Ground state of a confined Yukawa plasma

The ground state of an externally confined one-component Yukawa plasma is derived analytically. In particular, the radial density profile is computed. The results agree very well with computer simulations of three-dimensional spherical Coulomb crystals. We conclude in presenting an exact equation for the density distribution for a confinement potential of arbitrary geometry.

Figure 1

Plasma cloud radius $R$ [positive real solution of Eq. (13)] for a parabolic confinement potential $\Phi \left(r\right)=\frac{\alpha }{2}{r}^2$ and Yukawa interaction with screening parameter $\kappa$.

Figure 2

(Color online) Radial density profile for a parabolic confinement potential $\Phi \left(r\right)=\alpha r^2∕2$ and a constant screening parameter $\kappa r_0=1$ and four different particle numbers $N$ shown in the figure. For comparison, also the result for $\kappa r_0=0.3$ and $N=2000$ is shown by the dashed line.

Figure 3

(Color online) Dependence of the central density $n\left(0\right)$ (red dotted line), density at the boundary, $n\left(R\right)$ (blue dashed line), and compression $n\left(0\right)∕n\left(R\right)$ of the plasma (green solid line) as a function of particle number and screening parameter.

Figure 4

(Color) Radial density profile, solutions of Eq. (11), of a three-dimensional plasma of $N=2000$ for four values of the screening parameter (lines), from bottom to top: $\kappa =0$ (red), $\kappa r_0=0.3$ (yellow), $\kappa r_0=1$ (green), and $\kappa r_0=3$ (blue). Symbols the denote molecular dynamics results of a plasma crystal for the same parameters where the average density at the positions of the shells is shown (for details see discussion in Sec. 4B).