Inertial Effects on Tearing Instability
DOI:
https://doi.org/10.14311/ppt.2016.3.155Keywords:
resistive instabilities, Ohm’s law, current relaxationAbstract
In this work, we explore inertial effects, due to charged species in a resistive plasma, on the tearing instability. The standard theory of tearing modes assumes a long wavelength limit. At shorter wave lengths, inertial effects can become important and the current density flowing in the fluid can acquire a finite relaxation time. The introduction of such a correction into the problem leads to an extension of the standard dispersion relation. In the long wave length limit, we recover the standard scaling of the growth rate γ with the plasma resistivity η, namely γ ≈ η3/5. However, in the short wavelength limit, we find that the scaling of γ with the relevant plasma parameters changes significantly due to the influence of inertia. Notwithstanding, the dependence of γ on the relaxation time of the current density is not determined. In order to achieve such a description, we propose to further rediscuss the problem in the framework of the boundary layer technique.References
Killeen J. Rosenbluth M. N. Furth, H. P. Finite resistivity instabilities of a sheet pinch. Phys. Fluids, 6:459, 1963.
Johnson J L Coppi B., Greene J M. The non-linear evolution of resistive interchange modes in a reversed-field pinch. Nucl. Fusion, 6:101, 1961.
Johnson J L Glasser A. H., Greene J M. Resistive instabilities in general toroidal plasma configurations. Phys. Fluids, 18:875, 1975.
Pellat R Rosenbluth M N Rutherford P H Sov. J. Coppi B., Galvão R M O. Sov. J. Plasma Phys., 2, 1976.
Dependence of ideal-mhd kink and ballooning modes on plasma shape and profiles in tokamaks. Phys. Rev. Lett., 38:826, 1977.
J. Mondt J. P., Weiland J. Nonlinear theory of large-mode-number ballooning modes in fully toroidal geometry. Plasma Phys., 34:143, 1985.
Rosenbluth M N Waddell B V White R. W., Monticello D A. Saturation of the tearing mode. Phys. Fluids, 20:800, 1977.
Wesson J Turner M. F. Nucl. Fusion, 22:1069, 1982.
Sov. J. Smolyakov A. I. Plasma Phys., 15:667, 1989.
Matsumoto H McGuire K Peebles W A Ritz Ch P Terry P W Zweben S J Wootton A. J., Carreras B A. Fluctuations and anomalous transport in tokamaks. Phys. Fluids B, 2:2879, 1990.
Kadomtsev B. Plasma transport in tokamaks. Nucl. Fusion, 31:1301, 1991.
Parker E. N. Sweet’s mechanism for merging magnetic fields in conducting fluids. J. Geophys. Res., 62:509, 1957.
Biskamp D. Magnetic reconnection via current sheets. Phys. Fluids, 29:1520, 1986.
Sridhar S Goldreich P. Toward a theory of interstellar turbulence. 2: Strong alfvenic turbulence. Astrophys. J., 438:763, 1995.
Vishniac E Lazarian A. Reconnection in a weakly stochastic field. Astrophys. J., 517:700, 1999.
Vishniac E Otmianowska-Mazur K Kowal G., Lazarian A. Numerical tests of fast reconnection in weakly stochastic magnetic fields. Astrophys. J., 700:63, 2009.
Vishniac E Otmianowska-Mazur K Kowal G., Lazarian A. Reconnection studies under different types of turbulence driving. Nonlinear Proc. Geoph., 19:297, 2012.
Spitzer L. Physics of Fully Ionized Gases. Second edition. Dover Publications, New York, 1969.
Silveira F. E. M. Alfven waves and current relaxation: attenuation at high frequencies and large resistivity. J. Phys.: Conf. Ser., 370:012005, 2012.
Silveira F. E. M. Magnetosonic waves and current relaxation. J. Plasma Phys. and Technol., 79:45, 2013.
Galvão R M O Silveira F. E. M. Magnetorotational instability, current relaxation, and current-vortex sheet. Phys. Plasmas, 20:082126, 2013.
Harris E. G. On a plasma sheath separating regions of oppositely directed magnetic field. Nuovo Cimento, 23:115, 1962.
Bertotti B. Fine structure in current sheaths. Ann. Phys., 22:271, 1963.
Haines M. G. Plasma containment in cusp-shaped magnetic fields. Nucl. Fusion, 17:811, 1977.
Dawson J M Leboeuf J. N., Tajima T. Dynamic magnetic x points. Phys. Fluids, 25:784, 1982.
Ion acceleration and direct ion heating in three-component magnetic reconnection. Phys. Rev. Lett., 76:3328, 1996.
Kosugi T Somov B. V. Collisionless reconnection and high-energy particle acceleration in solar flares. Astrophys. J., 485:859, 1997.
Rutherford P. H. Goldston R. J. Introduction to plasma physics. Institute of Physics, Bristol, 2000.
Jeffreys B S Jeffreys H. Methods of Mathematical Physics. Third edition. Cambridge University Press, Cambridge, 1999.
Orszag S A Bender C. M. Advanced Mathematical Methods for Scientists and Engineers: Asymptotic Methods and Perturbation Theory. Vol. 1. Springer-Verlag, New York, 1999.
Downloads
Published
Issue
Section
License
Authors who publish with this journal agree to the following terms:
- Authors retain copyright and grant the journal right of first publication with the work simultaneously licensed under a Creative Commons Attribution License that allows others to share the work with an acknowledgement of the work's authorship and initial publication in this journal.
- Authors are able to enter into separate, additional contractual arrangements for the non-exclusive distribution of the journal's published version of the work (e.g., post it to an institutional repository or publish it in a book), with an acknowledgement of its initial publication in this journal.
- Authors are permitted and encouraged to post their work online (e.g., in institutional repositories or on their website) prior to and during the submission process, as it can lead to productive exchanges, as well as earlier and greater citation of published work (See The Effect of Open Access).