We derive a partial differential equation for the determination of the electric potential in a fully ionized plasma. Using the time independent solutions for electrostatic potential we calculate the Coulomb interaction energy of the particles in a superconducting plasma. We show that, when electrons become superconducting, the energy change corresponding to the Coulomb interaction part is positive, while the correlation part is negative. The same phenomenon occurs in the core of the neutron stars when protons become super-conducting.
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