Hostname: page-component-cd9895bd7-gbm5v Total loading time: 0 Render date: 2024-12-25T19:07:12.308Z Has data issue: false hasContentIssue false

The Harris sheet in a dusty plasma

Published online by Cambridge University Press:  23 April 2010

SAMUEL A. LAZERSON*
Affiliation:
Geophysical Institute, University of Alaska, Fairbanks, AK 99775, USA (lazersos@gmail.com)

Abstract

In 1962 E. G. Harris published a solution to the problem of a current sheet separating regions of oppositely directed magnetic field in a fully ionized plasma. The resulting solution has become known as the ‘Harris sheet’ and has been of great utility to the plasma physics community. In this paper, the footsteps of Harris are retraced with the addition of a multiply charged massive dust component. A set of highly nonlinear differential equations for a current sheet in a dusty plasma are presented. An analytic solution, similar to that of Harris, is found for the depleted electron regime. This solution is of great relevance to many astrophysical and laboratory dusty plasmas. Current sheet thickness and asymptotic field strength are calculated for various dusty plasma environments.

Type
Papers
Copyright
Copyright © Cambridge University Press 2010

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Birk, G. T. and Wiechen, H. M. 2001 Resistive tearing mode instabilities in partially ionised dusty plasmas. In Proceedings of the Sixth International School/Symposium for Space Plasma Simulations (ISSS-6), Garching, Germany, 3-7 September, 2001. (ed. Bchner, J., Dum, C. T. and Scholer, M.), pp. 222225. Berlin: Schaltungsdienst Lange o.H.G., 2001.Google Scholar
Birk, G. T. and Wiechen, H. 2002 Shear flow instabilities in magnetized partially ionized dense dusty plasmas. Phys. Plasmas 9, 964970.CrossRefGoogle Scholar
Chen, F. F. 1995 Industrial applications of low-temperature plasma physics. Phys. Plasmas 2, 21642175.CrossRefGoogle Scholar
Harris, E. G. 1962 On a plasma sheath separating regions of oppositely directed magnetic field. Il Nuovo Cimento 23, 115121.CrossRefGoogle Scholar
Joung, M. K., Mac Low, M. M. and Ebe, D. S. 2004 Condrule formation and protoplanetary disk heating by current sheets in Nonideal Magnetohydrodynamic turbulence. Astrophys. J. 606, 532541.CrossRefGoogle Scholar
Jovanović, D., Shukla, P. K. and Morfill, G. E. 2005 Magnetic reconnection on the ion-skin-depth scale in the dusty magnetotail of a comet. Phys. Plasmas 12, 042904.1042904.9.CrossRefGoogle Scholar
Lazerson, S. A. & Wiechen, H. M. 2008 Three-dimensional simulations of magnetic reconnection in a dusty plasma. J. Plasma Phys. 74, 493513.CrossRefGoogle Scholar
Mendis, D. A. and Rosenberg, M. 1994 Cosmic dusty plasmas. Annu. Rev. Astron. Astrophys. 32, 419463.CrossRefGoogle Scholar
Shukla, P. K. and Eliasson, B. 2009 Colloquium: fundamentals of dust-plasma interations. Rev. Mod. Phys. 81, 2544.CrossRefGoogle Scholar
Shukla, P. K. and Mamun, A. A. 2002 Introduction to Dusty Plasma Physics. Bristol: Institute of Physics Publishing.CrossRefGoogle Scholar
Shukla, P. K., Mendis, D. A. and Desai, T. 1997 Advances in Dusty Plasmas. River Edge, NJ: World Scientific.CrossRefGoogle Scholar
Thomas, E. 2006 Measurements of spatially growing dust acoustic waves in a dc glow discharge plasma. Phys. Plasmas 15, 042107.1042107.5.Google Scholar
Verheest, F. 2001 Waves in Dusty Space Plasmas. Springer. Dordecht, The Netherlands.Google Scholar
Williams, J. D. and Thomas, E. 2006 Initial measurement of the kinetic dust temperature of a weakly coupled dusty plasma. Phys. Plasmas 13, 063509–063509–6.CrossRefGoogle Scholar
Williams, J. D. and Thomas, E. 2007 Measurement of the kinetic dust temperature of a weakly coupled dusty plasma. Phys. Plasmas 14, 063702–063702–8.CrossRefGoogle Scholar