Cylindrical and spherical electro-acoustic waves in a strongly coupled cryogenic quantum plasma

The propagation of the nonplanar (both cylindrical and spherical) electro-acoustic waves, particularly ion-acoustic waves in a strongly coupled cryogenic electron-ion plasma has been studied utilizing the generalized quantum hydrodynamic model applicable for the cryogenic situation. The Korteweg–de Vries and Burgers equations are derived by adopting the reductive perturbation technique. The basic features (e.g., phase speed, amplitude, and width, etc.) of the ion-acoustic solitary and shock waves, are identified by analyzing the stationary solitary, and shock wave solutions of the Korteweg–de Vries and Burgers equations, respectively. It is found that the basic characteristics of the IA nonlinear structures in non-planar geometry are significantly modified by the effects of the ratio of plasma particle number densities, the Fermi temperature and pressure of electrons, the viscous coefficient, etc. The results of this theoretical investigation may be useful in describing the physics of the ion-acoustic nonlinear features of the localized electrostatic disturbances in quantum cryogenic plasmas (viz. laser-produced plasmas, super-intense laser-dense matter experiments, etc.).