= Compact radiation moments of a pulsating spherical bubble
{title2=$\rho'_M=\rho_0(a^2\dot a)'/(c_0^2r)$}
In the incompressible near field of a spherical bubble, $u_r=a^2\dot a/s^2$. Its volume-flux <acoustic monopole> is the displayed term at <retarded time>. The integrated surface pressure <force> vanishes by spherical symmetry, while the <Lighthill stress tensor> approximation $\rho_0u_iu_j$ has moment $S_{ij}=4\pi\rho_0a^3\dot a^2\delta_{ij}/3$. Its leading compact <acoustic quadrupole> contribution is $\rho_0(a^3\dot a^2)''/(3c_0^4r)$. For small fractional radius oscillation $\delta$ and compactness parameter $\alpha=\omega a_0/c_0$, its size relative to the leading monopole is $O(\delta\alpha^2)$.
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