15. The neutral point discharge theory of solar flares. A reply to Cowling's criticism

Abstract

The discharge theory has been criticized by Professor Cowling in §5·3 of The Sun, ed. Kuiper (Chicago[1]). A discharge theory requires the thickness of the accelerating layer to be only 5 m, which he finds unacceptable. This criticism is not soundly based, because no lower limit for the layer width is obtained from observation.

Secondly, Cowling invokes Lenz's law: ‘the effect of induced currents is always to oppose the change to which they are due.’ Lenz's law needs verifying for conducting fluids, however, and though it is usually true, it is shown to be false when there is a neutral point. Since Lenz's law refers to electromagnetic induction, other effects such as the pressure gradient may be omitted in this test, and then a completely rigorous proof is possible: it is shown that in an ideal fluid which is perfectly conducting, perfectly compressible and inviscid, the current density at a neutral point must become infinite.

The pressure gradient is irrelevant to Lenz's law, but it usually opposes any motion and should also be discussed. A physical picture suggests that the pressure gradient will not stop a vortical motion, but merely retard it. The related problem of equilibrium between the pressure gradient and the electromagnetic force may be discussed mathematically for the special case with two-dimensional symmetry. It is found that equilibrium requires an infinite current density at the neutral point. This is a subsidiary argument in favour of discharges at neutral points.