Continuum Theory of a Plasma

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Abstract
A continuum description of a classical plasma in equilibrium is presented. Thermodynamic properties and equilibrium fluctuations are discussed in terms of the fluctuations of the net charge density function n(r). The probability distribution function of the potential at a typical point, and the joint distribution of the potential at two points are calculated. As was noted in the preceding paper, these results lead to the chemical potential and two‐particle distribution function of classical Debye‐Hückel theory. A first order correction to the potential distribution of the continuum theory is obtained by treating the nearest neighbor charge as a discrete charge and the remainder of the plasma as a continuum. The corresponding correction to the free energy is obtained and compared with the results of diagrammatic calculations, to which the present results are similar.