Acoustic oscillations of multielectron bubbles in liquid helium

The surface-wave oscillations of large multielectron bubbles in liquid helium are considered; their stability is attributed to a novel nonlinear coupling between their radial and angular modes of oscillation. The time dependence and the power spectra of the mode amplitudes are computed for free and acoustically driven oscillations. Small slow oscillations allow analytical estimates for the region of stability for the multielectron bubbles in terms of known properties of Mathieu equations; in the general case the computations are performed numerically. We find that the Taylor instability first sets in for the l=3 angular mode with free radial oscillations above a threshold amplitude, followed closely by the instability for the l=2 mode, while all higher modes become unstable at appreciably larger radial oscillation amplitudes. Resonant enhancement phenomena are discussed in detail in connection with acoustically driven bubble oscillations. Experiments are suggested to investigate the oscillation modes and their stability