Can waves advect magnetic fields?

I sometimes have research ideas that I think are cool, but that don’t make sense for me to pursue. I generally just make a note of them and move on. This is the 23rd post in a series describing some of the ideas I’ve accumulated. This idea is closely related to conversations I once had with Dong Lai.

Can waves advect magnetic fields?

What’s the idea?

The electrical conductivity in stars is enormous, so the magnetic diffusivity is small. That means that magnetic field lines are effectively frozen in to the material they pass through, so they can only move if that material moves.

Waves can produce net material motion via Stokes drift, where non-linear interactions between the wave and itself nudge material in a consistent direction (rather than back and forth).

So the question is: How large of an effect is this, and does it matter in any astrophysical settings?

Why is this important?

Transport of magnetic field lines matters for understanding stellar rotation and interpreting observations (especially asteroseismic magnetic field measurements).

How can I get started?

I’d start by looking at some of the classic literature on Stokes drift (e.g. Knobloch & Merryfield, Kenyon, etc.), and use some of those results to formulate a simple model of how far waves can push a magnetic field. I’d focus on settings where there is net motion (rather than diffusion), which might come up in e.g. coherent pulsators, as that makes the problem a lot easier. Then I’d see if the magnitude of the effect is ever large enough to matter.

I think this has a high chance of just never mattering, but it seems worth some investigation.