Effect on Synchrotron Motion Caused by Dipole Field Perturbation and Cooling

WU Mu-ying; LUO Shi-yu; SHAO Ming-zhu

doi:10.11804/NuclPhysRev.29.02.154

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Article Navigation > Nuclear Physics Review > 2012 > 29(2): 154-157

WU Mu-ying, LUO Shi-yu, SHAO Ming-zhu. Effect on Synchrotron Motion Caused by Dipole Field Perturbation and Cooling[J]. Nuclear Physics Review, 2012, 29(2): 154-157. doi: 10.11804/NuclPhysRev.29.02.154

Citation:

WU Mu-ying, LUO Shi-yu, SHAO Ming-zhu. Effect on Synchrotron Motion Caused by Dipole Field Perturbation and Cooling[J]. Nuclear Physics Review, 2012, 29(2): 154-157. doi: 10.11804/NuclPhysRev.29.02.154

Effect on Synchrotron Motion Caused by Dipole Field Perturbation and Cooling

doi: 10.11804/NuclPhysRev.29.02.154

Dongguan University of technology, Dongguan 523106, Guangdong, China

Received Date: 1900-01-01
Rev Recd Date: 1900-01-01
Publish Date: 2012-06-20

Abstract

The Betatron oscillation and the synchrotron oscillation for the particles are effected by the dipole field perturbation and the cooling effect. Both effects are considered in the paper and the synchrotron motion equation of the particle in the synchroton is reduced to the general pendulum equation in the classical mechanics frame. The stabilities of the system caused by dipole field perturbation and cooling are analyzed by using Melnikov method. The thresholds entered a Smale horseshoe chaos are derived in detail and the stability conditions for the system caused by dipole field perturbation and cooling are dicussed. The results show that the critical condition or the stability thresholds are related to the system parameters. The chaos or an instability can be avoided or controlled in principle by regulating some parameters of the system.
- synchrotron motion,
- dipole field,
- cooling effect,
- chaos,
- stability
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通讯作者: 陈斌, bchen63@163.com

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沈阳化工大学材料科学与工程学院沈阳 110142

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Effect on Synchrotron Motion Caused by Dipole Field Perturbation and Cooling

doi: 10.11804/NuclPhysRev.29.02.154

Dongguan University of technology, Dongguan 523106, Guangdong, China

Received Date: 1900-01-01
Rev Recd Date: 1900-01-01
Publish Date: 2012-06-20

Key words:

Abstract: The Betatron oscillation and the synchrotron oscillation for the particles are effected by the dipole field perturbation and the cooling effect. Both effects are considered in the paper and the synchrotron motion equation of the particle in the synchroton is reduced to the general pendulum equation in the classical mechanics frame. The stabilities of the system caused by dipole field perturbation and cooling are analyzed by using Melnikov method. The thresholds entered a Smale horseshoe chaos are derived in detail and the stability conditions for the system caused by dipole field perturbation and cooling are dicussed. The results show that the critical condition or the stability thresholds are related to the system parameters. The chaos or an instability can be avoided or controlled in principle by regulating some parameters of the system.

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