A STEADY-STATE OF THE DISC DYNAMO

We discuss the steady states of the alphaomega-dynamo in a thin disc w hich arise due to alpha-quenching. Two asymptotic regimes are consider ed, 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 bif urcation 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 surro unded by vacuum). Otherwise, when alpha = O(Absolute value of B -s) fo r 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 boundar y layers. The results obtained here admit direct comparison with obser vations of magnetic fields in spiral galaxies, so that an appropriate model of nonlinear galactic dynamos hopefully could be specified.