4.6. Magnetic fields from cosmic strings
At the beginning of this chapter we shortly discussed the Harrison-Rees mechanism for vortical production of magnetic fields in the primordial plasma. In this section we will shortly review as cosmic string may implement this mechanism by providing a vorticity source on scales comparable to galactic sizes. Cosmic strings are one-dimensional topological defects which are supposed to have been formed during some primordial phase transition through the Kibble mechanism , which we already discussed in Sec. 4.3 (for a review on cosmic strings see Ref. ). The idea that cosmic string may produce plasma vorticity and magnetic fields was first proposed by Vachaspati and Vilenkin . In this scenario vorticity is generated in the wakes of fast moving cosmic strings after structure formation begins. Differently from Harrison's  scenario (see Sec. 4.1), in this case vorticity does decay with Universe expansion since the vortical eddies are gravitationally bounded to the string. Even if the mechanism we are considering is supposed to take place after recombination, a sufficient amount of ionization should be produced by the violent turbulent motion so that the Harrison-Rees  mechanism can still operate. The scale of coherence of the generated magnetic fields is set by the scale of wiggles of the string and, for wakes created at recombination time it can be up to 100 kpc. The predicted field strength is of the order of ~ 10-18 G, that could enough to seed the galactic dynamo. The main problem with this scenario is that is not clear whether stable vortical motion can be really generated by the chaotic motion of the string wiggles.
An alternative mechanism has been proposed by Avelino and Shellard . In their model, vorticity is generated not by the wiggles but by the strings themselves which, because of the finite dynamical friction, drag matter behind them inducing circular motions over inter-string scales. Unfortunately, the magnetic field strength predicted by this model at the present time is very weak ~ 10-23 G, which can only marginally seed the galactic dynamo.
Larger fields may be produced if cosmic strings are superconducting. String superconductivity was first conceived by Witten . The charge carriers on these strings can be either fermions or bosons, and the critical currents can be as large as 1020 Ampere. If primordial magnetic fields pre-exist, or formed together with, cosmic string they may play a role charging up superconducting string loops and delaying their collapse . Otherwise, superconducting cosmic strings can themselves give rise to magnetic fields in a way similar to that proposed by Avelino and Shellard. An important difference, however, arises with respect to the non-superconducting case discussed in Ref. . As shown by Dimopoulos and Davis , superconducting strings networks may be more tangled and slower than conventional cosmic strings because of the strong current which increases dynamical friction. It was shown by Dimopoulos  that if the string velocity is small enough the gravitational influence of the string on the surrounding plasma becomes a relevant effect. As a consequence, plasma is dragged by the string acquiring substantial momentum. Such a momentum may induce turbulence which could generate magnetic fields on scale of the order of the inter-string distance. Such a distance is smaller than the conventional cosmic string distance. Quite strong magnetic fields may be produced by this mechanism. The only known constraint come from the requirement that the string network does not produce too large temperature anisotropies in the CMBR. By imposing this constraint, Dimopoulos estimated that present time magnetic fields as large as 10-19 G with a coherence scale of ~ 1 Mpc may be produced.
Contrarily to previous claims, in a very recent paper by Voloshin it was showed that the generation of large scale magnetic fields by domain walls is not possible .