On the stability of a classical plasma

Highlights: • Ion-ion interaction potentials are derived for a classical plasma. • Total energy of a classical plasma is computed. • Solid phase occurs for a classical plasma. • The precursory liquid phase is identified and a van der Waals equation is established for a classical plasma. -- Abstract: A linearized self-consistent variational approach is employed to investigate the (thermodynamic) stability of a classical plasma (electrons and positive ions). It is shown, by using this approach, that a classical plasma, which consists of ions "dressed" with electrons, has a well-defined thermodynamics. In the strong-coupling regime the "plasma" is a solid, while, on passing to the weak-coupling regime, it becomes gradually a liquid, a non-ideal gas, and, finally, in the weak-coupling limit, it behaves as an ideal classical gas. A van der Waals-type equation is established for the plasma non-ideal gas.