Abstract
Recently, it has been found that, when operated at large input power, the linewidth $\ensuremath{\Delta}f$ 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, $\ensuremath{\Delta}f$ 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, $\ensuremath{\Delta}f$ deceases with increasing ${T}_{b}$, similar to the experimental observation.
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