Derivation of nonlinear chromaticity by higher-order ''smooth approximation''

Technical Report · Sun Aug 01 00:00:00 EDT 1976

OSTI ID:6591789

Morton, P

The ''low-beta insertions'' that are incorporated into most of the new storage ring designs result in very high values of beta in the strong quadrupoles near the interaction regions, and in large natural values of the average chromaticity, xi = d..nu../ddelta with ..nu.. the betatron wave number and delta = ..delta..p/p. In the past the average chromaticity was controlled by the introduction of sextupole magnets into the ring lattice and it was only necessary to correct the linear portion of the betatron tune shift with momentum deviation. In the design of recent storage rings, however, it has become necessary to correct the non-linear terms of the tune shift with momentum deviation. The purpose of this paper is to present analytic formulae for the small-amplitude betatron tune shift with momentum through cubic terms in the momentum deviation. 5 refs.

• Research Organization: Stanford Linear Accelerator Center, Menlo Park, CA (USA)
• DOE Contract Number: AC03-76SF00515
• OSTI ID: 6591789
• Report Number(s): SLAC-PEP-NOTE-221; ON: DE89004847
• Country of Publication: United States
• Language: English

Related Subjects

43 PARTICLE ACCELERATORS
430200* -- Particle Accelerators-- Beam Dynamics
Field Calculations
& Ion Optics
BEAM DYNAMICS
BEAM OPTICS
BETATRON OSCILLATIONS
CHROMATIC ABERRATIONS
DIFFERENTIAL EQUATIONS
EQUATIONS
EQUATIONS OF MOTION
FLOQUET FUNCTION
FUNCTIONS
NONLINEAR PROBLEMS
OSCILLATIONS
PARTIAL DIFFERENTIAL EQUATIONS
PEP STORAGE RINGS
STORAGE RINGS