We consider an implementation of the novel accelerator-based fusion reactor scheme using a setup in which ion and electron beams are injected into the end openings of an axisymmetric magnetic mirror. While the magnetic mirror ensures transverse confinement of the plasma, the injected beams contribute to axial confinement, thereby extending the overall plasma lifetime. The ion beam energy is initially set above the resonance region of the fusion reactions, allowing fusion to occur both via resonance and thermal mechanisms as the beam slows down to the plasma temperature. Beam energy loss (stopping power) contributes to plasma heating, offsetting radiative losses and sustaining the temperature. The thermalized beam accumulates over the plasma lifetime, with its density growing algebraically, leading to an average fusion power that increases with the confinement time. We consider a gas dynamic trap mirror, which is stable against magnetic flute instabilities, as a potential confinement system. A feasibility study is carried out for the fusion reactions , and , based on energy considerations. In these reactions, the charged fusion products have energies higher than the incoming beam ions and can escape through the end mirrors, allowing for direct conversion to electricity. Given the plasma density, temperature, magnetic field, beam current, and beam energy, we perform a baseline calculation to estimate the stopping power, radiation losses, plasma heating time, and average fusion power, in order to determine the confinement time required for the feasibility of such reactors.