Abstract
We present an equation of state for mildly coupled ions in ultra-cold neutral (UCN) plasmas. By introducing the mean field approximation, we obtain expressions for free energy and pressure of ions. It is found that below a critical temperature, the ions undergo a first-order phase transition and exist in a mixed vapor–liquid phase for a range of values of the ion Coulomb coupling parameter Γi (= the ion Coulomb energy/the ion kinetic energy), and in a mildly coupled liquid state for values of Γi above this range. Our analytical results demonstrate that the phenomena of phase transitions, as reported herein, are relevant for the existing computer simulations and are expected to be observed in the forthcoming UCN laboratory plasma experiments.
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