50. Moffatt, H.K. & Proctor, M.R.E. 1985 Topological constraints associated with fast dynamo action. J. Fluid Mech154, 493-507. 

The ‘fast dynamo’ concept was introduced by Vainshtein & Z’eldovich (1972).  It is a dynamo whose growth rate remains finite in the limit of infinite fluid conductivity.  Michael Proctor and I showed that such dynamos,  if they exist at all in the conventional sense,  must have pathological spatial structure, non-differentiable nearly everywhere in the limit.


When I raised the problem of existence of a fast dynamo with Zel’dovich in 1983, he removed his belt, deformed it in the stretch-twist-fold cycle, and said “There you see it”.  Well yes, and now you don’t,  as became apparent in the book of Childress & Gilbert (1995).

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Vainshtein, S. & Zel’dovich, Ja,B. 1972 Origin of magnetic fields in astrophysics. Sov.Phys.Usp. 15, 159-172.

Childress, S. & Gilbert, A.D. 1995 Stretch, Twist, Fold: the Fast Dynamo. Springer-Verlag.

53. Moffatt, H.K. 1985 Magnetostatic equilibria and analogous Euler flows of arbitrarily complex topology Part 1, Fundamentals. J. Fluid Mech159, 359-378.

55. Moffatt, H.K. 1986 Magnetostatic equilibria and analogous Euler flows of arbitrarily complex topology. Part 2, Stability considerations. J. Fluid Mech. 166, 359-378.

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This pair of papers originated in an attempt to find an analogue of the Betchov-da Rios equations for a magnetic flux tube instead of a vortex tube.  This led to the idea of  ‘relaxation under topological constraints’, which indeed yields equilibrium structures of  arbitrarily complex topology.  Arnol'd’s 1974 paper was the starting point of this investigation, although paradoxically this was only realised retrospectively. 

Arnol’d, V.I. (1974) The asymptotic Hopf invariant and its applications [in Russian]. Proc. Summer School in Diff. Eqns., Erevan, Armenian SSR Acad. Sci. 

Betchov, R. 1966 On the curvature and torsion of an isolated vortex filament. J.Fluid Mech. 22, 471-479.

Da Rios, L.S. 1906 Sul moto di un liquid0 indefinito con un filleto vorticoso di forma qualunque.Rend. Circ. Mat. Palermo, 22, 117-125

Ricca, R.L. 1991 Rediscovery of Da Rios equations. Nature, 352, 561-562.