Transverse beam shape in an electron storage ring with rotated quadrupole and solenoid magnets
A general method for finding particle distribution function by solving the Fokker-Planck equation for a stored electron beam in the presence of radiation damping, quantum excitation and linear coupling has been formulated in previous PEP notes. The stationary distribution has been shown to be a gaussian which can be written as exp (..sigma../sub i/..sigma../sub j/x/sub i/A/sub ij/x/sub j/) with x/sub k/ a particle canonical coordinate, A/sub ij/ a constant whose value depends upon the strength of the coupling elements, and the average value equal to /minus/1/2 A/sup /minus/1//sub ij/. This procedure offers us a logical way for obtaining the dependences of these quantities upon the coupling element strengths. The purpose of this paper is to present a derivation for A/sup /minus/1//sub ij/ in terms of the usual coupling coefficiency calculated from smooth approximation. Then computation of these quantities and comparison with measured magnet misalignment and a possible rotated quadrupole magnet system in PEP is presented. Derivations of some well-known results are included in the appendices for completeness. 15 refs., 6 figs.
- Research Organization:
- Stanford Linear Accelerator Center, Menlo Park, CA (USA)
- DOE Contract Number:
- AC03-76SF00515
- OSTI ID:
- 6657137
- Report Number(s):
- SLAC-PEP-NOTE-207; ON: DE89004594
- Resource Relation:
- Other Information: Portions of this document are illegible in microfiche products
- Country of Publication:
- United States
- Language:
- English
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Related Subjects
PEP STORAGE RINGS
BEAM EMITTANCE
BEAM OPTICS
BEAM PROFILES
BETATRON OSCILLATIONS
CALCULATION METHODS
COUPLING CONSTANTS
EQUATIONS OF MOTION
FOKKER-PLANCK EQUATION
MATRIX ELEMENTS
QUADRUPOLES
SOLENOIDS
BEAM DYNAMICS
DIFFERENTIAL EQUATIONS
ELECTRIC COILS
ELECTRICAL EQUIPMENT
EQUATIONS
EQUIPMENT
MULTIPOLES
OSCILLATIONS
PARTIAL DIFFERENTIAL EQUATIONS
STORAGE RINGS
430200* - Particle Accelerators- Beam Dynamics
Field Calculations
& Ion Optics