PPT-Nonlinear Optics as a Path to High-Intensity Circular Machines

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 8pole magnet. Nonlinear Model Problem Let us consider the nonlinear model problem 87228711 f in 8486 1a 0 on 8486 1b where is a given positive function depending on the unknown solution As usual is a given source function which we for simplicity assume not to 6 Linearization of Nonlinear Systems In this section we show how to perform linearization of systems described by nonlinear dif ferential equations The procedure introduced is based on the aylor series expansion and Di64256erentiating 8706S 8706f Setting the partial derivatives to 0 produces estimating equations for the regression coe64259cients Because these equations are in general nonlinear they require solution by numerical optimization As in a linear model Viscoelastic Material Analysis. Objectives. The objective of this module is to provide an introduction to the theory and methods used in the analysis of components containing materials described by viscoelastic material models.. Framework in . Py. . A. . Da. . Ronch. University of. L. iverpool. , . UK. Liverpool, . 16. March 2012. Target. . Nonlinear models . for flexible aircraft (hierarchy). Nonlinear . model reduction. CMSC 435/634. Light. Electromagnetic wave. E & M perpendicular to each other & direction. Photon wavelength . l. , frequency f = c/. l. Visbile. . l. ≈ 380 nm (blue) to 720 nm (red). Photon energy q = h f = h c/. Circular motion. We will be looking at a special case of kinematics and dynamics of objects in uniform circular motion (constant speed). Cars on a circular track (or on a curved road). Roller coasters in loop. Optics Paraxial (first order) approximationMonochromatic aberration (Seidel and wave aberrations)Chromatic aberration (Longitudinal, Transverse) s law, FermatParaxial (first order) approximationMonoch by Mike Plum. Ring Area Manager. Spallation Neutron Source. Workshop on Optics . Measurements, Corrections, and Modeling at High Performance Storage . Rings, CERN, . June 20-22, 2011 . High . i. ntensity challenges. A. . Da . Ronch. , K. J. . Badcock. University of. . L. iverpool, Liverpool, U.K.. Y. Wang, A. Wynn, and R. Palacios. Imperial College, London, U.K.. AIAA Paper 2012-. 4404. Minneapolis, 13 August 2012. nouveaux guides d’ondes, nouvelles non linéarités, . nouvelles directions … . John Dudley. CNRS Institut FEMTO-ST. Université de Franche-Comté . Besançon, France. Mardi 2 décembre 2014. Workshop INSIS - Optique électromagnétique. Third order nonlinear optics offers a wide range of interesting phenomena which are very . different. from . what is expected from linear optics. The most important are due to changes in the . properties. Andrea Franchi (ESRF, Grenoble). on behalf of the . Beam Dynamics & Diagnostics groups. TW-DULER 2018, DIAMOND, 19. th. -20. th. April 2018. Andrea Franchi Optics Measurements @ ESRF. 2. Outlines. Nam-Ho Kim. 1. Goals. What is a nonlinear problem?. How is a nonlinear problem different from a linear one?. What types of nonlinearity exist?. How to understand stresses and strains. How to formulate nonlinear problems.