960).
- [19] S.A. Balbus and J.F. Hawley, Astrophys. J. 376, 214 (1991).
- [20] J.P. Freidberg, Ideal Magnetohydrodynamics (Plenum Press, New York, 1987).
- [21] E. Frieman and M. Rotenberg, Rev. Mod. Phys. 32, 898 (1960).
- [22] M. Furukawa, V. Krishan et al., Astrophys. J. 659, 1496 (2006).
- [23] R. Chini, V. Hoffmeister et al., Nature 429, 155 (2004).
- [24] C. Curry, R.E. Pudritz and P.G. Sutherland, Astrophys. J. 434, 206 (1994).
- [25] I.V. Khalzov, V.I. Ilgisonis et al., Phys. Fluids 18, 124107 (2006).
- [26] J.P. Goedbloed and P.H. Sakanaka, Phys. Fluids 17, 908 (1974).
- [27] A. Bondeson, R. Iacono and A. Bhattacharjee, Phys. Fluids 30, 2167 (1987).
This paper may be cited as follows:
Masaru FURUKAWA, Zensho YOSHIDA, Makoto HIROTA and Vinod KRISHAN, Plasma Fusion Res. 2, 016 (2007).