Photons represent one of the most important heat carriers. The ability to convert photon heat flow to electricity is therefore of substantial importance for renewable energy applications. However, photon-based systems that convert heat to electricity, including thermophotovoltaic systems where photons are generated from passive thermal emitters, have long been limited by low power density. This limitation persists even with near-field enhancement techniques. Thermophotonic systems, which utilize active photon emitters such as light-emitting diodes, have the potential to significantly further enhance the power density. However, this potential has not been realized in practice, due in part to the fundamental difficulty in thermodynamics of designing a self-sustaining circuit that enables steady-state power generation. Here, we overcome such difficulty by introducing a configuration where the light-emitting diodes are connected in series, and thus multiple photons can be generated from a single injected electron. As a result we propose a self-sustaining thermophotonic circuit where the steady-state power density can exceed thermophotovoltaic systems by many orders of magnitude. This work points to possibilities for constructing heat engines with light as the working medium. The flexibility of controlling the relations between electron and photon flux, as we show in our design, may also be of general importance for optoelectronics-based energy technology. [ABSTRACT FROM AUTHOR]