PPT-Collective effects in Damping rings

Yannis PAPAPHILIPPOU Accelerator and Beam Physics group Beams Department CERN Ninth International Accelerator School for Linear Colliders 26 October 6 November 2015 Whistler BC Canada. Response to Damping As we saw the unfor ced damped harmonic oscillator has equation 0 1 with 0 0 and 0 It has characteristic equation 2 0 with characteristic oots 2 2 Ther e ar e thr ee cases depending on the sign of the expr ession u Natural frequency and damping ratio Well consider the second order homogeneous linear constant coe57358 cient ODE bx cx with positive spring constantmass In the absence of damping term this spring constant wo General . L. inear . B. eam Dynamics. S. Guiducci, INFN-LNF. Seventh International Accelerator School for Linear Colliders . Hosted by Raja . Ramanna. Centre for Advanced Technology. 4 December 2012. Structure and Dynamics. Augusto de la Torre, Erik . Feyen. , and Alain . Ize. WB Conference. Washington DC, 16 June 2011. 1. 1. Chief . Economist . Office. Latin America and the Caribbean. The World Bank. orderspin-orbitresonanceat4.8GeV.Seeforexampleg.1in[4].AsimilarconclusionemergesfromsimulationswithSLICKTRACKforthe(newer)OCS6latticeat5.0GeV.Thesimulationswereperformedbothforasmallenergyspread(45K G. Dugan. PAC TDR review . 12/13/12. Dec. 13, 2012. ILC Damping Rings. 1. Outline. Requirements. Configuration, parameters, operating modes. Lattice. Beam dynamics issues. Emittance. tuning and nonlinear effects. Good Vibrations:. Standing waves can be produced on a string fixed at both ends if the length of the string . L. is a multiple of half the wavelength . l. ,. so that the ends of the string are nodes. These waves are called “harmonics” and are identified by “. . is a dissipation . of. . energy from a vibrating structure. .. The . term dissipate is used to . mean. . the transformation of . mechanical. . energy into other form of energy and, therefore, a removal . Describe . examples of damped oscillations.. . Need to know. - It is sufficient for students to know that damping involves a force that is always in the opposite direction to the direction of motion of the oscillating particle and that the force is a dissipative force.. Mauro Pivi CERN/SLAC. CLIC Collabortion Meeting CERN 9-11 May 2012. Thanks . to:. F. . Antoniou, . Y. Papaphilippou . (. CERN) T. Demma (LAL), A. Chao (SLAC). (Supplemental to . LHO aLOG 6392. ). J. Kissel. G1300561-v1. 1. G1300537-v2. 2. aLIGO BSFM "Level 2" Damping Loop Design. Mission Statement. The damping loops installed during the SUS testing phase . Lawrence Berkeley National Laboratory. John Byrd. Topical Workshop on Instabilities, Impedances and Collective Effects. 17 January 2014. Acknowledgements. Stefano De . Santis. Matthias . Georgsson. . Yannis . PAPAPHILIPPOU. Accelerator and Beam Physics group. Beams Department. CERN. Ninth International Accelerator School for Linear Colliders. 26 October – 6 November 2015, . Whistler BC, Canada. 2.. . Polynomial and Euclidean Rings. 3.. . Quotient Rings. 1. 1. Rings, Integral Domains and Fields. 1.1.Rings. 1.2. Integral Domains and Fields. 1.3.Subrings and Morphisms of Rings. 2. 1. Rings, Integral Domains and Fields.