New developments in the application of the method of moments in Plasma Physics

This review article is based on a number of our research papers complemented by some mathematicaldevelopments which are usually not included to texts in Physics, and which can permit a reader to enterinto the details of the self-consistent method of moments, recently suggested, and understand how it couldbe improved even further. The idea of the method of moments which appeared some 35 years ago is toemploy several sum rules and other exact relations to determine the dynamic properties of strongly coupledclassical or partially degenerate plasmas. Now this approach is complemented by new empirical andmathematical observations which permit to determine dynamic characteristics of strongly coupledcompletely ionized classical one-component plasmas without any data input from simulations or directexperiments and express the dynamic properties of the above systems entirely in terms of their staticcharacteristics like the static structure factors. The obtained results are quite satisfactory and promising.