A multi-order nonlinear meta-analysis of bifluidic fireball sheath fluctuations

Abstract

The stability of steady plasma fireball sheath (PFS) fluctuations in a bifluidic plasma model approach is explored by applying the standard method of multi-order nonlinear normal mode meta-analysis in a spherical geometry. We consider the fourth-order nonlinear local fluctuations of the relevant plasma parameters evolving across the PFS region for the first time. It includes the Mach number, population density, electrostatic potential, electric field, and so forth. The order-by-order analysis of the basic governing equations results in a unique system of the third-order non-homogenous ordinary differential equations (ODEs) on the perturbed potential. The explicit solutions, obtained with the help of MATLAB programming, especially developed in judicious conditions, yield atypical nonlinear PFS eigenmode structures as a unique peakon family. It is demonstrated that the order of plasma nonlinearity acts as a fluctuation steepening agent (anti-dispersive factor). The investigated peakonic patterns are found to be in fair corroboration with the experimental findings reported elsewhere. The main implications and applications of our results in the context of the diversified PFS circumstances in the astrolabcosmic domains are finally indicated, such as commercial patterned nanodots, plasma medicines, thermonuclear fusion devices, gamma-ray bursts, and so forth.