This article discusses and tests the validity of the frozen in magnetic field paradigm (or 'ideal magnetohydrodynamics (MHD) constraint') which is usually adopted by many authors dealing with heliospheric physics. To show the problem of using ideal MHD in such a counterflow configuration like the heliosphere, we first recapitulate the basic concepts of freezing-in of magnetic fields, respectively magnetic topology conservation and its violation (= magnetic reconnection) in 3-D, already done by other authors with different methods with respect to derivations and interpretations. Then we analyse different heliospheric plasma environments. As a model of the stagnation region/stagnation point in front of the heliospheric nose, we present and discuss the general solution of the ideal MHD Ohm's law in the vicinity of a 2-D stagnation point, which was found by us. We show that ideal MHD either leads necessarily to a diverging magnetic field strength in the vicinity of such a stagnation point, or to a vanishing mass density on the heliopause boundaries. In the case that components of the electric field parallel to the magnetic field do not exist due to the chosen form of the non-ideal Ohm's law, it is always possible to formulate the transport equation of the magnetic field as a modified ideal Ohm's law. We find that the form of the Ohm's law which is often used in heliospheric physics (see e.g. Baranov and Fahr, 2003), is not able to change magnetic topology and thus cannot lead to magnetic reconnection, which necessarily has to occur at the stagnation point. The diverging magnetic field, for instance, implies the breakdown of the flux freezing paradigm for the heliosphere. Its application, especially at the heliospheric nose, is therefore rather doubtful. We conclude that it is necessary to search for an Ohm's law which is able to violate magnetic topology conservation.
Nickeler, D. H., & Karlický, M. (2006). Are heliospheric flows magnetic line- or flux-conserving? Astrophysics and Space Sciences Transactions, 2(2), 63–72. https://doi.org/10.5194/astra-2-63-2006