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P. Piot, PHYS 571 – Fall 2007Introduction• 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) [[email protected]]• 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 2007Notes on textbooks• Required: (the reference in E&M)– J. D. Jackson classical electrodynamics, J. Wiley and Sons 3rdEd• 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 3rdedition just out (I did not check it).P. Piot, PHYS 571 – Fall 2007Maxwell’s equation I• Maxwell’s equations in a medium (ε,µ) and charge/current density (ρ,J)• Where polarizationmagnetizationelectric fieldinductionElectric displacementMagnetic displacementP. Piot, PHYS 571 – Fall 2007Maxwell’s equation II• Generally • Consider “simple case” of homogenous, non conducting, non dissipating isotropic medium then:HBrtvµ=EEEDvtrtrrεχεε≡++= ...Tensor (or matrix)Linear susceptibilityLinear opticsNL opticsEEDvrrεε==100010001µBHrv=P. Piot, PHYS 571 – Fall 2007Maxwell’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:00µµεε→→P. Piot, PHYS 571 – Fall 2007Boundaries conditions• You already saw this (PHYS 570) [check JDJ p. 154 & p. 194]• For at the boundary of a perfectperfectconductor we have: (2) conductor (1) material with (ε,µ) : ()()=×−=−0ˆˆ.21122112nEEnDDvrvrσ()()=−×=−KHHnnBBrrrrr12212112ˆ0ˆ.∞→∞→22µεSurface current densitySurface charge densitySurface’s normal pointing from (1) to (2)P. Piot, PHYS 571 – Fall 2007Resonant 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 2007Resonant cavities -- introductory remarks II• Example of cavities• 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 aperturesHeavy ions accelerating cavitiesaccelerating cavities for the International Linear ColliderPhotonic band-gap type accelerating cavity (new concept)P. Piot, PHYS 571 – Fall 2007e.m. field in a cylindrical-symmetric cavity• Consider the e.m. fields of the form:• Note thatP. Piot, PHYS 571 – Fall 2007Wave equation• Take of Faraday’s law:• Take of Ampere-Maxwell’s equation:• Summary:P. Piot, PHYS 571 – Fall 2007Relation between transverse and axial e.m. fields I• From Maxwell’s equations• Generally•So(B)(E)P. Piot, PHYS 571 – Fall 2007• Apply to the “B”-equation:• Similarly for the “E”-equation(B’)(E’)Relation between transverse and axial e.m. fields IIP. Piot, PHYS 571 – Fall 2007• Insert (E’) into (B)• Insert (B’) into (E)Relation between transverse and axial e.m. fields IIIP. Piot, PHYS 571 – Fall 2007Prescription for e.m. field


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NIU PHYS 671 - LECTURE NOTES

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