Homopolar oscillating-disc dynamo driven by parametric resonance

TL;DR

This paper investigates how harmonic oscillations in a Bullard-type disc dynamo can induce or suppress magnetic field generation through parametric resonance, analyzed via a damped Mathieu equation.

Contribution

It introduces a model showing magnetic field generation at subcritical rotation rates and suppression at supercritical rates due to oscillation parameters.

Findings

Dynamo can be excited at subcritical rotation rates with harmonic oscillations.

Dynamo can be suppressed at supercritical rates in narrow frequency bands.

Magnetic field growth rates depend on oscillation amplitude and frequency.

Abstract

We use a simple model of Bullard-type disc dynamo, in which the disc rotation rate is subject to harmonic oscillations, to analyze the generation of magnetic field by the parametric resonance mechanism. The problem is governed by a damped Mathieu equation. The Floquet exponents, which define the magnetic field growth rates, are calculated depending on the amplitude and frequency of the oscillations. Firstly, we show that the dynamo can be excited at significantly subcritical disc rotation rates when the latter is subject to harmonic oscillations with a certain frequency. Secondly, at supercritical mean rotation rates, the dynamo can also be suppressed but only in narrow frequency bands and at sufficiently large oscillation amplitudes.