Generalized parametrization methods for centroid and envelope dynamics of charged particle beams in coupled lattices
- Ulsan National Inst. of Science and Technology, Ulsan (South Korea). Dept. of Physics
- Princeton Plasma Physics Lab. (PPPL), Princeton, NJ (United States); Univ. of Science and Technology of China, Hefei (China). Dept. of Modern Physics
For almost 60 years, the well-known Courant-Snyder (CS) theory has been employed as the standard method to describe the uncoupled dynamics of charged particle beams in electromagnetic focusing lattices. Meanwhile, the generalization of the CS theory to coupled dynamics with two or more degrees of freedom has been attempted in numerous directions. The parametrization method developed by Qin and Davidson is particularly noteworthy, because their method enables the treatment of complicated coupled beam dynamics using a remarkably similar mathematical structure to that of the original CS theory. Here in this paper, we revisit the Qin-Davidson parametrization method and extend it to include beam centroid motions. The linear terms in the quadratic Hamiltonian for the coupled dynamics are handled by introducing a special time-dependent canonical transformation. In this manner, we show that the centroid dynamics is decoupled from the envelope dynamics, even for the cases of coupled lattice, and all formulations of the Qin-Davidson method can be applied in a straightforward manner.
- Research Organization:
- Princeton Plasma Physics Laboratory (PPPL), Princeton, NJ (United States)
- Sponsoring Organization:
- USDOE; National Research Foundation of Korea (NRF)
- Grant/Contract Number:
- NRF-2015R1D1A1A01061074; NRF-2017M1A7A1A02016413; AC02-09CH11466
- OSTI ID:
- 1464463
- Alternate ID(s):
- OSTI ID: 1414617
- Journal Information:
- Physics of Plasmas, Vol. 25, Issue 1; ISSN 1070-664X
- Publisher:
- American Institute of Physics (AIP)Copyright Statement
- Country of Publication:
- United States
- Language:
- English
Web of Science
A necessary and sufficient condition for the stability of linear Hamiltonian systems with periodic coefficients
|
journal | February 2019 |
| A necessary and sufficient condition for the stability of linear Hamiltonian systems with periodic coefficients | text | January 2018 |
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