SU(2)非自治系统中的互补混沌——加速器中离子极化的稳定性

利用SU(2)代数动力学方程研究了加速器中带自旋离子的极化对磁场的含时无规扰动的稳定性问题,发现低度极化的系统对磁场无规扰动十分敏感,而高度极化的系统对磁场无规扰动比较稳定;自旋守恒导致自旋纵向分量的无规涨落和横向分量的无规涨落存在着互补性.这一结果表明,在产生离子束极化的实验中,在离子束低度极化的前期阶段,磁场应具有较高的稳定性,而在离子束极化度较高的后期阶段,磁场的稳定性要求可以放松;自旋纵向分量的无规涨落和横向分量的无规涨落的互补性有可能用来做成稳定离子极化的负反馈.

Complementary Chaos and Spin Polarization Stability in Cyclotrons Studied from the Nonautonomous SU(2) Dynamical System

Complementary chaos and spin polarization stability in cyclotrons are studied from the nonautonomous SU(2) dynamical system by the algebraic dynamical method. The results are as follows:for the case of initially low polarization,the magnetically induced polarization is sensitive to the irregular perturbation,while for the case of initially high polarization,the magnetically induced polarization is stable with respect to the irregular perturbation. The fluctuations of the transverse and longitudinal components of the spin polarization are complementary to each other due to the existence of an invariant of the SU(2) dynamical system,which can be used as a feedback signal to control the spin polarization stability.