Optimization of the magnetic dynamo

Abstract

In stars and planets, magnetic fields are believed to originate from the motion of electrically conducting fluids in their interior, through a process known as the dynamo mechanism. In this Letter, an optimization procedure is used to simultaneously address two fundamental questions of dynamo theory: "Which velocity field leads to the most magnetic energy growth?" and "How large does the velocity need to be relative to magnetic diffusion?" In general, this requires optimization over the full space of continuous solenoidal velocity fields possible within the geometry. Here the case of a periodic box is considered. Measuring the strength of the flow with the root-mean-square amplitude, an optimal velocity field is shown to exist, but without limitation on the strain rate, optimization is prone to divergence. Measuring the flow in terms of its associated dissipation leads to the identification of a single optimal at the critical magnetic Reynolds number necessary for a dynamo. This magnetic Reynolds number is found to be only 15% higher than that necessary for transient growth of the magnetic field.

Optimal velocity field given approximate analytic form. 4 pages, 4 figures

References in corpus (3)

• Generation of magnetic field by dynamo action in a turbulent flow of liquid sodium
• Minimal seeds for shear flow turbulence: using nonlinear transient growth to touch the edge of chaos
• Searching for the fastest dynamo: Laminar ABC flows

Cited by in corpus (8)

• An optimisation approach for analysing nonlinear stability with transition to turbulence in fluids as an exemplar
• The Turbulent Dynamo
• Cosmic Rays in Intermittent Magnetic Fields
• Galactic Dynamos
• Turbulent processes and mean-field dynamo
• A systematic route to subcritical dynamo branches
• The nature of mean-field generation in three classes of optimal dynamos
• On nonlinear transitions, minimal seeds and exact solutions for the geodynamo