Wall mobility and velocity saturation in bubble-domain materials

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Abstract
The conventional dynamical equations of wall motion are modified by a phenomenological nonlinear damping factor to describe the nonlinearity and velocity saturation observed in some bubble materials. We show that under certain restrictive but common conditions the solution of the resultant nonlinear differential equation can be obtained from the conventional linear solution by the simple transformation t → t ± x/v, where v is the saturation velocity. The conditions for this solution are (a) that the inertial terms are negligible and (b) that the motion is such that the velocity does not change sign. Solutions of the modified dynamical equation are compared with measurements of step‐function wall response and of bubble collapse in Y2.4Eu0.6Fe3.8Ga1.2O12, and it is shown that the measurements are consistently and adequately described by the nonlinear dynamical equation. The nonlinear damping also modifies the equation describing bubble velocity in gradient fields, and it is shown that the modified equation is consistent with propagation data.