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 and P Piot PHYS 571 Fall 2007 Scattering of light on charged particle We have Taking and similarly for we have this is the usual Compton scattering formula The non relativistic limit yields which is the regime of Thomson scattering P Piot PHYS 571 Fall 2007 Linear Thomson Scattering cross section I Cross section in a figure of merit Since the electron is at rest where acceleration So finally P Piot PHYS 571 Fall 2007 Linear 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 0 P Piot PHYS 571 Fall 2007 Linear Thomson Scattering cross section III Given the geometry of the problem we have Thus So the time averaging gives P Piot PHYS 571 Fall 2007 Linear Thomson Scattering cross section IV Assume the incoming wave is unpolarized then So So finally The Poynting vector is given by P Piot PHYS 571 Fall 2007 Linear Thomson Scattering cross section V The time averaged power per unit of area is And so the cross section is this is the scattering Thomson cross section The integrated cross section is P Piot PHYS 571 Fall 2007 Notes on Nonlinear Thomson Scattering I Classical Thomson scattering the scattering of low intensity light by e is a linear process it does not change the 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 during the scattering process with velocities approaching c In this relativistic regime the effect of the magnetic and electric fields on the electron motion should become comparable P Piot PHYS 571 Fall 2007 Notes on Nonlinear Thomson Scattering II First experimentally observed in 1998 Nature 396 issue of Dec 17th 1998 3rd harmonic patterns 2nd harmonic patterns P Piot PHYS 571 Fall 2007 Case 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 external force acceleration restoring force friction term As before we take and P Piot PHYS 571 Fall 2007 then Case of a bounded electron II We further assume that i e x then so And finally Same as before but the denominator is different P Piot PHYS 571 Fall 2007 Case of a bounded electron III The radiated power is therefore and the associated cross section is 0 and corresponds to Thomson scattering 0 and gives the Raleigh scattering cross section The reason why the sky is blue P Piot PHYS 571 Fall 2007