Collective excitations of a spherically confined Yukawa plasma

The complete spectrum of eigenmodes of a spherically confined Yukawa plasma is presented, based on first-principle molecular dynamics simulations. These results are compared with a recent fluid theory for the multipole modes of this system [H. Kählert and M. Bonitz, Phys. Rev. E 82, 036407 (2010)] and with the exact $N$-particle eigenmodes in the crystalline phase. Simulations confirm the existence of high-order modes found in cold fluid theory. We investigate the influence of screening, coupling, and friction on the mode spectra in detail. Good agreement between theory and simulation is found for weak to moderate screening and low-order modes. In addition, a number of new modes are observed which are missing in the fluid theory. The relations between the breathing mode in the fluid theory, simulation, and the crystal eigenmode are investigated in further detail.

Figure 1

Screening dependence of the $m=0$ multipole spectra ${\mathcal{Q}}_{\ell 0}(\omega )$ (arb. units) for various $\ell$ with $N=1000$ (left column) and $N=4000$ particles (right column) at $\Gamma =150$ without friction. The solid lines show the results of cold fluid theory.

Figure 2

(a) Monopole and (b) dipole spectra for various screening parameters with $N=1000$ particles at $\Gamma =150$. The thick arrow in (b) indicates the low frequency peak in the dipole spectrum.

Figure 3

Screening dependence of the $m=0$ multipole spectra ${\mathcal{Q}}_{\ell 0}(\omega )$ (arb. units) for various $\ell$ with $N=1000$ (left column) and $N=4000$ particles (right column) at $\Gamma =30$ without friction. The solid lines show the results of cold fluid theory.

Figure 4

Same as Fig. 2 for $\Gamma =30$. The thick arrow indicates the position of the low frequency mode for $\Gamma =150$.

Figure 5

Influence of the coupling strength on the $m=0$ multipole spectra ${\mathcal{Q}}_{\ell 0}$ (arb. units) for $N=1000$ and $10⩽\Gamma ⩽400$. The screening parameters are $\kappa a=0.6$ (a,b) and $\kappa a=2$ (c,d).

Figure 6

Quadrupole and octupole spectra for $N=1000$ and $\kappa a=2$ for three values of the coupling parameter $\Gamma$ as indicated in the figure.

Figure 7

Influence of a finite damping coefficient on the quadrupole spectrum for the parameters indicated in the figure. Results are shown for $\nu /{\omega }_0=0,0.01,0.1,1$.

Figure 8

Projection of the $n=1$ monopole mode ($\ell =m=0$) of fluid theory on the $3N$ crystal eigenmodes. Results are shown for $\kappa a=0.4,1.2,2$ (from left to right peak). The modes are ordered by their frequency (from high to low).

Figure 9

Deviation of the $n=1$ monopole mode from the frequency of the exact eigenmode with the greatest projection on the fluid mode for (a) $N=100$ and (b) $N=400$ at $\Gamma =5,10,30,150$. The solid lines show a linear fit.

Figure 10

Frequency deviation of the exact eigenmode with the greatest projection on the fluid mode from the results of cold fluid theory as a function of (a) screening and (b) number of particles.