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

Artículo de publicación ISIWe 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 ionizationrecombination 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.This work was financed by the Gemini-CONICYT Fund, project no 32070014; FONDECYT regular projects 1060644 and 1070854; the FONDAP Center for Astrophysics (15010003); Proyecto Basal PFB-06/2007 and the joint project ‘Estudio Computacional del decaimiento de campos magn´eticos en estrellas de neutrones’ between Universidad de Medell´ın (Summa Group), Pontificia Universidad Cat´olica de Chile and Universidad de Chile. The post-doctoral stay of JHH at Astrophysikalisches Institut Potsdam was possible due to the financial support of Deutscher Akademischer Austauschdienst (DAAD), Germany, and Comisi´on Nacional de Investigaci´on Cientifica y Tecnol´ogica (CONICYT), Chile, through the postdoctoral fellowship no A0772255-2007-07-DOCDAAD-25. We also thank the FONDECYT International Cooperation Project 7090020