Synchrotron Radiation: Properties and Production
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BC0-&""5'FGHH''':4559' Discovery of x-rays ~100 years ago
! X-rays were discovered (accidentally) in 1895 by Wilhelm Konrad Roentgen.
! Roentgen won the first Nobel Prize in 1901 “for the discovery with which his name is linked for all time: the... so-called Roentgen rays, as he himself called them, X-rays…”
”X-ray Cream Furniture Polish - Guaranteed since 1891” Umm… x-rays weren't discovered until 1895!"
BC0-&""5'FGHH''':4559' Synchrotron Radiation
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BC0-&""5'FGHH''':4559' Discovery of Synchrotron Radiation - ~50 years ago 0=#-&2"%2"#'2$+4$?"#'R0PS'L$9'@29%'">9.2,.+' R$--4+.#%$55=S'62"O'$'TG':.U'9=#-&2"%2"#'HVWT;'
On April 24,[1947] Langmuir and I [Herbert Pollack] were running the machine and as usual were trying to push the electron gun and its associated pulse transformer to the limit. Some intermittent sparking had occurred and we asked the technician to observe with a mirror around the protective concrete wall. He immediately signaled to turn off the synchrotron as "he saw an arc in the tube." The vacuum was still excellent, so Langmuir and I came to the end of the wall and observed. At first we thought it might be due to Cherenkov radiation, but it soon became clearer that we were seeing Ivanenko and Pomeranchuk [i.e., synchrotron] radiation.
Excerpted from Handbook on Synchrotron Radiation, Volume 1a, Ernst-Eckhard Koch, Ed., North Holland, 1983.
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BC0-&""5'FGHH''':4559' From Synchrotrons to Storage Rings
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( ![Å] = 12.4 / E[keV] )
Square brackets indicate the units to be used in the calculation. BC0-&""5'FGHH''':4559' Evolution of Synchrotron Radiation Sources
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BC0-&""5'FGHH''':4559' APS Linear Accelerator and Booster
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BC0-&""5'FGHH''':4559' Radiation from Moving Charges :$_L.55`9'Ne1$?"#9'
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&' BC0-&""5'FGHH''':4559' Radiation Patterns From Accelerating Charges
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BC0-&""5'FGHH''':4559' Radiation Patterns When v Approaches c
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BC0-&""5'FGHH''':4559' Radiation Sources at 3rd Generation Facilities There are two different sources of radiation at 3rd generation sources: ! bending magnets (BMs)
! insertion devices (IDsSn'periodic arrays of magnets inserted between the BMs (wigglers or undulators)
