Abstract
We investigate the properties of a linear ion crystal in a combination of quadratic and quartic potentials. Both the discrete and the continuous models are employed to explore the homogeneity of a linear ion crystal by tuning the proportional parameter between the quadratic and quartic components. It is found that the size of the uniform region is significantly larger than that in either a purely quadratic or a quartic potential. The zigzag transition is also investigated in the hybrid potential, and its critical condition and phase diagram are determined numerically, which agrees well with previous theoretical and experimental results. Our results pave the way for experimental investigation of superlarge linear ion crystals in the combination of quadratic and quartic potentials.
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