  It is well known that charged particles stored in a Paul trap, one of the
most versatile tools in atomic and molecular physics, may undergo a phase
transition from a disordered cloud state to a geometrically well-ordered
crystalline state (the Wigner crystal). In this paper we show that the average
lifetime $\bar\tau_m$ of the metastable cloud state preceding the cloud
$\rightarrow$ crystal phase transition follows a powerlaw, $\bar\tau_m \sim
(\gamma-\gamma_c)^{-\beta}$, $\gamma>\gamma_c$, where $\gamma_c$ is the
critical value of the damping constant $\gamma$ at which the cloud
$\rightarrow$ crystal phase transition occurs. The critical exponent $\beta$
depends on the trap control parameter $q$, but is independent of the number of
particles $N$ stored in the trap and the trap control parameter $a$, which
determines the shape (oblate, prolate, or spherical) of the cloud. For
$q=0.15,0.20$, and $0.25$, we find $\beta=1.20\pm 0.03$, $\beta=1.61\pm 0.09$,
and $\beta=2.38\pm 0.12$, respectively. In addition we find that for given $a$
and $q$, the critical value $\gamma_c$ of the damping scales approximately like
$\gamma_c=C \ln [ \ln (N)] + D$ as a function of $N$, where $C$ and $D$ are
constants. Beyond their relevance for Wigner crystallization of nonneutral
plasmas in Paul traps and mini storage rings, we conjecture that our results
are also of relevance for the field of crystalline beams.
