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The Equilibrium Stability of a System of Disk Dynamos

Published online by Cambridge University Press:  24 October 2008

Norman R. Lebovitz
Norman R. Lebovitz
Affiliation:
Yerkes ObservatoryThe University of Chicago
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Abstract

The stability of the equilibrium solutions of the equations describing the behaviour of a system of coupled disk dynamos is investigated. In the absence of viscous damping, it is found that systems consisting of more than two dynamos are unstable. That a single disk dynamo is stable is known. The stability of the undamped two-dynamo system has not been ascertained. When viscous damping is present, there are two equilibrium solutions, one in which all the currents are zero, and one in which they are finite. In the zero-current case, a stability criterion is found. Stability criteria are also found in the finite-current case. Further, the existence of the finite-current equilibrium state excludes the stability of the zero-current equilibrium state.

Type
Articles
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 56 , Issue 2 , April 1960 , pp. 154 - 173
Copyright
Copyright © Cambridge Philosophical Society 1960

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References

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