Radiation from accelerating charges Radiation emitted by particle at time t reach observer at time t Retardation occurs due to the finite value of speed of light Position of the particle at time t not relevant need to know the particle history Mark your calendar 11 30 Dr Rui Li of Jefferson Laboratory will discuss retardation effect in synchrotron radiation and the inherent associated problem in charged particle beams P Piot PHYS 571 Fall 2007 Radiation from accelerating charges application Synchrotron radiation Undulator radiation Smith Purcell Transition radiation P Piot PHYS 571 Fall 2007 Radiation from accelerating charges problems Wakefield Coherent and Incoherent synchrotron radiation 20 40 60 80 100 120 140 160 180 200 Overtaking length 50 100 150 200 250 300 350 400 L0 24 z 2 1 3 P Piot PHYS 571 Fall 2007 4 potential associated to a moving charge I Start with Maxwell s equation inhomogeneous Consider the Lorenz gauge Which can be rewritten Solution of the equation is in term of Green s function If free space P Piot PHYS 571 Fall 2007 4 potential associated to a moving charge II With previous eq rewrites Solve using Fourier transform define In Fourier space the d Alembert equation reduces to where P Piot PHYS 571 Fall 2007 4 potential associated to a moving charge III The Green function is obtained by inverse Fourier transform poles Consider the integral of k0 P Piot PHYS 571 Fall 2007 k0 4 potential associated to a moving charge IV So D becomes Introducing integrated the angular part can be P Piot PHYS 571 Fall 2007 4 potential associated to a moving charge V Using the identity D becomes P Piot PHYS 571 Fall 2007 4 potential associated to a moving charge VI And the retarded potential is Retarded and advanced P Piot PHYS 571 Fall 2007 Li nard Wiechert I And the retarded potential is The 4 current Expliciting Or using P Piot PHYS 571 Fall 2007 Li nard Wiechert II So the 4 potential takes the form Which can be re expressed P Piot PHYS 571 Fall 2007
View Full Document
Unlocking...