Power radiated in linear accelerators 1 In linear accelerators - - PowerPoint PPT Presentation

• P. Piot, PHYS 571 – Fall 2007

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 θ, 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 θ+ 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 approxi-

mation 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