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BC0-&""5'FGHH''':4559' Radiation Sources at 3rd Generation Facilities There are two different sources of radiation at 3rd generation sources: ! bending magnets (BMs)
! insertion devices (IDsSn'periodic arrays of magnets inserted between the BMs (wigglers or undulators)
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BC0-&""5'FGHH''':4559' Planar Insertion Devices
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BC0-&""5'FGHH''':4559' Characterizing Insertion Devices
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BC0-&""5'FGHH''':4559' Wigglers and Undulators
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BC0-&""5'FGHH''':4559' Wiggler Radiation Sources
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BC0-&""5'FGHH''':4559' Undulator Radiation
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'r''c&.'<.24"+'"6'%&.'N'$#+'h'@.5+'$2.'("2.#%Q'-"#%2$-%.+'9"'%&$%7''!.D62$O.'k'!a8's'% Rb;b'-O'%"'F;b' ÉOS $#+'9"'%&.'.5.-%2"#'"9-455$%.9'R$#+'&.#-.'2$+4$%.9S'L4%&'%&$%'9$O.'<.24"+'+24,.#'>='%&.' N:'@.5+9;' ' O4 V0JJ8)2"D-+WR"'h$-M'4#'%&.'5$>'62$O.7' &r''81.'%"'%&.'6$-%'%&$%'%&.'.5.-%2"#'49'%2$,.54#)'%"L$2+9'19K'%&.'2$+4$?"#'.O4E.+'>='%&.' .5.-%2"#'49'8"<<5.2'9&4Ñ.+'%"'&4)&.2'62.e1.#-4.9'R9&"2%.2'L$,.5.#)%&9S;''c&.'2.5$?,49?-' 8"<<5.2'9&4Ñ')".9'$9'ÖHD#'s'ÖHÄ#') 1/2% K'$#+'9"'%&.'L$,.5.#)%&'">9.2,.+'4#'%&.'5$>'497' ' F !ID = 3.3cm T4 "?0L<+'&;0'R"" """!5$>')'R !a8s%SR1/2%) = R !a8sF% S' & " !14000(APS) "8 !x"ray (cm) #0.8x10 #0.08 nm
BC0-&""5'FGHH''':4559' Tuning the Peaks of Undulator Radiation d#D$_49'R$ kGSK'L.'-$#'L24%.7' _D2$= F F '!# 'k'R !a8sF% #SRH'Ä'z sFS' ' _D2$= !# 'K'-$#'>.'$+J19%.+'>='hK'4;.;'>=',$2=4#)'z'Rk'G;GVbW'!a8{-O|'h"{MZ|'S;' c&49'-$#'>.'$-&4.,.+'>=',$2=4#)'%&.'-122.#%'4#'%&.'L4#+4#)9'"6'.5.-%2"O$)#.?-'+.,4-.9'"2'>=',$2=4#)' %&.'9.<$2$?"#'>.%L..#'%&.'1<<.2'$#+'5"L.2'<"5.9'Rw%&.')$
/?C"N!Y"(L" O!X"(L" D08+$"3: BC0-&""5'FGHH''':4559' Undulator Energy Spread and Angular Distribution The energy spread of the interference peak (central cone) is given by:' ' ''''''''''''''''''''''*NsN'k'*$/$'m'Hs#B'''(like a grating!). F F 2 F For a given K-value (gap), the wavelength at angle $ is !H'k'R !a8sF% SRH'Ä'z sF'Ä'% $H S' ' ' The central cone opening angle, $HK for the odd harmonics is given by:! ! ' _D2$= HsF' $1/ F k'R$ sF(S BC0-&""5'FGHH''':4559' Undulator Radiation Patterns and Spectra C'$18&.02">&$+&;0'" 3D))"#JJ)'$+K"E4" ! 1#+15$%"29'+.@#.+'$9'a89'L4%&'&"24Q"#%$5'+.u.-?"#' $#)5.'m'Hs%'K'4;.;K''z'mH' ! 9<.-%21O'<.$M.+'$%'_D2$='9<.-4@-'_D2$='.#.2)4.9K' >1%'<.$M9'$2.'%1#$>5.'>=',$2=4#)'z'''Rz'k'G;VW'h{c| !a8{-O|S'' ! $%'%&.'<.$M9'R&$2O"#4-9S'%&.'&"24Q"#%$5'$#+',.2?-$5' "<.#4#)'$#)5.9'"6'%&.'2$+4$?"#'49')4,.#'>=7' HsF'' ' R!_D2$='s'F(S {%=<4-$55='$'6.L'O4-2"2$+4$#9| ! %"').%'%&.'%21.'"<.#4#)'$#)5.K'#..