I wonder where exactly this double layer is supposed to be located. The easiest way of measuring the topology of reconnection is in the Earth's magnetotail. There are very good observations presented in a paper
by Runov et al. (2003) (I am co-author on that paper) where the structure of the magnetic field is clearly shown to be in agreement with Hall reconnection. However, there is no such thing as a double layer.
Now, why is there no double layer?
michaelsuede is claiming that there are regions of differing plasmas. Indeed, a double layer can be created on the boundary of two different plasmas (e.g. of different temperature, or composition). But in reconnection this is not the case, there is, e.g. in the tail, two regions of oppositely directed magnetic field. However, in the simplest case the magnetic field is a Harris current sheet, where there is only a field in the X-direction which is a function of z and given by B(z) = B0 * tanh(z/L). Note that at z=0 there is NO magnetic field, which is to be expected at the center of a current sheet which separates these two regions. So, the only thing that is changing is the magnetic field strength, and that is gradually. Although there is a small region where the ions and the electrons get demagnetized in the centre, there is no reason there for a double layer (probably with the E-field in the z direction, but none of this anti-reconnection group of people have ever said how this DL should be situated).
Now, indeed the magnetic field is a vector field and at every point (x,y,z) with all three of them elements of R, and thus at any value the field is determined. And doing reconnection research, naturally the magnetic field is a vector field. However, to visualize some steps, to get an idea of how the topology of the field looks like, one can draw field lines. This is just a tool, but an important tool, as e.g. it will show how there is curvature in the magnetic field, that there is tension in the magnetic field etc. etc.
For the rest we can just copy/paste all the post that were made in MM's numerous threads talking about MRx, there is nothing new about all these comments, and most of them don't even make sense and some are blatently false (the magnetic field of a charged ball? No 3D zero magnetic field, one should look at the magnetometer calibration lab at my insitute).
So, first question, please draw a picture of how exactly we should visualize this double layer.