I'll start with this link to Somov's explanation of reconnection in a vacuum. FYI, I own one of Somov's other books on the topic of plasma physics. While it does describe "reconnection", my book doesn't discuss reconnection in a "vacuum", and it's got a whole chapter devoted to tying the B and E orientations together. It's a great book This is the only place that I'm aware of that Somov discusses the topic of reconnection in a vacuum and IMO he made some errors which I'll get to in a moment.
The important (and correct) points to note in his theoretical example are:
A) The E fields that drive both of the currents in Somov's example actually does all the work in terms of providing all the magnetic and kinetic energy to the point of "reconnection" (and everywhere else), and....
B) Somov's example is *INCLUSIVE* (not exclusive) of charged particles in his vacuum and his example is INCLUSIVE (not exclusive) of charged particle acceleration as a result of "reconnection". It therefore can describe a reconnection rate that is based upon particle acceleration. What Somov explains is that *IF* the currents are displaced (move) toward one another, magnetic FLUX occurs. That FLUX has a physical effect on the charged particles in the currents in his example.
Unfortunately Somov uses some unfortunate verbiage in his example IMO, specifically the following two sentences are incorrect:
That's wrong for two reasons. First off, field lines CANNOT "merge/cross". If you notice his in both of his diagrams, his individual B LINES terminate at the X with an arrow at the X. B Lines don't actually do that. They should be drawn as continuous loops *EVERYWHERE* and none of them should end in arrows at the X or even cross at the X, not before, nor after the "reconnection" process. It's not the B LINES that move, the CURRENTS from one current carrying filament can and will move to the other filament through that X point. Those aren't simple B LINES that "reconnect" in a "separatrix". Those are actually CURRENTS that "reconnect" though a "double layer" that forms at the X between the two current carrying filaments. The magnetic B LINES are not "reconnecting' at the X as Somov contends, rather the CURRENTS jump from one filament to another and the filaments ELECTRICALLY begin to interact through a DOUBLE LAYER. While Somov's work is first rate, his description of the reconnection process in a vacuum is critically flawed. It's not that B LINES do any "reconnecting" at the X as he does seem to believe. Rather there are flux changes that occur there (and everywhere around the moving filaments), and particle movement that occurs at the X as a result, but the individual magnetic lines do not "disconnect from" any other magnetic lines, nor do they reconnect to any other magnetic B lines. B lines form as a full and complete FIELD, not simplistic lines. The entire fields of both currents experience FLUX CHANGES. Those FLUX changes can and will induce particle movement at the X (and other locations), but no B lines reconnect there.Two field lines approach the X point, merge there forming a separatrix and then they reconnect forming a field line that encloses both currents. Such a process is called reconnection of field lines or magnetic reconnection.