On bunch lengthening using the fourth harmonic cavity in the NSLS VUV ring

Technical Report · Mon Feb 01 00:00:00 EST 1988

DOI:https://doi.org/10.2172/5247573· OSTI ID:5247573

Wachtel, J M

It has been suggested that the phase of the beam excited voltage in the harmonic cavity can be controlled by detuning its resonant frequency from the beam current harmonic. Unfortunately the detuning needed to flatten the acceleration waveform also corresponds to the region of Robinson instability for the harmonic cavity. Therefore, lengthening the bunch may be followed by large amplitude synchrotron oscillation of the bunch center of mass. Bunch lengthening is discussed in this note from several points of view. There follows a simple review of single electron oscillations in a quartic potential. Then equations are developed for the coupled oscillations of a cavity and a rigid bunch as a fully nonlinear, time dependent initial value problem. Next, a computer program that solves these equations for one, two or more cavities, with and without externally driven fields, is described and some simulations of the harmonic cavity interaction are shown. Finally, the fully nonlinear equations are linearized to derive a dispersion relation for the case of beam excitation in the harmonic cavity. 6 refs., 5 figs.

• Research Organization: Brookhaven National Lab. (BNL), Upton, NY (United States)
• DOE Contract Number: AC02-76CH00016
• OSTI ID: 5247573
• Report Number(s): BNL-40929; ON: DE88007392; TRN: 88-015717
• Country of Publication: United States
• Language: English

Related Subjects

43 PARTICLE ACCELERATORS
CAVITY RESONATORS
BEAM BUNCHING
NSLS
S CODES
COMPUTERIZED SIMULATION
ENERGY LOSSES
EQUATIONS OF MOTION
HARMONICS
NONLINEAR PROBLEMS
STABILITY
STORAGE RINGS
SYNCHROTRON OSCILLATIONS
SYNCHROTRON RADIATION
ACCELERATORS
BEAM DYNAMICS
BREMSSTRAHLUNG
COMPUTER CODES
CYCLIC ACCELERATORS
DIFFERENTIAL EQUATIONS
ELECTROMAGNETIC RADIATION
ELECTRONIC EQUIPMENT
EQUATIONS
EQUIPMENT
LOSSES
OSCILLATIONS
PARTIAL DIFFERENTIAL EQUATIONS
RADIATION SOURCES
RADIATIONS
RESONATORS
SIMULATION
SYNCHROTRON RADIATION SOURCES
SYNCHROTRONS
430200* - Particle Accelerators- Beam Dynamics
Field Calculations
& Ion Optics