Analytical Extension of the Yukawa Diagram for Large-Scale Structures

It is shown that the classical equation describing the Yukawa diagram cannot satisfactorily describe a system of charged grains in a dusty plasma in a wide range of the structure factor values. A new approach to the diagrammatic analysis of Yukawa systems is proposed. Equations are obtained for the analytical description of the Yukawa diagram in a wide range of the structure factor values in the framework of the thermodynamic theory of similarity (scaling). Power-law dependences of the coupling parameter on the parameters of the structure are obtained. The relationships between the exponential functions describing Yukawa diagrams and the fractal dimension of the plasma system are revealed. The possibility of describing large-scale structures of dust particles (grains) such as Saturn’s E-ring using the same functions, but with different values of the fractal dimension, is discussed.