+'%"'-"#94+.2'%&.' "<.#4#)'$#)5.'"6'%&.'.O4o#)'<$2?-5.9' ! I4)&5='54#.$25='<"5$24Q.+'"#'&$2O"#4-;''X$#'19.' 9<.-4$54Q.+'+.,4-.9'%"'-"#%2"5'<"5$24Q$?"#' BC0-&""5'FGHH''':4559' Electromagnetic Helical Undulator (4-ID-C) 3155'<"5$24Q$?"#'-"#%2"5'62"O' 9"12-.' X42-15$2'9L4%-&4#)'2$%.' '''fHGG'O9'RG;\'IQS'R'fFGG'*S' (4#.$2'9L4%-&4#)'2$%.' '''fbG'9'R'fHFGG'*'S' :$)#.?-'34.5+'$5"#)'+.,4-.' _' N5.-%2"DO$)#.%9'19.+'%"'O$M.'.5.-%2"#')"'4#'$'&.54-$5'"2>4%;''c&49'<2"+1-.9' -42-15$25='<"5$24Q.+'_D2$=9'R)""+'6"2'O$)#.?9O'._<.24O.#%9S;' #$%&'()$"@-0.0'"/012()"CJ,2&$)"3#@/AC4"J20])(." bW' Time Structure of the Radiation ! /$2?-5.9'$2.')2"1<.+'%").%&.2'>='%&.'$-?"#'"6'%&.'P3'-$,4?.9'4#%"'>1#-&.9'Rb\G' :IQS;''' *%'%&.'*/07' g #$%12$5'>1#-&'5.#)%&'R4;.;'4#'%&.'54O4%'"6'Q.2"'-122.#%S'b\'<9.-'3^I:' g %=<4-$55='$>"1%'HGG'<9.-'3^I:'' ! HHGW'O'-42-1O6.2.#-.'Rb;Y]'O4-2"9.-"#+'<.24"+n'fFTG'MIQS' g &$2O"#4-'#1O>.2'HFVY'4;.;'HFVY'.,.#5='9<$-.+'wP3'>1-M.%9x'$2"1#+'%&.'24#)' g O4#4O1O'9<$-4#)'49'F;]'#9.-' ! '8.%$459'"6'%&.'?O.'9%21-%12.'+.<.#+9'"#'%&.'@55'<$E.2#K'4;.;'L&4-&'>1-M.%9'&$,.' .5.-%2"#9'4#'%&.O;' ! BC0-&""5'FGHH''':4559' Typical APS Filling Patterns ! bFW'.e1$55='9<$-.+'>1#-&.9' D'$<<2"_4O$%.5='HH'#9.-'>.%L..#'>1#-&.9' D$<<2"_4O$%.9'$'-"#?#1"19'9"12-.'' ! FW'.e1$55='9<$-.+'>1#-&.9' D'$<<2"_4O$%.5='H\W'#9.-'>.%L..#'>1#-&.9' D-"O<2"O49.'>.%L..#'-"#?#1"19'9"12-.'$#+'<159.+'9"12-.' ! H'Ä'T_]'R&=>24+'O"+.S'' D'$'94#)5.'>1#-&'6"55"L.+'>=']')2"1<9'"6'T'>1#-&.9' D'?O4#)'._<.24O.#%9' 0-&.O$?-'"6'*/0' &=>24+'O"+.'' BC0-&""5'FGHH''':4559' Pump-probe Chemistry FC Storage Ring ES1 h! GS ES Laser 2 Pump Pulse Laser pulse pump X-ray pulse probe Intrinsic time resolution: X-ray Probe 30 – 100 ps fwhm Pulse Excited State Time Transverse Properties of Particle Beams ! A<'1#?5'#"LK'L.'&$,.'-$5-15$%.+'%&.'2$+4$?"#'<2"<.2?.9'62"O'$'94#)5.'.5.-%2"#K' &"L.,.2'4#'$'9%"2$).'24#)K'%&.'2$+4$?"#'49'.O4E.+'62"O'$#'.#9.O>5.'"6'.5.-%2"#9' L4%&'9"O.'@#4%.'94Q.'$#+'+4,.2).#-.'+49%24>1?"#;'' ! h"%&'%&.'%2$#9,.29.'$#+'5"#)4%1+4#$5'<2"<.2?.9'"6'%&.'<$2?-5.'>.$O'4#'$'9%"2$).' 24#)'$2.'%&.'.e1454>241O'<2"<.2?.9'"6'%&.'<$2?-5.'>.$OK'>1%'&.2.'L.'$2.' 4#%.2.9%.+'4#'%&.'!"#$%&'"%''<2"<.2?.9;' ! c&.'<2"+1-%'"6'%&.'<$2?-5.'>.$O'94Q.'$#+'+4,.2).#-.'49'<2"<"2?"#$5'%"'$' <$2$O.%.2'"6'%&.'>.$O'-$55.+'%&.'.O4E$#-.'R1#4%9'$2.'5.#)%&'_'$#)5.S;'R0..' *<<.#+4_'YS '! The emittance is a constant of the storage [' ring, although one can trade off beam size for divergence as long as the (something proportional to the product) remains constant. C' Ü' BC0-&""5'FGHH''':4559' Transverse Properties and Photon Beam Brightness G-9"$0"5)"'))$".0"7'05"&<01.".-)".2&'D%)2D)"J&2;(8)"<)&L"J20J)2;)D^' ' *5%&"1)&'%&.'u1_'62"O'h:'$#+'a8'9"12-.9'-$#'>.'+.%.2O4#.+'L4%&"1%'+.