Flux and field line conservation in 3-D non-ideal MHD flows: Remarks about criteria for 3-D reconnection without magnetic neutral points and their application to the heliospheric interface

In this paper, we address the issue of finding velocity fields which conserve magnetic flux or at least magnetic fieldline connectivity. We start from the basic principles of flux and line conservation and present and discuss the criterion, given by Newcomb (1958), Stern (1966), and Vasyliunas (1972). In addition, we find a new formulation of the line-conserving velocity field by solving the system of partial differential equations which corresponds to Newcomb's criterion for line conservation. This velocity field is given by a correlation between the non-idealness, described by a generalized form of the Ohm's law and a general transporting velocity, which is fieldline conserving. Our considerations give additional insights into the discussion on violations of the frozen-in field concept which started recently with the papers by Baranov and Fahr (2003a,b). These authors analyzed a generalized form of Ohm's law, which is valid for the heliosphere and claimed that the transport velocity for the magnetic flux may be different from the plasma velocity. We can show that the non-idealness given in the paper by Baranov and Fahr could not change the magnetic topology and can therefore not be responsible for magnetic reconnection. But we found that it is in general not clear if the flux-conserving velocity field is identical to the plasma flow or to any species velocity field.