Multi-scalar Techniques and Stabilities of Longitudinal Motion of Particles in Quasi-isochronous Synchrotron

XIAO Hui-juan; LUO Shi-yu; #; SHAO Ming-zhu

doi:10.11804/NuclPhysRev.28.03.300

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XIAO Hui-juan, LUO Shi-yu, #, SHAO Ming-zhu. Multi-scalar Techniques and Stabilities of Longitudinal Motion of Particles in Quasi-isochronous Synchrotron[J]. Nuclear Physics Review, 2011, 28(3): 300-304. doi: 10.11804/NuclPhysRev.28.03.300

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XIAO Hui-juan, LUO Shi-yu, #, SHAO Ming-zhu. Multi-scalar Techniques and Stabilities of Longitudinal Motion of Particles in Quasi-isochronous Synchrotron[J]. Nuclear Physics Review, 2011, 28(3): 300-304. doi: 10.11804/NuclPhysRev.28.03.300

Multi-scalar Techniques and Stabilities of Longitudinal Motion of Particles in Quasi-isochronous Synchrotron

doi: 10.11804/NuclPhysRev.28.03.300

1 Computer College, Dongguan University of Technology, Dongguan 523106, Guangdong, China;2 College of Electronic Engineering, Dongguan University of Technology, Dongguan 523106, Guangdong, China

Received Date: 1900-01-01
Rev Recd Date: 1900-01-01
Publish Date: 2011-09-20

Abstract

In the classical mechanics frame and with small amplitude approximation, the longutudial motion equation of particles in quasi\|isochronous syhchrotron is reduced to the general Weierstrass equation with a damping term and a forced term. In the non-perturbed case, the phase plane properties are analysed by using Weierstrass function; in the perturbed case, the stabilities are discussed in terms of the multi\|scalar techniques.The results show that the separatrix orbit is a homoclinic orbit through the instable point in the phase plane, the surrounding area is the fish form or α\|form.The stabilities are determined by the fish area, the large the area, the better the stability; also the results show that there are ωm=2, 1/2 super\| and sub\|harmonics resonance except the main resonance ωm=1, the critical condition of an instability is found.
- synchrotron,
- phase motion,
- multi\,
- scalar technique,
- Weierstrass equation
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通讯作者: 陈斌, bchen63@163.com

1.
沈阳化工大学材料科学与工程学院沈阳 110142

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Multi-scalar Techniques and Stabilities of Longitudinal Motion of Particles in Quasi-isochronous Synchrotron

doi: 10.11804/NuclPhysRev.28.03.300

1 Computer College, Dongguan University of Technology, Dongguan 523106, Guangdong, China;2 College of Electronic Engineering, Dongguan University of Technology, Dongguan 523106, Guangdong, China

Received Date: 1900-01-01
Rev Recd Date: 1900-01-01
Publish Date: 2011-09-20

Key words:

Abstract: In the classical mechanics frame and with small amplitude approximation, the longutudial motion equation of particles in quasi\|isochronous syhchrotron is reduced to the general Weierstrass equation with a damping term and a forced term. In the non-perturbed case, the phase plane properties are analysed by using Weierstrass function; in the perturbed case, the stabilities are discussed in terms of the multi\|scalar techniques.The results show that the separatrix orbit is a homoclinic orbit through the instable point in the phase plane, the surrounding area is the fish form or α\|form.The stabilities are determined by the fish area, the large the area, the better the stability; also the results show that there are ωm=2, 1/2 super\| and sub\|harmonics resonance except the main resonance ωm=1, the critical condition of an instability is found.

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