Maximally-efficient-generation approach in the dynamo theory

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Abstract
We propose a method of derivation of global asymptotic solutions of the hydromagnetic dynamo problem at large magnetic Reynolds number. The procedure reduces to matching the local asymptotic forms for the magnetic field generated near individual extrema of generation strength. The basis of the proposed method, named here the Maximally-Efficient-Generation Approach (MEGA), is the assertion that properties of global asymptotic solutions of the kinematic dynamo are determined by the distribution of the generation strength near its leading extrema and by the number and distribution of the extrema. The general method is illustrated by the global asymptotic solution of the α2-dynamo problem in a slab. The nature of oscillatory solutions revealed earlier in numerical simulations and the reasons for the dominance of even magnetic modes in slab geometry are clarified. Applicability of the asymptotic solutions at moderate values of the asymptotic parameter is also discussed. We confirm this applicability using comparisons with complementary asymptotic expansions and numerical simulations. In particular, this justifies application of the MEGA solutions to estimation of the generation threshold.

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