In the fusion of muon catalyst, it is very important to find the optimal conditions to increase the number of fusions. Usually, the environment is examined either as a mixture of liquid and gas or considered as solid layers. In this thesis, a two-layer hydrogen system is considered. These two layers are frozen on a thin layer of silver. The first layer contains H_2D_2 and the second layer D_2T_2. The first layer is considered as the spring. The output of this spring strongly affects the formation of tmu in the second layer. Here, we first examine the source of dmu ion atom production using point kinetic equations. We also study the effect of the emission of this muon atom in the second layer and obtain the benefit of the mut muon atom, whose number is very effective in fusion