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.

中文翻译：

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大型结构的汤川图的解析扩展

结果表明，描述汤川图的经典方程不能令人满意地描述具有广泛结构因子值的尘埃等离子体中的带电粒子系统。提出了一种对汤川系统进行图解分析的新方法。在热力学相似性理论（标度）的框架内，获得了用于在广泛的结构因子值范围内对汤川图进行分析描述的方程。获得耦合参数对结构参数的幂律依赖性。揭示了描述汤川图的指数函数与等离子体系统的分形维数之间的关系。使用相同功能描述尘埃粒子（颗粒）的大规模结构的可能性，例如土星的 E 环，