P. Piot, PHYS 571 – Fall 2007“Scattering” of light on charged particle• A charged particle has no surface, so “scattering” of light is a metaphor.• Quantum view: collision photon/electron• Then• andP. Piot, PHYS 571 – Fall 2007“Scattering” of light on charged particle• We have• Taking and similarly for γ’, we have this is the usual Compton scattering formula. The non-relativistic limityields λ=λ’, which is the regime of Thomson scatteringP. Piot, PHYS 571 – Fall 2007Linear Thomson Scattering: cross section I• Cross section in a figure-of-merit.• Since the electron is at rest:where• So finally accelerationP. Piot, PHYS 571 – Fall 2007Linear Thomson Scattering: cross section II• Note that in the non-relativistic limit• Let’s now specialize our problem and consider a plane wave:• The acceleration is therefore given by:• We ignore the B-field associated to the plane wave because we assume β=0P. Piot, PHYS 571 – Fall 2007Linear Thomson Scattering: cross section III• Given the geometry of the problem we have• Thus• So the time averaging givesP. Piot, PHYS 571 – Fall 2007Linear Thomson Scattering: cross section IV• Assume the incoming wave is unpolarized then•So• So finally • The Poynting vector is given byP. Piot, PHYS 571 – Fall 2007Linear Thomson Scattering: cross section V• The time averaged power per unit of area is• And so the cross-section isthis is the scattering Thomson cross section. The integrated cross section is:P. Piot, PHYS 571 – Fall 2007Notes on Nonlinear Thomson Scattering I• Classical Thomson scattering, the scattering of low-intensity light by e-, is a linear process: it does not changethe frequency of the radiation;• The magnetic-field component of light is not involved. • But if the light intensity is extremely high (~1018W.cm-2), the electrons oscillate duringthe scattering process with velocities appro-aching c.• In this relativistic regime, the effect of the magnetic and electric fields on the electronmotion should become comparableP. Piot, PHYS 571 – Fall 2007Notes on Nonlinear Thomson Scattering II• First experimentally observed in 1998 Nature 396 issue of Dec. 17th, 19982ndharmonic patterns3rdharmonic patternsP. Piot, PHYS 571 – Fall 2007Case of a bounded electron I• Compton and Thomson scatterings apply to free electrons• What happen if an electron is bounded (i.e. to an atom)?• We assume the equation of motion of the bounded electron to be described by:• As before we take and then accelerationfriction termrestoring forceexternal forceP. Piot, PHYS 571 – Fall 2007Case of a bounded electron II• We further assume that i.e. |x|<<λ . • then•so•And finally• Same as before but the denominator is differentP. Piot, PHYS 571 – Fall 2007Case of a bounded electron III• The radiated power is therefore• and the associated cross section is• ω<<ω0and ω<<Γ corresponds to Thomson scattering• ω<<ω0and ω>>Γ gives the Raleigh scattering cross sectionThe reason why the sky is