A Quick primer on synchrotron radiation: How would an MBA source change my x-ray beam. Jonathan Lang Advanced Photon Source

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1 A Quick primer on synchrotron radiation: How would an MBA source change my x-ray beam Jonathan Lang Advanced Photon Source

2 APS Upgrade - MBA Lattice ε ο = 3100 pm ε ο = 80 pm What is emi7ance? I don t need a small beam all the =me (the beam will fry my sample). Will need smaller mirrors? Not sure how it affects my beamline

3 Radiation from relativistic particles β 0 β APS β=v/c γ=e/m o c 2 Δφ = 1/γ As energy (E) of the par=cles increases (β 1) radia=on becomes highly compressed parallel to velocity direc=on (1/γ) APS: β= % 1/γ= 0.51 MeV/ 7 GeV = ~73µrad Slide courtesy of D. Mills 3

4 Synchrotron Radiation Sources Two different sources of radia=on at 3rd genera=on sources: n bending magnets (BMs) n inser=on devices (IDs); periodic arrays of magnets inserted between the BMs (wigglers or undulators) Important parameters are: n Spectral distribu=on n Flux (number of x- rays/sec - 0.1%bw) n Brightness (flux/source size- source divergence) n Polariza=on (linear, circular) Slide courtesy of D. Mills

5 Bending Magnet Sources Bend Magnet Radia,on Critical Energy n Spectrum characterized by the cri=cal energy: E c = 3hcγ 3 /4πr. ~19.5 APS n Flux ~10 13 photons/sec/0.1% BW /mrad ε c ε n Ver=cal opening angle E c. APS: 1/γ = 73 x 10-6 radians n Horizontal opening angle determined by apertures APS: 6 mrad max n In the plane of the orbit, the polariza=on is linear and parallel to the orbital plane. The off- axis beam is ellip=cally polarized. Slide courtesy of D. Mills

6 Insertion Devices Inser=on devices (IDs) are periodic magne=c arrays with alterna=ng field direc=ons that force the par=cles to oscillate as they pass through the device. Characterized by Deflec=on Parameter K : K = eb o λ ID /2πm o c = λ ID [cm] B o [kg] where λ ID is the period and B o the peak magne=c field. Wigglers K>>1; Undulators K~1 The maximum deflec=on angle θ max, & amplitude x max : θ max = ±(K/γ), x max = (K/ γ)(λ ID /2π) λ ID Undulator A: λ ID =3.3 cm and K 1:! θ max 1/ γ and x max 0.38 microns.! Slide courtesy of D. Mills

7 Wiggler Radiation Sources Wiggler Radia,on n Like BM radia=on where each pole is a source n spectrum characterized by the cri=cal energy (different than BM cri=cal energy) n flux ~10 14 to photons/ sec/0.1% BW/mrad (10-100x Bend magnet) Critical Energy n Opening angle Ver=cal 1/γ APS ~73µrad Horizontal K/γ (~3-10) x ~73µrad n No wigglers at the APS. Wigglers with fields in both the x and y direc=ons) produce ellip=cally polarized radia=on. These are some=mes called ellip=cal mul=pole wigglers (EMWs). ε c ε Slide courtesy of D. Mills

8 Wiggler Radiation Sources X- ray Beam has lots of power!! 1-10 kw Makes designing op=cs (monochromators, mirrors) a challenge White beam from wiggler incident on Gate Valve for ~2-10 NSLS

9 Undulator Radiation Undulator radia=on is the coherent super- posi=on of radia=on from each pole of the undulator. Interference from different parts of the par=cle's trajectory in the undulator causes the radia=on to be squeezed into discrete spectral lines and into a narrower emission angle. Construc=ve interference occurs at wavelengths given by: λ n x- ray = ( λ ID /2γ 2 n)(1 + K 2 /2 + γ 2 θ 2 ), where n is the harmonic number. Adjust K (field, gap) to move harmonic (tuning curves). Total Power Distribu=on All Energies Horizontal size Power Distribu=on at E= 2.5* 1 st Harmonic Slide courtesy of D. Mills Power Distribu=on in 1 st Harmonic Horizontal size

10 Undulator Energy Spread and Angular Distribution The energy spread of the interference peak (central cone) is given by: ΔE/E = Δλ/λ 1/nN (like a grating!).!! For a given K-value (gap), the wavelength at angle θ is λ 1 = ( λ ID /2γ 2 )(1 + K 2 /2 + γ 2 θ 12 ) The central cone opening angle, θ,! is given by: θ/ 2 = (λ x- ray /2L) 1/2! Slide courtesy of D. Mills

11 Undulator Radiation Patterns and Spectra Undulator Radia,on! n undulators defined as IDs with horizontal deflec=on angle 1/γ, i.e., K 1 n spectrum peaked at x- ray specific x- ray energies, but peaks are tunable by varying K (K = 0.94 B[T] λ ID [cm]) n at the peaks (harmonics) the horizontal and ver=cal opening angles of the radia=on is given by: (λ x- ray / 2L) 1/2 [ ~ few microradians] n to get the true opening angle, need to consider the opening angle of the emi}ng par=cles Slide courtesy of D. Mills

