Tonks-Dattner resonances in a quantum plasma bubble.

We establish the spectrum of Tonks-Dattner mode resonances in a quantum plasma bubble and consider the spectral changes associated with plasma quenching and plasma expansion. The quantum corrections associated with the mode spectrum are specified, which can be used as a diagnostic tool to identify the quantum regime. The frequency shifts associated with time-varying plasma bubbles correspond to time refraction and can also be used as a plasma diagnostic. We also study the energy mode coupling, in the presence of a low-frequency perturbation. It will be shown that the mode coupling equations take the form of generalized Bloch equations, where a nonlinear Rabi frequency can also be identified.