A Structural Comparison of Sonoluminescence via the KG--RP Invariant Manifold: Sulfuric‑Acid Regimes

Sonoluminescence in concentrated sulfuric acid has been puzzling for twenty years because the system behaves in ways that seem to contradict basic hydrodynamics. At low xenon concentration (4 torr), the bubble looks and behaves almost exactly like standard SL in water. But at higher concentration (50 torr), everything changes: the bubble becomes dramatically brighter—up to two orders of magnitude—while collapsing more weakly, flashing for ten times longer, and wandering unpredictably from cycle to cycle. The original experimental paper by Hopkins and collaborators documented these anomalies in detail but could not identify a mechanism that unified them. This paper provides that mechanism. By embedding the sulfuric‑acid system into the hybrid Klein–Gordon/Rayleigh–Plesset (KG–RP) model and mapping it into the invariant manifold defined by the universal locking law, we show that the 4 torr and 50 torr regimes are not contradictory or mysterious—they are two branches of the same underlying geometric structure. Both regimes share the same RP backbone: the same radius scaling, the same geometric compression, and the same hydrodynamic response to forcing. The divergence appears only in the KG sector, where the 50 torr regime activates a nonlinear internal mode that stores and releases energy in a way the RP equation alone cannot capture. On the invariant manifold, the 4 torr and 50 torr states separate cleanly along the KG/RP coupling coordinate. The 4 torr regime sits in a stable region where the KG mode is weakly excited and tightly locked to the RP collapse. The 50 torr regime sits in a high‑energy, weak‑coupling region where the KG mode becomes strongly activated, drifts in and out of resonance, and generates long flashes, detuning windows, and cycle‑to‑cycle variability. This geometric separation explains why the 50 torr bubble is brighter despite collapsing more weakly, why it exhibits a sharp collapse‑velocity threshold, and why its flashes last an order of magnitude longer. By placing both sulfuric‑acid regimes on the same invariant manifold and analyzing them with the same solver, the same nondimensionalization, and the same invariant definitions, this paper provides the first structural explanation of the sulfuric‑acid anomalies. The brightness increase, the instability, the long emission times, and the presence of a hot interior masked by a cooler surface all emerge naturally from the geometry of the manifold. The sulfuric‑acid system therefore becomes the third major experimental regime—alongside NASA microgravity and the Putterman dark‑bubble anomaly—to fall onto the same universal KG–RP structure. The result is a unified, geometric understanding of sulfuric‑acid sonoluminescence that resolves long‑standing experimental puzzles and strengthens the case that the KG–RP invariant manifold captures the essential mechanism of nonlinear energy focusing in cavitating systems.