The Stability Analysis of the Relativity Motion of Charged Particles in Electromagnetic Fields and the Possibility to Establish Synchrocyclotron without Radiation Losses

According to the classical theory of electromagnetism, charged particles radiate electromagnetic waves when they are accelerated. However, actual situations are not completely the cases. For example, only when electrical current oscillates, antenna radiates radio waves. If parameters are not proper, no radio waves are produced. Although in both situations, electrons do period accelerating and decelerating motions. When electrons collide with atomic nucleus, braking radiation takes place. But electrons do not radiate when they are accelerated in uniform electric field. In synchrocyclotron, electrons radiate, but in electron induction accelerator, no radio radiations were founded (J. Blewett experiment). In fact, in the common loops of alternate or direct currents, as well as in the current loops made from low temperature supper-conductors, no radiations are found. A more foundational fact is that electrons do not radiate when they move around atomic nucleus and atoms are stable. These facts contradict with classical electromagnetic theory. We have no rational explanation for them at present. It is proved in this paper that the forms of forces can not be arbitrary in the dynamic equations of relativity. Otherwise the motions may become impossible. In order to make the motions possible in electromagnetic field, charged particles have to radiate. It is proved that the longitudinal velocities of charged particles in the uniform magnetic fields would exceed light’s speed in vacuum, and therefore the motions are unstable and charged particles have to radiate. In the center electric fields, the motions of charged particles may be both stable and unstable depending on the actual situations, and they may radiate or not radiate. Therefore, acceleration is not the real season for charged particles to radiate. The real one is the instability of relativity motion. The essence of antenna radiations is proved to be the braking radiation and the braking radiation is the effect of relativity actually. The radiation damping forces should be added in the motion equations of relativity to describe charged particle’s motions in electromagnetic fields when they radiate. The forms of damping forces are deduced. The synchrocyclotron oscillation of electron’s obits at longitudinal direction is obtained automatically. It is proved that if a proper electric force is acted at the direction of velocity, the relativity motion of electron in magnetic field will become stable so that it may not radiate. In this way, we can establish high energy synchrocyclotron without or less synchron