12 Emittance & Brightness n Synchrotron radia=on is emi7ed from an packet of electrons with some finite size and divergence distribu=on. n The product of the par=cle beam size and divergence is propor=onal to the emi7ance (units are length x angle). Y X Z The emi7ance is a constant of the storage ring (phase space is preserved). Rela=on between source size and divergence given by the beta func=ons. σ x,y = ε x,y β x,y σ ' x,y = ε x,y βx,y Slide courtesy of D. Mills

13 Emittance & Brightness Total source size and divergence (Σ) is a convolution of the radiation and particle beam distribution Σ x,y = σ 2 2 r +σ x,y Σ x',y' = σ 2 2 r' +σ x',y' σ r = 1 2π 2λL U σ r' = λ 2L U APS Undulator A: L=2.4m - 1Å σ r = 1.7 µm & σ r = 4.5 µrad For most energies par=cle source divergence dominates

14 Source Divergence vs. Energy Σ x,y = σ 2 2 σ r +σ r = 1 x,y 2π 2λL U Σ x',y' = σ 2 2 r' +σ x',y' σ r' = λ 2L U Radia=on contribu=on negligible to source size Radia=on contributes significantly to divergence at lower energies (coherence)

15 Emittance & Brightness Brightness is the flux normalized to the source size and divergence B = Flux 4π 2 Σ x Σ x' Σ y Σ y' Brightness parameter determines ability to focus and coherence of the beam

16 Source Comparison APS Now vs. MBA APS Now MBA 1 mm σ x = 276 µm σ x = 12.7 µrad σ y = 10.0 µm, σ y = 3.5 µrad 1 mm σ x = 7.4 µm σ y = 10.9 µm, σ x = 5.7 µrad σ y = 3.8 µrad Slide courtesy of L. Assoufid 16

17 X-ray Beam 30m 8 kev APS Now MBA Σ x = 471 µm (1105 µm FWHM) Σ y = 200 µm ( 472 µm FWHM) Σ x = 231 µm (543 µm FWHM) Σ y = 210 µm (495 µm FWHM) X- ray beam size in the ver=cal plane will be similar to current APS X- ray beam in horizontal will be ~x2 smaller, but much more coherent.

18 Focusing of beam MBA la}ce provides modest gains in flux (2-3x) but drama=c improvements in focusing, because can take full beam in horizontal plane

19 Coherence & Diffraction Limit Coherence describes the degree that the phase of the wave is correlated at two points. Transverse depends on source; Longitudinal depends on monochromator. As D s gets smaller D i gets smaller un=l D s Θ s ~ λ/2 At this point the source is said to be diffrac=on limited

20 Diffraction Limited Source Size and Divergence n The effec=ve phase space of the radia=on source (Σ i and Σ i ) has contribu=ons from size and divergence of the par=cle beam genera=ng the radia=on and the intrinsic source size and divergence of the radia=on itself. Is there are limit to how small the effec,ve phase space area (i.e., emi?ance) can be? Yes, you are s=ll bound by the Heisenberg Uncertainty Principle. Recall: ΔxΔp x /2 p x = Θ x or Δp x = ΔΘ x and p z = k = (2π /λ) p z p z so : ΔxΔp x = ΔxΔΘ x p z = ΔxΔΘ x [ (2π /λ)] /2 ΔxΔΘ x λ /4π n This is the so- called diffrac=on limit. For central cone of the undulator: σ r ' or (ΔΘ) = [λ/2l] and so σ r or (Δx) = [λl/8π 2 ] Slide courtesy of D. Mills

21 Partial Coherent Sources Diffrac=on Limit - > Partial Coherent Sources λ 4π For$$1Å$(12$keV)$xFrays$$#$8$picometers$ $radian$$for$fully$coherent$beam$.$! APS$operates$with:$ ε H =$3$x$10 F9 $mfrad$$or$3000$picometerfradian$ $ ε V =$0.025$x$10 F9 $mfrad$or$25$picometerfradian$$! Hence$the$APS$is$a$parBally$coherent$source$at$1$Å.$$! ParBally$coherent$sources$are$someBmes$characterized$by$the$coherent$fracBon.$ Coherent$fracBon$=$raBo$of$diffracBonFlimited$emiGance$to$total$emiGance,$ or$the$the$fracbon$of$the$xfray$flux$that$is$coherent.$$$ $! For$the$APS$at$1Å,$the$coherent$fracBon$is$ $10 F3.$! So$there$is$a$general$trend$to$try$to$reduce$the$parBcle$beam$emiGance$$to$increase$ coherence.$ Slide courtesy of D. Mills The$Advanced$Photon$Source$is$an$Office$of$Science$User$Facility$operated$for$the$U.S.$Department$of$Energy$Office$of$Science$by$Argonne$NaBonal$Laboratory$

22 Coherent fraction of beam: MBA vs. APS Now ξ = ( λ 4π ) 2 = B ( λ Σ x Σ x' Σ y Σ 2 ) 2 y' coh = λr d The basic emi7ance assumed is 73 pm for x and 7 pm for y (a 10% ra=o) Calcula=on performed for a typical se}ng of emi7ance ra=o. At 10 kev & 30 m from source: l oh (1Å) APS now: vert. ~100 µm horz. ~5 µm MBA: vert. ~100 µm horz. ~100µm 22

23 Bending Magnet Performance A critical energy of 17 kev matches or beats present performance over a wide range of photon energies 23 M. Borland et al., Preliminary Expected Performance of an APS MBA Lattice, September 9,

24 Bending Magnets Opening Angle of the Bending Magnet Radia=on will remain about the same