Adams Accelerator Institute 10 - E. Wilson - 1/24/ Slide 1 Lecture 14 ACCELERATOR PHYSICS MT 2004 E. J. N. Wilson

Adams Accelerator Institute 10 - E. Wilson - 1/24/ Slide 2 Recap of previous lecture - Waves Buckets and Cavities  WAVES  Two waves interfering (scissors) (2waves.avi)  Transverse magnetic mode in guide (wavegE.avi)  MORE BUCKETS  Small beta superconducting cavities (example RIA, Argonne)  RF frequency (scaling)  Rf frequency (injection)  RF bucket in collision  Bunch rotation (LHCBunchRotationPresentation.AVI)  CAVITIES  Multicell travellilng wave (electrons)  Fixed frequency electron cavity  50 MHz Ferrite tuned (FNAL)  Low energy cavity tuned with ferrite for SSC  Perspective view of ferrite loaded cavity for SSC  PS 19 MHz cavity (prototype, photo: 1966)  Ferrite cavity  Gap of PS cavity (prototype)  Examples of cavities  CERN/PS 40 MHz cavity (for LHC)  Iris loaded waveguide

Adams Accelerator Institute 10 - E. Wilson - 1/24/ Slide 3 Lecture 14 - Electrons I -contents  Synchrotron radiation  Electrons in circular motion  Retarded Potential  Energy loss per turn  Consequences of Radiation Loss  Dipole radiation emission pattern  Tangential observer’s view  The spectrum  Rate of emission of quanta  Virtues of synchrotron radiation

Adams Accelerator Institute 10 - E. Wilson - 1/24/ Slide 4 Electromagnetic Radiation Electrons accelerating by running up and down in a radio antenna emit radio waves Radio waves are nothing more than Long Wavelength Light-

Adams Accelerator Institute 10 - E. Wilson - 1/24/ Slide 5  Particles radiate when v close to c and  Happens at a few GeV for electrons but at a few TeV for protons because  Really bremsstrahlung - power proportional to deceleration  In a synchrotron force is radial and there is an extra from the Lorentz transformation.  See below which explains this more rigorously and arrives at Synchrotron radiation

Adams Accelerator Institute 10 - E. Wilson - 1/24/ Slide 6 Synchrotron radiation II  From last page  For motion in a circle Hence  Remember magnetic rigidity  Substitute for  to obtain (Equ. 14)  Remember too  Finally a formula to remember

Adams Accelerator Institute 10 - E. Wilson - 1/24/ Slide 7 Electrons in circular motion Electrons in circular motion are also undergoing acceleration When electrons are moving slowly the radiation comes out in all directions When the electron speed gets close to the speed of light, the radiation comes out only in a narrow forward cone; a laser-like concentrated stream

Adams Accelerator Institute 10 - E. Wilson - 1/24/ Slide 8 Retarded Potential  Magnetic vector potential at point 1 from 2  But it was emitted at time t’ but observed when charge has moved at time t

Adams Accelerator Institute 10 - E. Wilson - 1/24/ Slide 9 Retarded Potential – Magnetic field  Assume blob is a point  Remember  Giving and Long range term

Adams Accelerator Institute 10 - E. Wilson - 1/24/ Slide 10 Retarded Potential – Magnetic field  Similarly we have for the electric field  Giving the power emitted over a sphere is  Using the rule for Lorenz transformation of transverse acceleration

Adams Accelerator Institute 10 - E. Wilson - 1/24/ Slide 11 Energy loss per turn  From last page we have a formula that tells us the power consumption (per particle)  We are very interested in how much energy is lost in the time it takes of a particle to circulate  Substitution gives this “energy loss per turn”:

Adams Accelerator Institute 10 - E. Wilson - 1/24/ Slide 12 Consequences of Radiation Loss  The last line show how a future electron machine would lose half its energy each turn.

Adams Accelerator Institute 10 - E. Wilson - 1/24/ Slide 13 Dipole radiation emission pattern (a) circular particle motion (b) the trajectory and dipole radiation emission pattern as seen in a frame moving with the average electron speed  c (c) the corresponding radiation pattern transformed into the lab. frame

Adams Accelerator Institute 10 - E. Wilson - 1/24/ Slide 14 Tangential observer’s view

Adams Accelerator Institute 10 - E. Wilson - 1/24/ Slide 15 The spectrum  Spectrum is broad and looks the same when normalised to  Every quantity is normalised to the frequency of a characteristic quantum which is proportional to

Adams Accelerator Institute 10 - E. Wilson - 1/24/ Slide 16 Rate of emission of quanta  If every quanta had the characteristic value  And the power emitted is  Then the rate of emission would be:  When the average over the spectrum is properly integrated:

Adams Accelerator Institute 10 - E. Wilson - 1/24/ Slide 17 Virtues of synchrotron radiation high intensity of photon flux; continuous spectrum covering a broad range from the far infra-red to hard X-rays; small vertical angular divergence; small source size, determined mainly by the electron beam dimensions; high "brightness" and hence high partial coherence, resulting from the combination of small source size and divergence; polarization - linear in the orbit plane, with a circular component above and below the orbit plane; pulsed time structure, determined by that of the electron beam; calculable spectral intensity, allowing use as a calibrated source.

Adams Accelerator Institute 10 - E. Wilson - 1/24/ Slide 18 Electrons I – Summary  Synchrotron radiation  Electrons in circular motion  Retarded Potential  Energy loss per turn  Consequences of Radiation Loss  Dipole radiation emission pattern  Tangential observer’s view  The spectrum  Rate of emission of quanta  Virtues of synchrotron radiation