An RMS particle core model for rings

Journal Article · Sun Nov 01 04:00:00 EST 1998 · AIP Conference Proceedings

DOI:https://doi.org/10.1063/1.56760· OSTI ID:700419

Holmes, J A; Galambos, J D

A self-consistent set of equations for the azimuthal variation of rms betatron oscillation amplitudes, including the effects of dispersion and space charge, is derived. These effective envelope equations can be integrated over the beam energy distribution to provide space charge forces in a particle core model for rings. The derivation of the envelope equations involves an accelerator ordering scheme for the beam dynamics and a statistical moments analysis of the canonical distribution function in the six-dimensional phase space of the beam Hamiltonian. The azimuthal variation of the second moments of the transverse canonical coordinates, x{sup {beta}} and z{sup {beta}}, integrated over the kinetic distribution function of the beam, provides the rms equations. These equations, at fixed beam energy, are integrated over the beam energy distribution to provide the overall space charge distribution and force. Because the envelope equations and dispersion function both depend upon and determine the space charge forces, the consistency of the particle core model requires either analytic closure assumptions or numerical iteration. {copyright} {ital 1998 American Institute of Physics.}

• Research Organization: Oak Ridge National Laboratory
• Sponsoring Organization: USDOE
• DOE Contract Number: AC05-96OR22464
• OSTI ID: 700419
• Report Number(s): CONF-980567--
• Journal Information: AIP Conference Proceedings, Journal Name: AIP Conference Proceedings Journal Issue: 1 Vol. 448; ISSN 0094-243X; ISSN APCPCS
• Country of Publication: United States
• Language: English

Related Subjects

43 PARTICLE ACCELERATORS
BEAM BUNCHERS
BETATRON OSCILLATIONS
DISPERSION RELATIONS
HAMILTONIAN FUNCTION
ION BEAMS
SPACE CHARGE
STORAGE RINGS