We consider the inverse spectral problem for a singular Sturm-Liouville operator with Coulomb potential. In this paper, we give an asymptotic formula and some properties for this problem by using methods of Trubowitz ...We consider the inverse spectral problem for a singular Sturm-Liouville operator with Coulomb potential. In this paper, we give an asymptotic formula and some properties for this problem by using methods of Trubowitz and Poschel.展开更多
In conventional research on beam gas coulomb scattering （BGCS）, only the related beam lifetime using the analytical method is studied. In this paper, using the particle-in-cell Monte Carlo collisions （PIC-MCC） met...In conventional research on beam gas coulomb scattering （BGCS）, only the related beam lifetime using the analytical method is studied. In this paper, using the particle-in-cell Monte Carlo collisions （PIC-MCC） method, we not only simulated the beam lifetime but also explored the effect of BGCS on the beam distribution. In order to better estimate the effect on particle distribution, we study the ultra-low emittance electron beam. Here we choose the HeFei Advanced Light Source. By counting the lost particles in a certain time, the corresponding beam lifetime we simulated is 4.8482 h/13.8492 h in x/y, which is very close to the theoretic value （5.0555 h/13.7024 h in x/y）. By counting the lost particles relative to the collided particles, the simulated value of the loss probability of collided particles is 1.3431e-04, which is also very close to the theoretical value （1.3824e-04）. Besides, the simulation shows there is a tail in the transverse distribution due to the BGCS. The close match of the simulation with the theoretic value in beam lifetime and loss probability indicates our simulation is reliable.展开更多
文摘We consider the inverse spectral problem for a singular Sturm-Liouville operator with Coulomb potential. In this paper, we give an asymptotic formula and some properties for this problem by using methods of Trubowitz and Poschel.
基金Supported by Natural Science Foundation of China(11175182,11175180)
文摘In conventional research on beam gas coulomb scattering （BGCS）, only the related beam lifetime using the analytical method is studied. In this paper, using the particle-in-cell Monte Carlo collisions （PIC-MCC） method, we not only simulated the beam lifetime but also explored the effect of BGCS on the beam distribution. In order to better estimate the effect on particle distribution, we study the ultra-low emittance electron beam. Here we choose the HeFei Advanced Light Source. By counting the lost particles in a certain time, the corresponding beam lifetime we simulated is 4.8482 h/13.8492 h in x/y, which is very close to the theoretic value （5.0555 h/13.7024 h in x/y）. By counting the lost particles relative to the collided particles, the simulated value of the loss probability of collided particles is 1.3431e-04, which is also very close to the theoretical value （1.3824e-04）. Besides, the simulation shows there is a tail in the transverse distribution due to the BGCS. The close match of the simulation with the theoretic value in beam lifetime and loss probability indicates our simulation is reliable.
