ON SELF-EXCITING COUPLED FARADAY DISK HOMOPOLAR DYNAMOS DRIVING SERIES MOTORS

We present the results of a preliminary analytical and numerical study of one of the simpler members of a hierarchy of N (where N greater th an or equal to 1) coupled self-exciting Faraday disk homopolar dynamos , incorporating motors as additional electrical elements driven by the dynamo-generated current, as proposed by Hide (1997). The hierarchy i s a generalisation of a single disk dynamo (N = 1) with just one elect ric motor in the system, and crucially, incorporating effects due to m echanical friction in both the disk and the motor, as investigated by Hide et al. (1996), This is describable by a set of three coupled auto nomous nonlinear ordinary differential equations, which, due to the pr esence of the motor, has solutions corresponding to co-existing period ic states of increasing complexity, as well as to chaotic dynamics. We consider the case of two such homopolar dynamos (N = 2) with generall y dissimilar characteristics but coupled together magnetically, with t he aim of determining the extent to which this coupled system differs in its behaviour from the single disk dynamo with a series motor (Hide et al. 1996). In the case when the units are identical, the behaviour of the double dynamo system (after initial transients have decayed aw ay) is identical to that of the single dynamo system, with solutions ( including ''synchronised chaos'') locked in both amplitude and phase. When there is no motor in the system and the coefficient of mechanical friction in the disks is small, these transients resemble the well-kn own 'non-synchronous', but structurally unstable Rikitake solution. Co pyright (C) 1998 Elsevier Science B.V.