  The non-equilibrium dynamics of an ion chain in a highly anisotropic trap is
studied when the transverse trap frequency is quenched across the value at
which the chain undergoes a continuous phase transition from a linear to a
zigzag structure. Within Landau theory, an equation for the order parameter,
corresponding to the transverse size of the zigzag structure, is determined
when the vibrational motion is damped via laser cooling. The number of
structural defects produced during a linear quench of the transverse trapping
frequency is predicted and verified numerically. It is shown to obey the
scaling predicted by the Kibble-Zurek mechanism, when extended to take into
account the spatial inhomogeneities of the ion chain in a linear Paul trap.
