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

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

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

Radiation from relativistic particles β 0 β 1 @ 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= 99.999999% 1/γ= 0.51 MeV/ 7 GeV = ~73µrad Slide courtesy of D. Mills 3

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

Bending Magnet Sources Bend Magnet Radia,on Critical Energy n Spectrum characterized by the cri=cal energy: E c = 3hcγ 3 /4πr. ~19.5 kev @ APS n Flux ~10 13 photons/sec/0.1% BW /mrad ε c ε n Ver=cal opening angle 1/γ @ 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

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 = 0.0934 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

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 10 15 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

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 minutes @ NSLS

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

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

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

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

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

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)

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

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

X-ray Beam Size @ 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.

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

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

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

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$

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

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, 2013 14

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