Efficiency at Maximum Power of Low-Dissipation Carnot Engines

We study the efficiency at maximum power, ${ensuremath{eta}}^{*}$, 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 ${ensuremath{eta}}_{C}=1ensuremath{-}{T}_{c}/{T}_{h}$ in the reversible limit (long cycle time, zero dissipation), we find in the limit of low dissipation that ${ensuremath{eta}}^{*}$ is bounded from above by ${ensuremath{eta}}_{C}/(2ensuremath{-}{ensuremath{eta}}_{C})$ and from below by ${ensuremath{eta}}_{C}/2$. 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 ${ensuremath{eta}}_{mathrm{CA}}=1ensuremath{-}sqrt{{T}_{c}/{T}_{h}}$ is recovered.