Oscillating Ponomarenko dynamo in the highly conducting limit

TL;DR

This paper develops an asymptotic theory for Ponomarenko dynamos with periodic flows in cylindrical geometry, predicting growth rates and frequencies at high magnetic Reynolds numbers, and validates it through numerical simulations.

Contribution

It introduces an asymptotic framework for analyzing oscillating Ponomarenko dynamos in the highly conducting limit, linking theory with numerical validation.

Findings

Growth rates and frequencies are accurately predicted by the asymptotic theory.

Modes tend to localize on resonant stream surfaces at high magnetic Reynolds numbers.

Numerical simulations confirm the theoretical predictions.

Abstract

This paper considers dynamo action in smooth helical flows in cylindrical geometry, otherwise known as Ponomarenko dynamos, with periodic time dependence. An asymptotic framework is developed that gives growth rates and frequencies in the highly conducting limit of large magnetic Reynolds number, when modes tend to be localized on resonant stream surfaces. This theory is validated by means of numerical simulations.