Modes of storage ring coherent instabilities

Conference · Mon Dec 01 04:00:00 EST 1986

OSTI ID:6835132

Wang, J M

Longitudinal impedance in a beam and various modes of longitudinal coherent instabilities are discussed. The coasting beam coherent instability, microwave instability, and single-bunch longitudinal coherent instabilities are considered. The Vlasov equation is formulated, and a method of solving it is developed. The synchrotron modes are treated, which take the possible bunch shape distortion fully into consideration. A method of treating the synchrotron mode coupling in the case of a small bunch is discussed which takes advantage of the fact that only a few of the synchrotron modes can contribute in such a case. The effect of many bunches on the coherent motion of the beam and the longitudinal symmetric coupled bunch modes are discussed. The transverse impedance is then introduced, and the transverse coasting beam instability is discussed. Various bunched beam instabilities are discussed, including both single bunch instabilities and coupled bunch instabilities. The Vlasov equation for transverse as well as longitudinal motion of particles is introduced as well as a method of solving it within a linear approximation. Head-tail modes and short bunch instabilities and strong coupling instabilities in the long bunch case are covered. (LEW)

• Research Organization: Brookhaven National Lab., Upton, NY (USA)
• DOE Contract Number: AC02-76CH00016
• OSTI ID: 6835132
• Report Number(s): BNL-39057; CONF-850768-12; ON: DE87005256
• Country of Publication: United States
• Language: English

Related Subjects

43 PARTICLE ACCELERATORS
430200 -- Particle Accelerators-- Beam Dynamics
Field Calculations
& Ion Optics
430400* -- Particle Accelerators-- Storage Rings
BOLTZMANN-VLASOV EQUATION
COUPLING
DIFFERENTIAL EQUATIONS
DOCUMENT TYPES
EQUATIONS
IMPEDANCE
INSTABILITY
LECTURES
PARTIAL DIFFERENTIAL EQUATIONS
STORAGE RINGS