Amazing. You folks insist upon math and insist upon published papers. Even when they are handed to you on a silver platter, you simply ignore them. Hoy.
That was my first impression of looking at the paper, and a lot of circuit theory on flares has been done in the late 80s and early 90s. Heck,
I even did it myself (but not at the sun). So, they make more complicated circuits, so what, what exactly do you want/expect me to say about the paper.
So, the model is a magnetic loop from one polarization region to another (hey that is not what Akasofu wants us to look at!)
Flows of the plasma at the footpoints of the loop producea Lorenz force, which drives currents. Basically, shear motion of magnetic loop footpoints drive currents through the loop (Hey that is in my paper, 1993)
Then they say currents take the route of least resistance (hey I calculated plasma resistance in my paper) and the current will flow along the field.
Then they come with "if there is a connection between
oppositely charged regions,
possibly as a result of magnetic reconnection (sic, page 5\) a current can close the circuit through the corona. (no mention about how exactly they get there, but that is irrelevant, I think)
Then they say: "then an electric field occurs along the coronal magnetic field lines and acts on the electrons within the coronal loop and accelerates them along the field to high energies.
This is all a bit simplified but in and of itself it is correct, but it has been done much much better decades ago.
Then they come up with a complicated circuit, sure why not.
They esitmate resistivities and sizes of the loops and the velocity and magnetic field strength.
And then the estimate whether the driver (photospheric motion) generates energy enough to account for the flare energy, and yes it is enough (but also known already for decades).
Then they accelerate the electrons in the corona along the magnetic field.
The electrons are also decelerated by coulomb interactions with other electrons and protons.
If the electrons are fast enough because of a strong enough electric field (the Dreicer field) they become "run away electrons" basically collisionless and continuously accelerated.
These electrons will emit Xrays when they move through the denser chromosphere (as there they become collisional again, bremsstrahlung).
Now, I don't see what they mean with their first conclusion:
1.
The energy generated by the photospheric motion is transported electrically into the corona where it is transferred into the flare. It is true that in their model it somehow gets to the corona, because the assume the current is closed there, but the "flare" part remains vague, in my opinion.I guess they are talking about the soft Xrays, but I am not sure. I guess dWs could be the power in the soft Xrays.
So, apart from using RHESSI data, I don't see very much new stuff in this paper.