Impact of nonlinearity on a homopolar oscillating-disc dynamo

A numerical method is developed to investigate the effect of the nonlinear factors on a homopolar oscillating-disc dynamo. Our results show that all the nonlinear factors of the oscillating-disc dynamo have no significant effect on the kinematic regime of the disc dynamo. But as the magnetic field grows larger, the nonlinear factors begin to take effect. The role of the nonlinear factor involving the cube of the magnetic flux is to make the dynamo magnetic flux tend to an oscillating solution with finite amplitude. For the case that the mean rotation rate vanishes the nonlinear factor involving the magnetic flux rate can only affect the manner of the magnetic flux tending to infinity; for another case that the disc rotation rate takes a strongly subcritical value, it may have two kinds of effects just mentioned above on the disc dynamo and its specific effect is dependent on the values of the amplitude and frequency of the oscillatory disc rotation rate.