Beam Energy Dependence of the Linear and Mode-Coupled Flow Harmonics Using the A Multi-Phase Transport Model

In the framework of the A Multi-Phase Transport (AMPT) model, the multi-particle azimuthal cumulant method is used to calculate the linear and mode-coupled contributions to the quadrangular flow harmonic ($v_{4}$), mode-coupled response coefficient as a function of centrality in Au+Au collisions at $\sqrt{s_{\mathrm{NN}}}$ = 200, 39, 27 and 19.6 GeV. This study indicated that the linear and mode-coupled contributions to the $v_{4}$ are sensitive to the beam energy change. Nevertheless, the correlations between different order flow symmetry planes and the mode-coupled response coefficients show a weak beam energy dependence. In addition, the presented results suggest that the experimental measurements that span a broad range of beam energies can be an additional constraint for the theoretical models' calculations.