Hostname: page-component-848d4c4894-nr4z6 Total loading time: 0 Render date: 2024-05-14T15:26:32.203Z Has data issue: false hasContentIssue false
  • English
  • Français

Lorentz invariant ‘potential magnetic field’ and magnetic flux conservation in an ideal relativistic plasma

Part of: Professor Francesco Pegoraro

Published online by Cambridge University Press:  30 August 2018

F. Pegoraro Open the ORCID record for F. Pegoraro [Opens in a new window]
F. Pegoraro*
Affiliation:
Department of Physics, University of Pisa, largo Pontecorvo 3, 56127 Pisa, Italy
*
†Email address for correspondence: francesco.pegoraro@unipi.it
Get access Rights & Permissions [Opens in a new window]

Abstract

A family of Lorentz invariant scalar functions of the magnetic field is defined in an ideal relativistic plasma. These invariants are advected by the plasma fluid motion and play the role of the potential magnetic field introduced by Hide in (Ann. Geophys., vol. 1, 1983, 59) along the lines of Ertel’s theorem. From these invariants we recover the Cauchy conditions for the magnetic field components in the mapping from Eulerian to Lagrangian variables. In addition, the adopted procedure allows us to formulate, in a Lorentz invariant form, the Alfvén theorem for the conservation of the magnetic flux through a surface comoving with the plasma.

Keywords

astrophysical plasmasplasma dynamicsplasma flows
Type
Research Article
Information
Journal of Plasma Physics , Volume 84 , Issue 4 , August 2018 , 725840403
Copyright
© Cambridge University Press 2018 

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

Andreussi, T., Morrison, P. J. & Pegoraro, F. 2013 Hamiltonian magnetohydrodynamics: Lagrangian, Eulerian, and dynamically accessible stability – theory. Phys. Plasmas 20, 092104.Google Scholar
Anile, M. 1989 Relativistic Fluids and Magneto-Fluids, Cambridge Monographs on Mathematical Physics. Cambridge University Press.Google Scholar
Asenjo, F. A. & Comisso, L. 2015 Generalized magnetofluid connections in relativistic magnetohydrodynamics. Phys. Rev. Lett. 114, 115003.Google Scholar
Asenjo, F. A., Comisso, L. & Mahajan, S. M. 2015 Generalized magnetofluid connections in pair plasmas. Phys. Plasmas 22, 122109.Google Scholar
D’Avignon, E., Morrison, P. J. & Pegoraro, F. 2015 Action principle for relativistic magnetohydrodynamics. Phys. Rev. D 91, 084050.Google Scholar
Del Zanna, L., Pili, A. G., Olmi, B., Bucciantini, N. & Amato, E. 2018 Relativistic MHD modeling of magnetized neutron stars, pulsar winds, and their nebulae. Plasma Phys. Control. Fusion 60, 014027.Google Scholar
Ertel, H. 1942 Ein neuer hydrodynamischer Wirhclsatz. Mereord. Zeit. 59, 271.Google Scholar
Fitzpatrick, R. 2008 Maxwell’s Equations and the Principles of Electromagnetism, 1st edn. Chap. 10.24. Jones & Bartlett Learning Ed.Google Scholar
Frisch, U. & Villone, B. 2014 Cauchy’s almost forgotten Lagrangian formulation of the Euler equation for 3D incompressible flow. Eur. Phys. J. H 39, 325.Google Scholar
Hide, R. 1983 The magnetic analogue of Ertel’s potential vorticity theorem. Ann. Geophys. 1, 59.Google Scholar
Hide, R. 1996 Potential magnetic field and potential vorticity in magnetohydrodynamics. Geophys. J. Intl 125, F1.Google Scholar
Kawazura, Y., Miloshevich, G. & Morrison, P. J. 2017 Action principles for relativistic extended magnetohydrodynamics: a unified theory of magnetofluid models. Phys. Plasmas 24, 022103.Google Scholar
Lichnerowicz, A. 1967 Relativistic Hydrodynamics and Magnetohydrodynamics. Benjamin.Google Scholar
Newcomb, W. A. 1962 Lagrangian and Hamiltonian methods in magnetohydrodynamics. Nucl. Fusion 2, 451.Google Scholar
Pegoraro, F. 2012 Covariant form of the ideal magnetohydrodynamic ‘connection theorem’ in a relativistic plasma. Europhys. Lett. 99, 35001.Google Scholar
Pegoraro, F. 2015 Generalised relativistic Ohm’s laws, extended gauge transformations and magnetic linking. Phys. Plasmas 22, 112106.Google Scholar
Pegoraro, F. 2016 Covariant magnetic connection hypersurfaces. J. Plasma Phys. 82, 555820201.Google Scholar
Zenitani, S., Hesse, M. & Klimas, A. 2010 Resistive Magnetohydrodynamic simulations of relativistic magnetic reconnection. Astrophys. J. Lett. 716, L214.Google Scholar