  We investigate the properties of a linear ion crystal in a combination of
quadratic and quartic potentials. Both the discrete and the continuous model
are employed to explore the homogeneity of a linear ion crystal by controlling
the proportional parameter between the quadratic and quartic components. It is
found that a uniform ion distribution in such a hybrid potential can be made
larger than that in a purely quadratic or quartic potential. The zigzag
transition is also investigated in the hybrid potential. Its critical condition
and phase diagram are determined numerically, which agrees well with previous
theoretical and experimental results. This paves the way for experimental
investigation of phase transition in a large linear coulomb crystal.
