Linear damping and depletion in flowing plasma with strong sheared magnetic fields

TL;DR

This paper analyzes the long-term behavior of solutions in ideal MHD with sheared magnetic fields, demonstrating convergence to shear profiles and a new depletion phenomenon at critical points.

Contribution

It proves convergence of velocity and magnetic fields to shear profiles and introduces a novel depletion phenomenon at critical points in ideal MHD.

Findings

Velocity and magnetic fields converge to sheared profiles over time

Horizontal fields at critical points decay to zero

New depletion phenomenon identified at critical points

Abstract

In this paper, we study the long-time behavior of the solution for the linearized ideal MHD around sheared velocity and magnetic field under Stern stability condition. We prove that the velocity and magnetic field will converge to sheared velocity and magnetic field as time approaches infinity. Moreover a new depletion phenomenon is proved: the horizontal velocity and magnetic field at the critical points will decay to 0 as time approaches infinity.