Spin Dynamics Of Electrons In Storage Rings And Its Application On Energy Calibration

Beam energy is one of the most important parameters for synchrotron radiation light source electron storage ring. It determines the distribution of photon spectrum of synchrotron radiation. In the normal operation, the beam energy of light source would have more or less some difference with the designed value, so precisely measur-ing beam energy is necessary to monitor and understand the operation status of light source. Moreover, Hefei Light Source will serve as a primary standard of radiation source in the spectrum range from vacuum ultraviolet to soft X-ray. This requires that the measurement accuracy of stored electron beams reaches the order of10-4so as to accurately calculate the spectral photon flux.Spin resonant depolarization method for beam energy calibration is nowadays an extensive used method to measure energy. The measurement accuracy of this method is very high and can reach the order of10-5～10-4,even10-6. This method for beam energy measurement has been successfully used in many light source storage rings and collider storage rings in European and American countries. But in China no accelerator laboratory has ever successfully used this technology. In this research project, we’ll use this technology to calibrate electron beam energy with high-precision at Hefei Light Source at National Synchrotron Radiation Laboratory in University of Science and Technology of China.The precondition to use spin resonant depolarization for energy calibration is that the stored beam must be polarized. The measurement technology is applicable on stor-age rings due to the fact that lepton beams in the storage rings can polarize sponta-neously, within a period of time normally shorter than beam lifetime, through emit-ting spin-flip synchrotron radiation. However, there might also many depolarization factors exist in a storage ring. This normally requires adequate understanding about spin dynamics and analysis about the attainable equilibrium polarization, so as to esti-mate the feasibility of spin resonant depolarization method for energy calibration. In the paper, we first elucidated the effect of synchrotron radiation on spin polarization of lepton beams and the affect of orbit diffusion and spin diffusion, due to stochas-tic characteristic of photon emission, on the self-buildup of polarization. Specially, when the so-called "spin resonance" occurs, the stochastic diffusion effect of radia-tion will cause the spins of each electron spread out and cause the depolarization of whole beam. Ultimately, the attainable equilibrium polarization of radiative polarized beam is determined together by radiative polarization mechanism and quantum diffu-sion depolarization mechanism. And this value can be numerically estimated by the famous Derbenev-Kondrateko-Mane formula. After deriving the equation of spin-orbit fully coupling motion of electron and giving the orbit maps and spin maps when elec-tron passes through various elements in the storage ring, we concentrated on analyzing the various spin resonance formalisms and used direct tracking method and analytical-numerical combined method respectively to study about spin resonances and beam po-larization. When tracking about spins of the whole electron beam, a poisson-distributed noise was used to simulate the random photon emission and study about the artificially excited spin resonance, i.e. the phenomenon of sweeping spin resonance. At last, when the information about spin and orbit motion was known adequately, we applied these theories to Hefei Light Source and successfully used spin resonant depolariza-tion method to calibrate the electron beam energy with high precision. In the paper, the fundamental principle for energy calibration, the needed experimental preparation and notable problems during the experiment are elucidated. The experimental result showed, the accuracy of calibrated electron beam energy using this technology at Hefei Light Source can reach the order of10-5～10-4. Furthermore, a series of measure-ments showed, the energy stability during the normal operation of Hefei Light Source is of the order of10-3, having the same order with observed stability of beam orbit. Therefore, the instability of power supply of magnets and instability of high-frequency rf system were thought to be the main reason that caused the instability of beam energy.