  We study the nonequilibrium dynamics of the linear to zigzag structural phase
transition exhibited by an ion chain confined in a trap with periodic boundary
conditions. The transition is driven by reducing the transverse confinement at
a finite quench rate, which can be accurately controlled. This results in the
formation of zigzag domains oriented along different transverse planes. The
twists between different domains can be stabilized by the topology of the trap
and under laser cooling the system has a chance to relax to a helical chain
with nonzero winding number. Molecular dynamics simulations are used to obtain
a large sample of possible trajectories for different quench rates. The scaling
of the average winding number with different quench rates is compared to the
prediction of the Kibble-Zurek theory, and a good quantitative agreement is
found.
