An Exact, Time-dependent Analytical Solution for the Magnetic Field in the Inner Heliosheath

Abstract

We derive an exact, time-dependent analytical magnetic field solution for the inner heliosheath, which satisfies both the induction equation of ideal magnetohydrodynamics in the limit of infinite electric conductivity and the magnetic divergence constraint. To this end, we assume that the magnetic field is frozen into a plasma flow resembling the characteristic interaction of the solar wind with the local interstellar medium. Furthermore, we make use of the ideal Ohm's law for the magnetic vector potential and the electric scalar potential. By employing a suitable gauge condition that relates the potentials and working with a characteristic coordinate representation, we thus obtain an inhomogeneous first-order system of ordinary differential equations for the magnetic vector potential. Then, using the general solution of this system, we compute the magnetic field via the magnetic curl relation. Finally, we analyze the well-posedness of the corresponding Dirichlet-type initial-boundary value problem, specify compatibility conditions for the initial-boundary values, and outline the implementation of initial-boundary conditions.

arXiv comment13 pages, 1 figure, details added, minor corrections and improvements

References in corpus (11)

• Solar Modulation of Cosmic Rays
• Three-dimensional Features of the Outer Heliosphere Due to Coupling between the Interstellar and Heliospheric Magnetic Field. V. The Bow Wave, Heliospheric Boundary Layer, Instabilities, and Magnetic Reconnection
• Heliosheath Processes and the Structure of the Heliopause: Modeling Energetic Particles, Cosmic Rays, and Magnetic Fields
• A model of the heliosphere with jets
• Interstellar neutral helium in the heliosphere from IBEX observations. VI. The He${}^{+}$ density and the ionization state in the Very Local Interstellar Matter
• The Twist of the Draped Interstellar Magnetic Field Ahead of the Heliopause: A Magnetic Reconnection Driven Rotational Discontinuity
• Draping of the Interstellar Magnetic Field over the Heliopause - A Passive Field Model
• An exact analytical solution for the interstellar magnetic field in the vicinity of the heliosphere
• Toward more realistic analytic models of the heliotail: Incorporating magnetic flattening via distortion flows
• On the Geometry of the IBEX Ribbon
• An Improved Analytical Model of the Local Interstellar Magnetic Field: The Extension to Compressibility