Calculation of Leggett–Takagi Relaxation in Vortices of Superfluid ^{3}He-B

We calculate the relaxation of Brinkman–Smith mode via Leggett–Takagi relaxation in the presence of an isolated vortex in superfluid \(^{3}\)He-B. The calculation is based on an analytical solution of the order parameter far from the vortex axis. We obtain an expression for the dissipated power per vortex length as a function of the tipping angle of the magnetization and the orientation of the static magnetic field with respect to the vortex.