Recently it has been found that, when operated at large input power, the linewidth of terahertz radiation emitted from intrinsic Josephson junction stacks can be as narrow as some megahertz. In this high-bias regime a hot spot coexists with regions which are still superconducting. Surprisingly, the linewidth was found to decrease with increasing bath temperature. We present a simple model describing the dynamics of the stack in the presence of a hot spot by two parallel arrays of pointlike Josephson junctions and an additional shunt resistor in parallel. Heat diffusion is taken into account by thermally coupling all elements to a bath at temperature T_b. We present current-voltage characteristics of the coupled system and calculations of the linewidth of the radiation as a function of T_b. In the presence of a spatial gradient of the junction parameters critical current and resistance, the linewidth deceases with increasing T_b, similar to the experimental observation.
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