Fluid Modes of a Spherically Confined Yukawa Plasma

The normal modes of a three-dimensional Yukawa plasma in an isotropic, harmonic confinement are investigated by solving the linearized cold fluid equations. The eigenmodes are found analytically and expressed in terms of hypergeometric functions. It is found that the mode frequencies solely depend on the dimensionless plasma parameter $\xi=\kappa R$, where $R$ is the plasma radius and $\kappa$ the inverse screening length. The eigenfrequencies increase monotonically with $\xi$ and saturate in the limit $\xi\to\infty$. Compared with the results in the Coulomb limit~[D. H. E. Dubin, Phys. Rev. Lett. \textbf{66}, 2076 (1991)], we find a new class of modes characterized by the number $n$ which determines the number of radial nodes in the perturbed potential. These modes originate from the degenerate bulk modes of the Coulomb system. Analytical formulas for the eigenfrequencies are derived for limiting cases.