A steady state of the disc dynamo |
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| Authors: | Ladislav Kvasz Dmitry Sokoloff Anvar Shukurov |
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| Institution: | 1. Mathematics Department , Comenius University , Bratislava, Czechoslovakia , 84215;2. Physics Department , Moscow State University , Moscow, USSR , 119899;3. IZMIRAN, Academy of Sciences , Troitsk, Moscow Region, USSR , 142092 |
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| Abstract: | Abstract We discuss the steady states of the αω-dynamo in a thin disc which arise due to α-quenching. Two asymptotic regimes are considered, one for the dynamo numberD near the generation thresholdD 0, and the other for |D| ? 1. Asymptotic solutions for |D—D 0| ? |D 0| have a rather universal character provided only that the bifurcation is supercritical. For |D| ? 1 the asymptotic solution crucially depends on whether or not the mean helicity α, as a function ofB, has a positive root (hereB is the mean magnetic field). When such a root exists, the field value in the major portion of the disc is O(l), 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 α = O(|B|?s) for |B| → ∞, we demonstrate that |B| = O(|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. |
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| Keywords: | Nonlinear dynamos asymptotic analysis galactic dynamos |
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