Introduction Course s webpage http nicadd niu edu piot phys 571 Grading Homework 50 ok to work discuss together MidTerm 20 class exam Final 30 class exam Instructor Philippe Piot NIU FNAL ANL philippe piot gmail com Generally at NIU on Tues Wed and Th At FNAL on Mondays At ANL on Fridays Handouts Current version distributed watch out for typos mistakes Updated regularly and available on web Slides only available on the web papers will be distributed when needed and made available on the web in protected way due to copyright P Piot PHYS 571 Fall 2007 Notes on textbooks Required the reference in E M J D Jackson classical electrodynamics J Wiley and Sons 3rd Ed Other very good books you may want to check C Brau Modern problems in classical electrodynamics Oxford Univ Press same level as JDJ but more applied with many references to contemporary problems e g lasers nonlinear optics Landau Lifchitz Classical Field Theory a reference S Parrott Relativistic Electrodynamics and Differential Geometry Springer Verlag 1986 very good for the mathematical formalism A O Barut Electrodynamics and Classical Theory of Fields and Particles The McMillan Company 1964 very good hard to find definitely a reference F Rohrlich Classical Charged Particle Addison Wesley Reading 1965 simply excellent but hard to find BUT new 3rd edition just out I did not check it P Piot PHYS 571 Fall 2007 Maxwell s equation I Maxwell s equations in a medium and charge current density J Where electric field Electric displacement polarization induction magnetization Magnetic displacement P Piot PHYS 571 Fall 2007 Maxwell s equation II Generally Linear susceptibility r r tr tv D E E E Linear optics v tr B H Tensor or matrix NL optics Consider simple case of homogenous non conducting non dissipating isotropic medium then 1 0 0 r r v D 0 1 0 E E 0 0 1 P Piot PHYS 571 Fall 2007 v H r B Maxwell s equation III If no source terms are present assume no charge in the medium then Maxwell s equations reduce to Note if medium is vacuum then 0 0 P Piot PHYS 571 Fall 2007 Boundaries conditions You already saw this PHYS 570 check JDJ p 154 p 194 Surface charge density r v D2 D1 n 21 v r E2 E1 n 21 0 Surface s normal pointing from 1 to 2 r r B2 B1 n 21 0 r r r n 21 H 2 H1 K Surface current density For at the boundary of a perfect conductor we have 2 conductor 1 material with 2 2 P Piot PHYS 571 Fall 2007 Resonant cavities introductory remarks I Why do we care The e m hamornic oscillator Acceleration manipulation of charged particle beams Solid state physics e g measurement of dielectric permittivity of materials Lasers amplification occurs as a medium is placed in an optical cavity e g a Fabry Perot resonators Non conducting wall cavities waveguides include dielectric slabs and fibers that can support eigenmodes You studied the simple case of rectangular waveguides and cavities the shoebox type eigenmodes are easy sin cos functions We are going to concentrate on the case of cylindrical symmetric cavities more exciting Bessel function We will not deal with spherically symmetric cavities the eigenmodes are linear combinations of Spherical Harmonic functions P Piot PHYS 571 Fall 2007 Resonant cavities introductory remarks II Example of cavities accelerating cavities for the International Linear Collider Heavy ions accelerating cavities Photonic band gap type accelerating cavity new concept The academic model we are going to consider is the case of a pillbox cavity note it has no practical application since we will assumed the cavity is closed no aperture Pillbox w apertures P Piot PHYS 571 Fall 2007 e m field in a cylindrical symmetric cavity Consider the e m fields of the form Note that P Piot PHYS 571 Fall 2007 Wave equation Take of Faraday s law Take of Ampere Maxwell s equation Summary P Piot PHYS 571 Fall 2007 Relation between transverse and axial e m fields I From Maxwell s equations Generally So B E P Piot PHYS 571 Fall 2007 Relation between transverse and axial e m fields II Apply to the B equation B Similarly for the E equation E P Piot PHYS 571 Fall 2007 Relation between transverse and axial e m fields III Insert E into B Insert B into E P Piot PHYS 571 Fall 2007 Prescription for e m field calculations P Piot PHYS 571 Fall 2007