How Spectral Shapes of Magnetic Energy and Magnetic Helicity Influence their Respective Decay Time Scales

Abstract

It is shown that in magnetohydrodynamics, the shapes of the magnetic energy and magnetic helicity spectra can influence whether the magnetic helicity resistive dissipation time scale is longer, equal to, or shorter than that of magnetic energy. The calculations highlight that magnetic helicity need not always dissipate significantly more slowly than magnetic energy. While this may be implicitly understood in detailed studies of magnetic helicity in plasma devices, it is not sufficiently emphasized in elementary discussions comparing magnetic helicity vs. magnetic energy evolution. Measuring magnetic energy and helicity decay times may provide a posteriori insight into the initial spectra.