Power radiated in linear accelerators 1 In linear accelerators We need to evaluate the acceleration Start from the momentum Thus the radiated power is Lighter particles are subject to higher loss P Piot PHYS 571 Fall 2007 Power radiated in linear accelerators 2 One important question is how does the emission of radiation influence the charge particle dynamics The accelerator induce a momentum change of the form where we assumed the acceleration is along the z axis Let be the power associated to the external force The particle dynamics is affected when Pext is comparable to the radiated power P Piot PHYS 571 Fall 2007 Power radiated in linear accelerators 3 Consider a relativistic electron then So the effect seems to be negligible This is actually part of the story some coherent effect can kick in an induce some distortion when considering highly charged electron bunches for instance P Piot PHYS 571 Fall 2007 Power radiated in circular accelerators 1 Now and The radiated power is where E is the energy Let s introduce So radiative energy loss per turn is P Piot PHYS 571 Fall 2007 Power radiated in circular accelerators 2 That is For an e synchrotron this becomes Take E 1 TeV R 2 km we have Conclusion bad idea to build electron circular accelerator for HEP but good as copious radiation sources e g APS in Argonne P Piot PHYS 571 Fall 2007 Angular distribution of radiation emitted by an accelerated charge Starting from the radiation field we have where we used P Piot PHYS 571 Fall 2007 Angular distribution for linear motion 1 Introducing we have And the numerator becomes So the radiated power writes P Piot PHYS 571 Fall 2007 Angular distribution for linear motion 2 The power distribution has maxima given by With solutions Only cos is possible so P Piot PHYS 571 Fall 2007 Angular distribution for linear motion 3 P Piot PHYS 571 Fall 2007 Angular distribution for linear motion 4 Small angle approximation for ultra relativistic case JDJ equation 14 41 P Piot PHYS 571 Fall 2007 Angular distribution for circular motion 1 We have That is Which gives In the ultra relativistic limit small angle approximation P Piot PHYS 571 Fall 2007 Angular distribution for circular motion 2 Note that So we have P Piot PHYS 571 Fall 2007