  The present work suggests rigorous criteria to determine phase transitions in
Coulomb crystals in a linear ion trap. The proposed method is based on the
analysis of a cross size $\rho_i$ and relative polar angle between neighboring
particles $\Delta\phi_i$ as functions of the system parameters such as number
of ions, mass and charge of ions, and trap geometry. The analytical
interpretation of the phase transitions relies on the analysis of the cross
size $\rho$ and a metric $\Phi$ dependent on the norm of the vector
$||\overline{\Delta\phi}||$. We further demonstrate an analysis procedure for
the numerical determination of extremes of interpolated functions $\rho$ and
$\Phi$. 1D-2D and 2D-3D phase transitions points are defined as points of the
greatest growth of functions $\rho$ and $\Phi$, respectively.
