Magnetically-induced buckling of a whirling conducting rod with applications to electrodynamic space tethers

TL;DR

This paper investigates how magnetic fields influence the stability and buckling behavior of conducting elastic rods, with implications for space tethers and nanoscale wires, revealing complex bifurcation phenomena and secondary instabilities.

Contribution

It provides a detailed analysis of magnetic buckling and instability in conducting rods using Kirchhoff equations, including post-buckling configurations and secondary instabilities, extending understanding of electrodynamic tether stability.

Findings

Magnetic buckling exhibits a degenerate bifurcation structure.

Transverse anisotropy and angular velocity unfold the bifurcation.

Various secondary instabilities are identified through linear stability analysis.

Abstract

We study the effect of a magnetic field on the behaviour of a slender conducting elastic structure, motivated by stability problems of electrodynamic space tethers. Both statical (buckling) and dynamical (whirling) instability are considered and we also compute post-buckling configurations. The equations used are the geometrically exact Kirchhoff equations. Magnetic buckling of a welded rod is found to be described by a surprisingly degenerate bifurcation, which is unfolded when both transverse anisotropy of the rod and angular velocity are considered. By solving the linearised equations about the (quasi-) stationary solutions we find various secondary instabilities. Our results are relevant for current designs of electrodynamic space tethers and potentially for future applications in nano- and molecular wires.