Fluid Modes of a Spherically Confined Yukawa Plasma

TL;DR

This paper analytically investigates the normal modes of a three-dimensional Yukawa plasma confined in a harmonic trap, revealing how mode frequencies depend on plasma parameters and identifying a new class of radial modes.

Contribution

It provides analytical solutions for the eigenmodes of a Yukawa plasma in harmonic confinement, including a novel class of modes not present in Coulomb systems.

Findings

Eigenfrequencies depend solely on the dimensionless parameter $\xi$

Mode frequencies increase monotonically with $\xi$ and saturate at large $\xi$

Discovery of a new class of modes characterized by radial nodes

Abstract

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.