Collisional and collisionless expansion of Yukawa balls

The expansion of Yukawa balls is studied by means of molecular dynamics simulations of collisionless and collisional situations. High computation speed was achieved by using the parallel computing power of graphics processing units. When the radius of the Yukawa ball is large compared to the shielding length, the expansion process starts with the blow-off of the outermost layer. A rarefactive wave subsequently propagates radially inward at the speed of longitudinal phonons. This mechanism is fundamentally different from Coulomb explosions, which employ a self-similar expansion of the entire system. In the collisionless limit, the outer layers carry away most of the available energy. The simulations are compared with analytical estimates. In the collisional case, the expansion process can be described by a nonlinear diffusion equation that is a special case of the porous medium equation.

Figure 1

Self-similar expansion of a Coulomb ball in the collisionless and collisional case by numerical integration of Eq. (4). The circles represent the analytical result Eq. (5).

Figure 2

Expansion of a half-space filled with Yukawa particles for $\Delta z=0.1\lambda$ and 500 mobile sheets. The circles mark the time when a sheet has been displaced by $\Delta z$ from its original position. The dashed line represents the sound speed ${\omega }_0\lambda$.

Figure 3

Short-time expansion of a Yukawa ball ($N=2^{16}$, $R/\lambda =40.3$). The inner part of the Yukawa ball maintains its unperturbed homogeneous density while the rarefaction wave propagates radially inwards.

Figure 4

Expansion of a Coulomb ball ($N=2^{16}$, $\lambda \to \infty$). The density profile remains homogeneous during the expansion.

Figure 5

Evolution of the total potential energy (solid line) and kinetic energy (dashed line) in the Yukawa ball expansion ($N=2^{16}$, $R/\lambda =40.3$). The dotted curves represent the corresponding Coulomb ball expansion. All energies are normalized to the initial potential energy $E_{\mathrm{pot}}\left(0\right)$.

Figure 6

Long-time expansion of a Yukawa ball of initial radius $R$ (dotted box) up to $\tau =100$ ($N=2^{16}$, $R/\lambda =40.3$). Density profiles (solid lines) and kinetic energy per particle (red dashed lines).

Figure 7

Decay time (in normalized units $\tau ={\omega }_{0}t$) of the Yukawa ball as a function of the shielding strength $R/\lambda$ in comparison with the normalized transit time ${\tau }_t=R/\lambda$ (full line). The Coulomb decay time is given by the short dashed line.

Figure 8

Mean trajectory of 500 randomly selected particles in the outermost bin of the density histogram in collisionless and collisional expansions of a Yukawa ball ($N=2^{16}$, $R/\lambda =40.3$).

Figure 9

Early evolution of the density profile (solid line) and kinetic energy per particle (red dashed line) in the weakly collisional case ($\nu =0.03$, $N=2^{16}$, $R/\lambda =40.3$). The dotted box indicates the initial density profile.

Figure 10

Fit of the density profiles for $\nu =0.1$, $N=2^{16}$, $R/\lambda =40.3$ by Barenblatt profiles (fine red lines).

Figure 11

Test of the Barenblatt model for nonlinear diffusion. Expansion of the free surface (circles) in comparison with power law $\propto {\left({\omega }_{0}t\right)}^{1/5}$ (dotted line). Decay of the central maximum (squares) in comparison with power law $\propto {\left({\omega }_{0}t\right)}^{-3/5}$ (dashed line).