Analytic model for sheath-plasma resonance in inverted fireballs

TL;DR

This paper develops a semi-analytical model for sheath-plasma resonance in inverted fireballs, revealing the conditions for resonance stability, the existence of a unique nonzero frequency mode, and its relation to observed standing wave patterns.

Contribution

It introduces a generalized hydrodynamic model for SPR in inverted fireballs, incorporating viscosity and curvature effects, and analytically derives the dispersion relation confirming a single feasible resonance mode.

Findings

Only one nonzero frequency mode exists in the system.

Sheath-plasma resonance creates trapped acoustic fluctuations.

Parametric changes affect the resonance features and transition to standing waves.

Abstract

The sheath plasma resonance (SPR) in an inverted fireball (IFB) system is semi-analytically investigated using a generalized hydrodynamic isothermal model formalism. It incorporates the constitutive ionic fluid viscosity, inter-species collisions, and geometric curvature effects. The SPR stability is studied for an anodic (hollow, meshed) IFB for the first time against the traditional cathode-plasma arrangements of regular electrode (solid, smooth) fireballs. The SPR develops near a spherical electrode enclosed by a plasma sheath amid a given electric potential. A generalized linear quartic dispersion relation (DR) with diverse plasma multi-parametric coefficients is methodically derived using a standard normal mode analysis. The mathematical construction of the obtained DR roots confirms that only one feasible nonzero frequency mode exists (emerging in the IFB). This root existence is confirmed both analytically and numerically. This consequent SPR creates trapped acoustic fluctuations in the IFB plasmas because of the internal reflections at the sheath plasma boundary. Also, sensible parametric changes in the SPR features, with both plasma density and viscosity, are seen. A local condition for the SPR excitation and its subsequent transition to collective standing wave-like patterns in the IFBs is illustrated. A fair corroboration of our results with the earlier SPR experimental observations of standing wave-like eigenmode patterns (evanescent) strengthens the reliability of our study alongside new applicability.