Motions in a Bose condensate. II. The oscillations of the rectilinear and large circular vortex lines

For Pt.I, see abstr. A71357 of 1971. The linearized perturbation equations for the rectilinear and large circular vortex lines in a Bose condensate are studied. An asymptotic matching procedure is given whereby the frequency omega for the (bound state) oscillations of the rectilinear vortex, for wavelengths large compared with the healing length a, is found. A similar asymptotic procedure is employed to investigate the behaviour of the large ring vortex when its circular axis is slightly perturbed. It is found that the vortex, whose radius c is large compared with a, is stable for all small displacements (and executes simple harmonic vibrations).