Betatron motion with coupling of horizontal and vertical degrees of freedom

Journal Article · Fri Oct 01 04:00:00 EDT 1999

OSTI ID:754650

Lebedev, V A; Bogacz, S A

The Courant-Snyder parameterization of one-dimensional linear betatron motion is generalized to two-dimensional coupled linear motion. To represent the 4 x 4 symplectic transfer matrix the following ten parameters were chosen: four beta-function, four alpha-functions and two betatron phase advances. The beta-functions have a meaning similar to the Courant-Snyder parameterization, and the definition of alpha-functions coincides with the standard one at regions with zero longitudinal magnetic field, where they are equal to negative half-derivatives of the beta-functions. Such a parameterization can be useful for analysis of coupled betatron motion in circular machines and transfer lines.

• Research Organization: Thomas Jefferson National Accelerator Facility, Newport News, VA (US)
• Sponsoring Organization: USDOE Office of Energy Research (ER) (US)
• DOE Contract Number: AC05-84ER40150
• OSTI ID: 754650
• Report Number(s): DOE/ER/40150-1275; JLAB-ACC-99-19
• Country of Publication: United States
• Language: English

Related Subjects

43 PARTICLE ACCELERATORS
ACCELERATOR
ACCELERATORS
BEAM TRANSPORT
BETATRON OSCILLATIONS
MATRICES
TRANSFER FUNCTIONS