The novel proposal of the Muon Catalyzed Fusion (MCF) concept is brought to light employing recent results on its relevant cross sections. In 1993, Kino et al. proposed an innovative scheme of MCF, employing non-adiabatic calculations of muonic atom-nucleus collision in the energy range from 10-3 eV to 100 eV, whereby the fusion in flight along with the formation of muonic molecular resonances was revisited . In 1994, Froelich independently calculated the cross section up to 2 keV, and found the behavior of like resonance . In 1996, Kino et al. examined these resonances, and concluded that the resonances were not suitable for MCF . As a result, the research has been continued to examine the possibility of non-resonant In-flight Muon Catalyzed Fusion (IFMCF) calculating the muonic atom-nucleus collision cross-section with an improved precision within the optical model for nuclear reactions. The resultant fusion cross section was 2000 barns at 1.4 keV  which should be good enough to be used as a fast neutron source . A research program has been initiated to confirm these results theoretically as well as experimentally. For the sake of the theoretical analysis, a few-body computer code has been put forward to handle the nuclear reactions for nucleon transfer. In this paper, an innovative compact reactor concept is proposed, based on IFMCF. In this concept, muons are injected to a gas target of D2 and T2, which is pressurized aerodynamically by the Mach shock wave using a supersonic stream generated in a Laval nozzle , . It generates the output power of 28 MW with 1019 cm-3s-1 of fusions by supplying fresh muons of 1016 cm-3s-1 providing 1000 times of catalyzed cycle of reactions. To maintain Q values > 1, assuming 30% efficiency for thermal to electric conversion, the energy supply for muon production can be as low as 8 GeV/muons. One of the possible applications of muon catalyzed fusion is transmutation of long-lived fission products (LLFPs).