Tim (or anyone for that matter),
Could you please explain to me what the physical (not mathematical) difference is between what Priest is calling "magnetic diffusion", "magnetic reconnection" and standard ordinary "induction"? There are so many different terms in play here I have no idea how or if magnetic diffusion is even different from "magnetic reconnection" let alone that either of them is actually not "induction" with a silly name. How (physically) are these three names "different" at the level of physics. IMO any transfer of magnetic field energy to particle kinetic energy is simply "induction'. What (physically) makes "magnetic reconnection' a "faster" process than ordinary induction?
Magnetic diffusion is the diffusion of a magnetic field through a conductor. E.g. if you have a magnetic field and put in a metal ball in it, it will take time for the magnetic field to penetrate through the ball. This is described by the (magnetic) diffusion equation
(this describes the behaviour of the magnetic field itself):
[latex]
(\sigma \mu)^{-1} \nabla^2 {\bf B} = - \frac{\partial {\bf B}}{\partial t}
[/latex]
Note that this is related to the break down of the frozen in condition in a non-ideal plasma.
Induction is the response of a conductor to a time varying magnetic field, which follows from Maxwell's equations:
[latex]
\nabla \times E = - \frac{\partial {\bf B}}{\partial t}
[/latex]
naturally, under certain conditions this equation can be turned into the diffusion equation. This leads to Lenz' law, where a conductor tries to negate a forced change in the magnetic field that is penetrating it. An example is the moon Europa, where the time varying magnetic field of Jupiter induces a secondary magnetic field in the conducting ocean under the ice.
Magnetic reconnection is the topological change of the magnetic field through an X-point, where anti-parallel magnetic fields are pushed together and the field goes through a change and field lines from being anti-parallel turn into strongly bent field lines connecting the "upper" and the "lower" regions, creating a strong magnetic tension.
Even though there is a wee bit of math here, I think the difference between the three should be apparent.
In a general plasma, with conductivity σ, the magnetic field is not frozen in and can move with respect to the plasma (diffuse) with the diffusion time scale given by (σμ)
-1, which means if you look at processes much shorter than this time scale, you can work with the frozen in condition, because before the magnetic field significantly moves from where it was in the plasma, the process has finished.
When this plasma is exposed to an time varying external magnetic field, like e.g. in a tokamak, as a conductor, it will resist this magnetic field, setting up currents, which are induced by that external field. This is a way of heating the plasma. However, it is different from diffusion, because the field is kept out of the conductor, because it is time varying. (If it no longer varies, then the diffusion kicks in again).
Neither of these two processes, however, can describe the topological changes that happens in reconnection. From an anti-parallel field
Code:
-------------------------->
-------------------------->
xxxxxxxxxxxxxxxxxxxxxxxxxxx
<--------------------------
<--------------------------
Where we cannot assume that the field has one strength. The xxx is the current sheet between the two field directions coming out tof the plane of the paper. And this changes into:
Code:
------\ /---------->
-----\ \ / /----------->
xxxxxx|x|xxxxxxxxxx|x|xxxxxxxxxxxx
<----/ / \ \----------
<------/ \----------
Now, even if there were a guide field along the current sheet, there is no way you can use diffusion to reach this, nor is it possible to use induction to get to this topology of the magnetic field. (well, the drawing is not so cool, but you get the picture.)
I meant "convection".