A hater's model of circuit reconnection
It has been said by MM:
I don't personally reject "reconnection' theory as "pseudoscience", I simply refer to it as "circuit reconnection" (my preference) or "electromagnetic reconnection". I don't actually outright "reject" it the way Alfven did, and I haven't now for many years.
So then, as MM never deigned us worthy enough to show how his model of circuit reconnection works, I took it upon myself to work it out. (sigh)
The easiest way to do that is to take a magnetic loop on the Sun, and have it erupt as in the the figure, and a plasmoid is ejected.
Now, the first problem one sees is that this is a 3D picture, let’s first try the 2D simple case.
First we have a loop of length L, exiting and entering the solar surface. This loop will carry a current I and has a driving battery V at the foot points and a resistivity R by the plasma and and inductance L. Note that these are all total numbers, integrated over the whole loop. This is necessary because otherwise we cannot give a circuit representation of this structure.
The RLC circuit is our starting point, which describes the loop at the beginning. Now something happens, the field somewhere in the middle of the elongated loop is brought together. And then through reconnection a plasmoid is created the flies away. We then have a situation in which there are two circuits, the smaller loop and the plasmoid. In this case circuit 1 will remain on the Sun and circuit 2 will slowly dissipate on the circuit time scale.
Now the question is, how do we replace the arrow labeled “How???” Here lies the crux of the problem, because there we are getting into smaller scale stuff than the length L of the loop, and that is bad for the circuit description. So, at the moment there is no fill-up for the “How???”
Maybe that is because we simplified things, by making it 2D, so we will take a 3D tube. Current flowing along the loop, twisted field lines, thus it might be appropriate to define two directions, one along the axis and one around the axis. So we split up the circuit, and I put in a loop for the part that gets split off from the solar loop.
When the tube is pushed together (where the X-line would form) there will be an increase in the current between the two parts of the loop (Maxwell), and that is represented by the Vextra in the circuit. Then the reconnection starts, so we have to make the current flow in the extra loop on the left, which will be separated from the part on the right. Now, one can think of a slowly increasing variable resistor (the box with the arrow), that goes to infinity over time, and that there is truly a capacitor in the loop (which would be the diffusing magnetic field, as there is no driver for the current and resistivity will slowly dissipate the current).
This is a very simple model of “circuit reconnection.” If one is an electrical engineer (which I am not) one could come up with some more complicated realistic circuit. However …
Note that this whole “circuit reconnection” is based on large scale properties, everything is defined for the whole tube, and thus, the real physics that is happening during the reconnection event is replaced in this case by a time varying resistor (from zero to infinity). Therefore, we cannot say anything about particle acceleration, or how the magnetic field looks like during the whole process. However, is it kind of useful to make an estimate of the total energy in the circuit that can (maximally) be released and some of the time scales (like the dissipation time of the cut-off loop).
So, there you have it, “circuit reconnection.” I have no idea what you might want to do with this kind of model, as the main interest of reconnection is on the meso and micro physics scale.
Well, that's my contribution, maybe that MM can take it as a starting point.
