Vortex vibrations and NMR T$_2$ relaxation in YBCO

The similarity of spin echo decay rates for planar and apical oxygen in the vortex state of YBCO suggest that T$_2$ is dominated by vortex motion. We present a calculation of T$_2$ assuming overdamped harmonic vibrations in an anisotropic 3D superconductor with the field applied parallel to the c axis. The resulting field, temperature and position dependence is compared with available data.