Hydrodynamic action functional and electromagnetic wave absorption in a plasma

A functional-integration technique is applied to certain aspects of the equilibrium statistical mechanics of charged-particle systems. Specifically, the absorption of longitudinal electromagnetic waves in a plasma as a result of scattering by transverse waves is analyzed by carrying out integration over the auxiliary vector-potential field. Scattering by transverse waves is shown to become the dominant absorption mechanism for a one-component plasma in the long-wave limit. A hydrodynamic action functional for a magnetized electron-ion plasma is constructed by successive integration, first over 'fast' fields and then over 'slow' fields. This functional is used to calculate the absorption of longitudinal electromagnetic waves in the specified plasma, as well as in an unmagnetized electron plasma with a homogeneous background of positive charges. Frequency ranges of the order of the plasma and cyclotron frequencies are considered.