PPT-N on-linear dynamics 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. 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. Computational Neuroscience. of Single Neurons. Week 1 – neurons and mathematics:. . a first simple neuron model. Wulfram. Gerstner. EPFL, Lausanne, Switzerland. 1.1 . Neurons. and Synapses: . orderspin-orbitresonanceat4.8GeV.Seeforexampleg.1in[4].AsimilarconclusionemergesfromsimulationswithSLICKTRACKforthe(newer)OCS6latticeat5.0GeV.Thesimulationswereperformedbothforasmallenergyspread(45K Take out homework and a pencil to prepare for the homework quiz!. Check the file folder for your class to pick up graded work. Located by the bookshelf, blue crate.. Look behind the tab for your class period and take home anything with your name on it.. 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. Light . Scattering. . Part 1: Aggregate Structure & Internal Dynamics. 786. Understanding SLS ‘static’ data. I. (. q. ): control . parameter . q. . [units 1/Length] . Large . q. probes small length scales . V. Danilov and S. . Nagaitsev . . 2010. Acknowledgements. Many thanks to Sasha Valishev (FNAL) for help and discussions.. 2. 3. Report at HEAC 1971. How to make the beam stable?. Landau damping – the beam’s “immune system”. It is related to the spread of betatron oscillation frequencies. The larger the spread, the more stable the beam is against collective instabilities.. . 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.. S. . Nagaitsev. , A. . Valishev. (. Fermilab. ), . and V. . Danilov. (ORNL) . Draft talk for HB2010. . Sep . 23. , . 2010. 2. Report at HEAC 1971. CBX layout (1962). 1965, . Priceton. -Stanford CBX: First mention of an 8-pole magnet. 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). Jiang. Feb 17. Model formulation.  .  .  .  .  .  . …. Recall the model of fully-connected neural networks.  . When .  . Linear Networks. In the following slides, we only consider linear networks without bias:. 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.