New particles and new nuclei have been discovered by artificial techniques recently. High-energy particle accelerators work the important roles to bring such discoveries. The applications of the particles are being discussed at various communities as a next step to get new technologies. The lifetime of the particles are very short to handle by conventional techniques. It can be extended by the theory of relativity. The compact particle accelerator, which enables rapid acceleration, is required especially for the industrial applications. The possibility to satisfy the isochronous condition in the case of DC and uniform magnetic field is discussed here by getting back to the fundamental theoretical approach.