Elliptic flow from Coulomb interaction and low density elastic scattering

In high energy heavy ion collisions and interacting cold atom systems, large elliptic flow anisotropies have been observed. For the large opacity ($\rho \sigma L\sim {10}^3$) of the latter hydrodynamics is a natural consequence, but for the small opacity ($\rho \sigma L\sim 1$) of the former the hydrodynamic description is questionable. To shed light onto the situation, we simulate the expansion of a low density argon ion (or atom) system, initially trapped in an elliptical region, under the Coulomb interaction (or elastic scattering). Significant elliptic anisotropy is found in both cases, and the anisotropy depends on the initial spatial eccentricity and the density of the system. The results may provide insights into the physics of anisotropic flow in high energy heavy ion collisions and its role in the study of quantum chromodynamics.

Figure 1

The elliptic flow parameter $v_2$ as functions of time, for (a) the Coulomb interaction, and (b) elastic scattering. Initial trap size: $a=10$ nm, $b=24$ nm, and $c=50$ nm. Three values for the number of particles $N$ are shown.

Figure 2

(a) The average ${\varepsilon }_2$ and (b) the average radial distance as functions of time. Initial trap size: $a=10$ nm, $b=24$ nm, and $c=50$ nm. Three values for the number of particles $N$ are shown.

Figure 3

(a) The ${\varepsilon }_2$ and (b) $v_2$ after the given number of elastic scatterings, $N_{\mathrm{coll}}$. Initial trap size: $a=10$ nm, $b=24$ nm, and $c=50$ nm. Three values of the number of particles $N$ are shown.

Figure 4

The final $v_2$ as a function of the initial ${\varepsilon }_2$. Initial trap size: $ab=240{\mathrm{nm}}^2, c=50$ nm. The number of particles is $N=1000$. The dashed lines are to guide the eye.

Figure 5

The final $v_2$ as a function of the number of particles $N$ for the two interaction cases: the Coulomb interaction and the elastic scattering. The values above the upper axis are the corresponding opacity $\rho \sigma L$ for the elastic scattering case only. Initial trap size: $a=10$ nm, $b=24$ nm, and $c=50$ nm.