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Muon catalyzed fusion (   $$\mu$$  μ CF) in which an elementary particle, muon, facilitates the nuclear fusion between the hydrogen isotopes has been investigated in a long history. In contrast to the rich theoretical and experimental information on the    $$\mu$$  μ CF in cold targets, there is relatively scarce information on the high temperature gas targets of deuterium-tritium mixture with high-thermal efficiency. We demonstrate new kinetics model of    $$\mu$$  μ CF including three roles of resonant muonic molecules, (i) changing isotopic population, (ii) producing epi-thermal muonic atoms, and (iii) inducing fusion in-flight. The new kinetics model reproduces experimental observations, showing higher cycle rate as the temperature increasing, over a wide range of target temperatures (   $$T&lt;800$$  T &lt; 800 K) and tritium concentrations. Moreover, it can be tested by measurements of radiative dissociation X-rays around 2 keV. High energy-resolution X-ray detectors and intense muon beam which are recently available are suitable to reveal these dynamical mechanism of    $$\mu$$  μ CF cycles. Towards the future    $$\mu$$  μ CF experiments in the high-temperature gas target we have clarified the relationship between the fusion yield and density-temperature curve of adiabatic/shock-wave compression.

Roles of resonant muonic molecule in new kinetics model and muon catalyzed fusion in compressed gas