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 $\kappa$ is 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. 66, 2076 (1991)], we find an additional 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.

Figure 1

(Color online) Screening dependence of (a) ratio of $n\text{th}$ to first density moment and (b) ground-state energy contributions.

Figure 2

(Color online) Eigenfrequencies and their dependence on $\xi$ for various modes $\left(n,\ell \right)$. Also shown (by the arrows) are the limits for $\xi =0$ and $\xi \to \infty$. The crosses denote the parameters at which new modes appear to the right of ${\xi }_{n\ell }^{\text{crit}}$.

Figure 3

(Color online) Radial eigenfunctions in the limit $\xi \to \infty$ for various modes as indicated in the figure.

Figure 4

(Color online) Radial eigenfunctions for various $\xi$’s and mode numbers $\left(n,\ell \right)$.

Figure 5

(Color online) Radial fluid velocity for the breathing mode.