Efficiency at maximum power of low dissipation Carnot engines

We study the efficiency at maximum power, ${\eta }^{\ast }$, of engines performing finite-time Carnot cycles between a hot and a cold reservoir at temperatures $T_h$ and $T_c$, respectively. For engines reaching Carnot efficiency ${\eta }_C=1-T_c\mathrm{/}{T}_h$ in the reversible limit (long cycle time, zero dissipation), we find in the limit of low dissipation that ${\eta }^{\ast }$ is bounded from above by ${\eta }_C\mathrm{/}(2-{\eta }_C)$ and from below by ${\eta }_C\mathrm{/}2$. These bounds are reached when the ratio of the dissipation during the cold and hot isothermal phases tend respectively to zero or infinity. For symmetric dissipation (ratio one) the Curzon-Ahlborn efficiency ${\eta }_{CA}=1-\sqrt{T_c\mathrm{/}{T}_h}$ is recovered.