A STEADY-STATE OF THE DISC DYNAMO

We discuss the steady states of the alphaomega-dynamo in a thin disc which arise due to alpha-quenching. Two asymptotic regimes are considered, one for the dynamo number D near the generation threshold D0, and the other for Absolute value of D >> 1. Asymptotic solutions for \D-D0\ << \D0\ have a rather universal character provided only that the bifurcation is supercritical. For Absolute value of D >> 1 the asymptotic solution crucially depends on whether or not the mean helicity alpha, as a function of B, has a positive root (here B is the mean magnetic field). When such a root exists, the field value in the major portion of the disc is O(1), while near the disc surface thin boundary layers appear where the field rapidly decreases to zero (if the disc is surrounded by vacuum). Otherwise, when alpha = O(Absolute value of B -s) for Absolute value of B --> infinity, we demonstrate that Absolute value of B = O(Absolute value of D 1/s) and the solution is free of boundary layers. The results obtained here admit direct comparison with observations of magnetic fields in spiral galaxies, so that an appropriate model of nonlinear galactic dynamos hopefully could be specified.