Vertical beam size due to orbit and alignment errors
The value of luminosity, synchrotron light source brightness, quantum lifetime, etc., for an electron storage ring is directly dependent upon the natural beam size and shape in the transverse phase space. These transverse beam parameters can be determined from the stationary particle distribution, psi, which depends upon (a) quantum excitations determined by the horizontal and vertical energy dispersion functions eta/sub x,y/ and eta'/sub x,y/ in the machine, (b) radiation damping provided by the rf acceleration, and (c) coupling between the transverse betatron motions caused by the skew quadrupole and solenoid magentic fields. A straightforward method to find psi is by solving the Fokker-Planck equation, which conveniently takes into account these factors. In this approach the quantum diffusion effects are described by three quantities, H/sub xx/, H/sub xy/, and H/sub yy/, which are integrals of the ..beta..- and eta-functions and their derivatives evaluated over the bending magnets in the machine; the radiation damping effects are characterized by the radiation damping constants ..cap alpha../sub x,y/ provided by an rf system. The coupling effects are represented by a coupling coefficient, Q, assuming smooth coupling between the betatron motions. Under these assumptions, psi can be found analytically and the expressions for transverse beam parameters in terms of Q, H/sub xx/, H/sub x,y/, H/sub yy/, ..cap alpha../sub x/, and ..cap alpha../sub y/ can be obtained. From these expressions, invariant conditions between some of the beam parameters can easily be shown. These results have been used to estimate the effects in PEP and SPEAR due to magnet alignment and vertical closed-orbit errors.
- Research Organization:
- Stanford Univ., CA
- OSTI ID:
- 7285511
- Journal Information:
- IEEE Trans. Nucl. Sci.; (United States), Vol. NS-24:3; Conference: Particle accelerator conference, Chicago, IL, USA, 16 Mar 1977
- Country of Publication:
- United States
- Language:
- English
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