Asymptotic, non-linear solutions for ambipolar diffusion in one dimension

We study the effect of the non-linear process of ambipolar diffusion (joint transport of magnetic flux and charged particles relative to neutral particles) on the long-term behaviour of a non-uniform magnetic field in a one-dimensional geometry. Our main focus is the dissipation of magnetic energy inside neutron stars (particularly magnetars), but our results have a wider application, particularly to the interstellar medium and the loss of magnetic flux from collapsing molecular cloud cores. Our system is a weakly ionized plasma in which neutral and charged particles can be converted into each other through nuclear beta decays (or ionization-recombination processes). In the ‘weak-coupling’ limit of infrequent inter-particle interactions, the evolution of the magnetic field is controlled by the beta decay rate and can be described by a non-linear partial integro-differential equation. In the opposite, ‘strong-coupling’ regime, the evolution is controlled by the inter-particle collisions and can be modelled through a non-linear diffusion equation. We show numerically that, in both regimes, ambipolar diffusion tends to spread out the magnetic flux, but, contrary to the normal Ohmic diffusion, it produces sharp magnetic-field gradients with associated current sheets around those regions where the magnetic field is weak.

• Fecha de publicación: 2010
• Institución: Universidad de Medellín
• Repositorio: Repositorio UDEM
• Idioma: eng
• OAI Identifier: oai:repository.udem.edu.co:11407/1366
• Acceso en línea: http://hdl.handle.net/11407/1366
• Palabra clave: We study the effect of the non-linear process of ambipolar diffusion (joint transport of magnetic flux and charged particles relative to neutral particles) on the long-term behaviour of a non-uniform magnetic field in a one-dimensional geometry. Our main focus is the dissipation of magnetic energy inside neutron stars (particularly magnetars), but our results have a wider application, particularly to the interstellar medium and the loss of magnetic flux from collapsing molecular cloud cores. Our system is a weakly ionized plasma in which neutral and charged particles can be converted into each other through nuclear beta decays (or ionization-recombination processes). In the 'weak-coupling' limit of infrequent inter-particle interactions, the evolution of the magnetic field is controlled by the beta decay rate and can be described by a non-linear partial integro-differential equation. In the opposite, 'strong-coupling' regime, the evolution is controlled by the inter-particle collisions and can be modelled through a non-linear diffusion equation. We show numerically that, in both regimes, ambipolar diffusion tends to spread out the magnetic flux, but, contrary to the normal Ohmic diffusion, it produces sharp magnetic-field gradients with associated current sheets around those regions where the magnetic field is weak. © 2010 The Authors. Journal compilation © 2010 RAS.
• Rights: restrictedAccess
• License: http://purl.org/coar/access_right/c_16ec