  We use a Langevin equation to examine the dynamics and fluctuations of a flux
line (FL) in the presence of an {\it alternating longitudinal current}
$J_{\parallel}(\omega)$. The magnus and dissipative forces are equated to those
resulting from line tension, confinement in a harmonic cage by neighboring FLs,
parallel current, and noise. The resulting mean-square FL fluctuations are
calculated {\it exactly}, and a Lindemann criterion is then used to obtain a
nonequilibrium `phase diagram' as a function of the magnitude and frequency of
$J_{\parallel}(\omega)$. For zero frequency, the melting temperature of the
mixed phase (a lattice, or the putative "Bose" or "Bragg Glass") vanishes at a
limiting current. However, for any finite frequency, there is a non-zero
melting temperature.
