As we cannot expect MM to actually discuss the relevance of this 45 year old paper, let's look at it.
The important part starts at section 4 "
Circuit Interruption," where it is mentioned that:
(my bold) Now, it would fall onto MM to explain what
a sort of and what
certain conditions are.
Then in section 5 "
Maximum Current Through a Plasma" has a discussion of the mercury rectifier. The current is flowing through the mercury plasma at 10
-3 Torr and cannot exceed a certain value, as mentioned above. The time scale of the current interruption is the inductive time scale: τ≈LI/V, for the rectifier this is about 10
-5 seconds.
Now, this may or may not be appropriate for solar flares.
Then in section 6 "
The Disruption of the Current" is not really informative, and only says that for strong currents the plasma can be considered as a vacuum diode, and the Langmuir limit for current in a vacuum diode is given.
Then we get to section 7 "
Instability of a Current in a Completely Ionized Gas." They take a normal plasma with n
e = n
i = n and the current is given by i = -e n v
e, where v
e is the electron velocity. And then they assume a perturbation of the density n (a small dip) and thus the v
e needs to increase to keep the current density i flowing and this gives rise to evacuation of the region, through the creation of an electric field. The ions also are expelled from this region. Actually this can be seen as the creation of a double double layer. From this simple model, one can derive a stability criterion for the plasma, the well known fact that when the drift velocity of the particles in the current exceeds the thermal velocity the plasma becomes unstable.
[latex]v_e^2 > \frac{kT_i}{m_e} \sim v_{th}[/latex]
Section 8 "
Application to Solar Conditions" and then it becomes speculative, not surprising, because of the age of this paper. They take a loop above the surface of the Sun and then close it below the surface. No problem there.
Then they discuss some generalities about the complicated structure of the fields and the currents inferred from the Zeeman effect etc. Then assuming that there is a pinch effect they say:
However, the question is if this is reached and what actually happens, as there are many flow driven instabilities. For one, there is the Buneman instability (1958, 1959) which tends to increase the velocity spread in v
th, i.e. heating the plasma so that the ratio v
e/v
th decreases, stabilizing the plasma again. (For a full overview of instabilities see
Melrose: Instabilities in Space and Laboratory Plasmas, an excellent book, if you're not afraid of equations.)
So, although this is a very nice and straightforward idea by A&C, it is probably too simple to actually work on the Sun. This is not criticism on A&C per se, as at the time that this model was developed the field of plasma physics was not so well developed yet. And indeed, the energy estimated and the time scale at which it is released seems to agree roughly with what is observed, and that is to be expected, but if the trigger mechanism is as they describe is to be questioned (IMHO).