Synchrotron Radiation An Introduction L. Rivkin Swiss Light Source
Some references CAS Proceedings CAS - CERN Accelerator School: Synchrotron Radiation and Free Electron Lasers, Grenoble, France, 22-27 Apr 1996 CERN Yellow Report 98-04 (in particular A. Hofmann s lectures on synchrotron radiation) A. W. Chao, M. Tigner Handbook of Accelerator Physics and Engineering, World Scientific 1999 WWW http://www-ssrl.slac.stanford.edu/sr_sources.html
Crab Nebula 6000 light years away GE Synchrotron New York State First light observed 1054 AD First light observed 1947
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THEORETICAL UNDERSTANDING 1873 Maxwell s equations made evident that changing charge densities would result in electric fields that would radiate outward 1887 Heinrich Hertz demonstrated such waves:.. this is of no use whatsoever!
Maxwell equations (poetry) War es ein Gott, der diese Zeichen schrieb Die mit geheimnisvoll verborg nem Trieb Die Kräfte der Natur um mich enthüllen Und mir das Herz mit stiller Freude füllen. Ludwig Boltzman Was it a God whose inspiration Led him to write these fine equations Nature s fields to me he shows And so my heart with pleasure glows. translated by John P. Blewett
Why do they radiate? Charge at rest: Coulomb field Uniformly moving charge v = const. Accelerated charge
Bremstrahlung
1898 Liénard: ELECTRIC AND MAGNETIC FIELDS PRODUCED BY A POINT CHARGE MOVING ON AN ARBITRARY PATH (by means of retarded potentials)
Liénard-Wiechert potentials ϕ t = 1 4πε 0 q r 1 n β ret A t = q 4πε 0 c 2 v r 1 n β ret and the electromagnetic fields: A + 1 c 2 ϕ t =0 (Lorentz gauge) B = A E = ϕ A t
Fields of a moving charge E t = q 4πε 0 n β 1 n β 3 γ 2 1 r 2 ret + q 4πε 0 c n n β β 1 n β 3 γ 2 1 r ret B t = 1 c n E
Transverse acceleration a v Radiation field quickly separates itself from the Coulomb field
Longitudinal acceleration a Radiation field cannot separate itself from the Coulomb field v
Moving Source of Waves
Time compression Electron with velocity β emits a wave with period T emit while the observer sees a different period T obs because the electron was moving towards the observer n θ β The wavelength is shortened by the same factor λ obs = ( 1 β cosθ ) λ emit in ultra-relativistic case, looking along a tangent to the trajectory since λ obs = 1 2γ 2 λ emit T = ( 1 n β) obs T emit 1 β = 1 β2 1+β 1 2γ 2
Angular Collimation Galileo: sound waves v s = 331 m/s θ = θ e v s v v s v s + v = v s v 1 s 1+ v v θ e 1 1+ v s v s v θ Lorentz: speed of light c = 3 10 8 m/s θ e θ v ~ c θ = 1 γ θ e
Radiation is emitted into a narrow cone
t ~ 2ρ γ c 1 2γ 2 1/γ ω ~ 1 t ~ γ 3 ω 0
Typical frequency of synchrotron light Due to extreme collimation of light observer sees only a small portion of electron trajectory (a few mm) l ~ 2ρ γ Pulse length: difference in times it takes an electron and a photon to cover this distance t ~ l βc l c = l βc 1 β
Synchrotron radiation power Power emitted is proportional to: P SR = cc γ 2π E 4 ρ 2 P E 2 B 2 P SR = 2 3 αhc 2 γ 4 ρ 2 C γ = 4π 3 r e 5 = 8.858 10 m 2 3 m e c GeV 3 α = 1 137 Energy loss per turn: hc = 197 Mev fm U 0 = C γ E 4 ρ U 0 = 4π 3 αhcγ 4 ρ
The power is all too real! cc γ E 4 PSR = 2π ρ 2
Spectrum of synchrotron radiation Synchrotron light comes in a series of flashes every T 0 (revolution period) the spectrum consists of harmonics of flashes are extremely short: harmonics reach up to very high frequencies At high frequencies the individual harmonics overlap ω 0 = 1 T 0 ω 3 typ γ ω0 continuous spectrum! T 0 time ω ~ 1 MHz γ ~ 4000 ω 0 typ ~ 10 16 Hz!
dp dω = P tot ω c S ω ω c Sx = 9 3 8π x K5 5 3 x dx x 0 Sx dx =1 P tot = 2 3 hc2 α γ4 ω c = 3 2 cγ 3 ρ ρ 2 1 0.1 0.01 ~ 2.1x 1 3 G 1 x =x K 5 3 x dx x ε c ev = 665 E 2 GeV BT 50% ~ 1.3 xe x 0.001 0.001 0.01 0.1 1 10 x = ω/ω c
Synchrotron radiation flux for different LEP energies Flux [photons/s/mrad/0.1%bw] 10 13 10 12 10 11 10 10 LEP Dipole Flux I = 1 ma 20 GeV 50 GeV 100 GeV 10 9 10 1 10 2 10 3 10 4 10 5 10 6 10 7 Photon energy [ev]
Flux from a dipole magnet: Flux photons s mrad 0.1%BW = 2.46 1013 E[GeV] I[A]G 1 x Power density at the peak: P tot ω c = 4 9 αhc γ ρ
Angular divergence of radiation The rms opening angle R at the critical frequency: ω = ω c R 0.54 γ well below ω «ω c R 1 γ ω c ω 1 3 0.4 λ ρ independent of γ! 1 3 well above ω» ω c R 0.6 γ ω c ω 1 2
Polarisation Synchrotron radiation observed in the plane of the particle orbit is horizontally polarized, i.e. the electric field vector is horizontal Observed out of the horizontal plane, the radiation is elliptically polarized E E