Influence of dielectric screening introduction Last time we derive the rate of energy loss for a charge particle q Compare to Bohr s result 1915 Bohr s result accurately describe measurement for non ultrarelativistic particle For ultra relativistic particle energy loss smaller than Bohr s prediction This discrepancy is due to density effects P Piot PHYS 571 Fall 2007 Field of a moving particle in a dielectric I In dense medium the particle field is altered by polarization effects We need to find the field of a charge particle moving in a medium i e we have to solve We take and 1 and solve this equation in the Fourier domain P Piot PHYS 571 Fall 2007 Field of a moving particle in a dielectric II Let s define the Fourier tranforms time i space i Typos in the handout P Piot PHYS 571 Fall 2007 Field of a moving particle in a dielectric III The sources of the field are of the form The time and space Fourier transform is So finally P Piot PHYS 571 Fall 2007 Field of a moving particle in a dielectric IV Transform the wave equation in the Fourier domain which give So finally P Piot PHYS 571 Fall 2007 Field of a moving particle in a dielectric V The e m field are given by hence We want to find the flow of energy i e the Poynting vector so we need P Piot PHYS 571 Fall 2007 Field of a moving particle in a dielectric VI The E field is Specialize the problem to the case P Piot PHYS 571 Fall 2007 Field of a moving particle in a dielectric VII Integrate over kz Integration over dky gives P Piot PHYS 571 Fall 2007 Field of a moving particle in a dielectric VIII So finally And The E field finally writes P Piot PHYS 571 Fall 2007 Field of a moving particle in a dielectric IX The B field can be computed in a similar manner Integrating over dkz gives This is the same as x component of the E field so P Piot PHYS 571 Fall 2007 Energy loss in a dielectric I The e m field energy flowing out of a cylinder surface of radius b extending from to in z is We have So P Piot PHYS 571 Fall 2007 Energy loss in a dielectric II Expliciting the E and B field in the latter equation gives First derived by Enrico Fermi Energy loss occurs if either or are complex P Piot PHYS 571 Fall 2007