Oscillating Ponomarenko dynamo in the highly conducting limit

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.