According to classical electromagnetic theory, the accelerated motion of charged particles produces electromagnetic radiation, but this is not always the case. Experiments have shown that electrons colliding with nuclei produce bremsstrahring radiation when they are decelerated, but electrons do not radiate when they are accelerated in a uniform electric field. In synchrocyclotron, electrons radiate, but in Lawrence’s Cyclotrons and induction accelerator and linear accelerators, electrons do not radiate (Blewett experiment). In this paper, the motion of charged particles in the electromagnetic field are analyzed by considering the mass-velocity formula of special relativity. It is pointed out that the accelerating motion of electrons in uniform magnetic field and strict electric field are stable, so they need not to radiate. In this way, the stability of atoms can be explained. But if the magnetic field is not uniform, or there is some kind of disturbing force, the speeds of electrons may become imaginary or faster-than-light, making the motion impossible. In this case, electrons had to radiate to change their state, making the motion possible. Therefore, acceleration is not the essential cause of radiation of charged particles, but the instability of motion is the real cause of radiation. It is proved that it is possible to eliminate the radiation of particles as long as the interference factors are eliminated so that the motion of charged particle is stable in synchrocyclotron. A simple design scheme is proposed by adding parallel current lines in the particle beam pipe of accelerator to eliminate the transverse oscillation of charge particles, to construct a new synchrocyclotron with high energy and low radiation or even no radiation.