Giant Cluster Expansion Theory and Its Application to High Temperature Plasma

The conventional virial expansion of thermodynamic functions is converted into a new expansion scheme, similar to the former but more powerful. The new method is particularly suitable to dealing with the interaction of long-range character, such as Coulomb potential, since it suffers from no divergence difficulties contrary to the conventional one. As an application of the method, the equilibrium properties of high temperature plasma is studied and the term of next higher orders than the Debye-Hiickel limiting law is obtained exactly. The order estimation indicates that the Debye-Hiickel law is accurate within the error of a few per cent in this case. A possible extension of the present method to the theory of non equilibrium properties of plasma or to quantum statistics is suggested.