The efficacy of Doppler laser cooling in radio-frequency Paul traps depends sensitively on the mutual orientation of the cooling-laser axis and the crystal principal axes, yet this angular dependence has not been systematically investigated across structural phase transitions. We report a comprehensive charged-particle dynamics study of a 50-ion ${}^{88}{\mathrm{Sr}}^{+}$ Coulomb crystal for endcap voltages $U_{\mathrm{ec}}=0.5–200\mathrm{V}$ (Mathieu $q=0.2$) and laser polar angles $\theta =0^{\circ }–{90}^{\circ }$ in $5^{\circ }$ steps, spanning the linear-chain, zigzag-ribbon, and prolate-ellipsoid regimes. By employing energy-decomposition thermometry to separately quantify secular and micromotion temperatures, we find that the cooling rate $\gamma$ increases overall with trap anisotropy $\alpha$, from $7.6{\mathrm{ms}}^{-1}$ in the linear and near-linear crystals to approximately $16.6{\mathrm{ms}}^{-1}$ in the ellipsoids, while the equilibrium temperature drops from $160\mathrm{mK}$ at $U_{\mathrm{ec}}=0.5\mathrm{V}$ (angle average) to approximately $3.6\mathrm{mK}$ in the optimally cooled ellipsoids. The temperature drop is driven primarily by the structural phase transition itself: As the crystal buckles from one-dimensional chains into multidimensional zigzag and ellipsoid morphologies, efficient Coulomb thermalization between axial and radial modes eliminates the radial cooling bottleneck, causing $T_{\mathrm{eq}}$ to saturate near $7T_D$, well above the Doppler limit but almost independent of the precise cooling rate. The anisotropy ratio $R=T_{\mathrm{radial}}/T_{\mathrm{axial}}$ drops from $R\approx 130$ in the one-dimensional chain to $R\approx 1–2$ in the ellipsoids, reflecting the progressive elimination of the radial cooling bottleneck by three-dimensional Coulomb thermalization. In linear chains the temperature anisotropy $T_{\mathrm{radial}}/T_{\mathrm{axial}}$ exceeds 10 at $\theta =0^{\circ }$ and decays toward isotropy as $\theta$ increases; zigzag and ellipsoid structures are far less sensitive to $\theta$ because three-dimensional Coulomb thermalization randomizes directional energy flow. The optimal cooling angle shifts from approximately ${10}^{\circ }$ in the one-dimensional chain to ${45}^{\circ }–{50}^{\circ }$ in the higher-dimensional structures, indicating that strong inter-ion coupling progressively relaxes the need for direct radial laser damping. These results establish a predictive map for cooling-protocol optimization in scalable ion-trap quantum processors.

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• Atom & ion cooling
• Cooling & trapping
• Ab initio molecular dynamics
• Molecular dynamics