Thanks for posting the animation Perpetual Student.
In the animation two B field loops merge to become a single loop.
Two loops...
View attachment 23920
...become a single loop
View attachment 23921
Isn't that B field connection?
J W Dungey's 1958 paper (to which
Michael Mozina refers almost daily) contains even clearer examples of magnetic reconnection in the
B field. His Figure 2 shows a magnetic field in the shape of a "figure eight". That's the field produced by two current-carrying rods placed in parallel, in a vacuum.
In
parts 1 and 2 of my simple derivation of magnetic reconnection, I derived equations for the
B field around a single current-carrying rod; these equations or their equivalent are found in any decent textbook on electromagnetism. The equation for the
B field in the vicinity of two current-carrying rods follows immediately by linear superposition, and I'll state that equation in part 3. When you graph that
B field and some of its magnetic field lines, you get
That's just a more colorful version of Dungey's Figure 2 (except I haven't yet added the arrows that show the counter-clockwise direction of every magnetic field line in that graph; I should be able to add those arrows by Monday evening). Notice the two magnetic field lines that are almost touching at the neutral (totally black) point in the center. If you make a very small change to the current passing through the rods at the centers of the white disks, those two magnetic field lines will either withdraw from each other or merge to become a single magnetic field line.
(Whether they withdraw or merge depends on whether you reduce or increase the current in the rods. It also depends on the mathematical conventions you adopt for talking about the identity of those magnetic field lines, because magnetic field lines have no persistent identity in and of themselves. Indeed, some of the less thoughtful Electric Sun folk will tell you that magnetic field lines don't really exist, even as they insist that Gauss's law for magnetism says these non-existent lines can't merge or separate over time.

)
Although people often speak of the merging and separation of magnetic field lines as magnetic reconnection, there's a more important notion that can't be dismissed as arbitrary or imaginary: When the topology of an entire magnetic field changes over time, the field is undergoing magnetic reconnection.