Title :
Nonlinear damping of injection oscillations
Author_Institution :
JINR, Dubna, Russia
Abstract :
The theory of a transverse feedback system with a nonlinear regime of injection oscillations damping in circular accelerators and colliders is described. For this feedback loop the dependence between the kick value in the deflector and the beam deviation at the pick-up location is a nonlinear function. The beam dynamic nonlinear equation of the transverse coherent motion for deviation from the closed orbit has been solved using the approximation procedure based on the Krylov-Bogoliubov method for nonlinear differential equations. Approximate expressions for damping time and beam oscillation amplitude are analysed for different nonlinear transfer functions
Keywords :
colliding beam accelerators; cyclic accelerators; nonlinear differential equations; particle beam dynamics; particle beam injection; particle beam stability; Krylov-Bogoliubov method; beam deviation; beam dynamic nonlinear equation; beam oscillation amplitude; circular accelerators; closed orbit; colliders; deflector; injection oscillations; kick value; nonlinear damping; nonlinear differential equations; nonlinear transfer functions; pickup location; transverse coherent motion; transverse feedback system; Colliding beam accelerators; Damping; Difference equations; Differential equations; Ear; Feedback loop; Linear accelerators; Nonlinear equations; Power amplifiers; Transfer functions;
Conference_Titel :
Particle Accelerator Conference, 1999. Proceedings of the 1999
Conference_Location :
New York, NY
Print_ISBN :
0-7803-5573-3
DOI :
10.1109/PAC.1999.795502