%$45.+' M#"L5.+).'"6'%&.'9"12-.'94Q.'$#+'+4,.2).#-.K'"#.',.2='4O<"2%$#%'-&$2$-%.249?-'"6'%&.' >.$OK'#$O.5="<2+,-.')DD['2.e142.9'$'O"2.'4#6"2O$?"#'"#'%&.'<$2?-5.'>.$O`9'94Q.'$#+' +4,.2).#-.;' 'h24)&%#.99'&$9'1#4%9'"67'''' ' <&"%"#9s9.-sG;Ht'h^s9"12-.'$2.$s9"12-.'9"54+'$#)5.' ' 2 Flux/4' +h +v +&`'+,`" " ' %& L&.2.'+4'R+4`S'49'%&.'.y.-?,.'"#.'94)O$',$51.'"6'%&.'9"12-.'94Q.'R+4,.2).#-.S'4#'%&.'4 ' +42.-?"#;''c&.'.y.-?,.'9"12-.'94Q.'$#+'+4,.2).#-.'&$9'-"#%24>1?"#9'62"O'>"%&'%&.' <$2?-5.'>.$O'$#+'%&.'2$+4$?"#'4%9.56;'' BC0-&""5'FGHH''':4559' Stuff a Storage Ring Source can’t do " G-&."J&2&L).)2D"5018$"1D)2D"8+7)".0"D))"_)'-&'()$`^" g a#-2.$9.+'>24)&%#.99'R4;.;K'5$2).2'-"&.2.#%'62$-?"#'k'3-"&.2.#%'s'3%"%$5S' g 0&"2%.2'<159.9'R62"O'HGG'<9'%"'HGG'69.-S' " G)"&2)"&<01."&.".-)"8+L+.D"0="5-&."D.02&,)"2+',D"(&'"$0R g /$2?-5.'>.$O'.O4E$#-.'R9"12-.'94Q.'_'+4,.2).#-.S7' r I"24Q"#%$5'.O4E$#-.7' 'b'_'HGDV'OD2$+9' r *,.2$).'>24)&%#.997' 'HGHVDHGFG'_D2$=9s9.-DG;Ht'>LDOOFDO2$+F' – Particle beam longitudinal properties: r h1#-&'5.#)%&7 ' 'FG'OO'RTG'<9.-S'' " _C8;L&.)"/.02&,)">+',D"&'$"I')2,9">)(0%)29"*+'&(D"-&%)".-)"J0.)';&8".0"$)8+%)2" 3')&24"=1889"DJ&;&889"(0-)2)'."<)&LD"<1."+="5)"5&'."=)L.0D)(0'$"J18D)D"&'$"=188" (0-)2)'()["1D)".-)"805")L+\&'()"&'$"D-02."J18D)D".-&."(&'"<)",)')2&.)$"<9"8+')&2" &(()8)2&.02D!" BC0-&""5'FGHH''':4559' X-ray Free Electron Lasers (X-FELs) " (4#$-D>$9.+'_D2$='62..'.5.-%2"#'5$9.29'RC3N(9S' 9&"15+'<2",4+.'O$#='"6'%&.'+.942.+' 4O<2",.O.#%9;" g 3155'-"&.2.#-.q' g 3.O%"9.-"#+'<159.'5.#)%&9q' " *#"KA2&9"aI*'19.9'%&.'&4)&'>24)&%#.99'"6'$#' )8)(.20'",1'"-"1<5.+'%"'$#'.O4E$#-.D<2.9.2,4#)' 54#$-;' " c&.')$4#'4#'%&.'5$9.2'49'">%$4#.+'%&2"1)&'$'<2"-.99' -$55.+'/)8=A#LJ8+b)$"/J0'.&')01D"IL+DD+0''-&'' /#/I. BC0-&""5'FGHH''':4559' Self-Amplified Spontaneous Emission The LCLS produces extraordinarily bright N!S!N!S!N!S!N!S!N!S!N!S!N!S!N!S!N!S!N!S!N!S!N!S!N!S!N!S!N!S!N!S!N!S!N!S!N!S!N!S!N!S!N!S!N!S!N!S!N!S! pulses of synchrotron radiation in a process called “self-amplified spontaneous emission” Undulator (SASE). In this process, an intense and highly Magnet collimated electron beam travels through an Electron undulator magnet. The alternating north and S!N!S!N!S!N!S!N!S!N!S!N!S!N!S!N!S!N!S!N!S!N!S!N!S!N!S!N!S!N!S!N!S!N!S!N!S!N!S!N!S!N!S!N!S!N!S!N!S!N! south poles of the magnet force the electron Bunch beam to travel on an approximately sinusoidal trajectory, emitting synchrotron radiation as it goes. c0-'"d&8&9$&["*?*/" BC0-&""5'FGHH''':4559' Self-Amplified Spontaneous Emission N!S!N!S!N!S!N!S!N!S!N!S!N!S!N!S!N!S!N!S!N!S!N!S!N!S!N!S!N!S!N!S!N!S!N!S!N!S!N!S!N!S!N!S!N!S!N!S!N!S! Undulator Magnet Electron S!N!S!N!S!N!S!N!S!N!S!N!S!N!S!N!S!N!S!N!S!N!S!N!S!N!S!N!S!N!S!N!S!N!S!N!S!N!S!N!S!N!S!N!S!N!S!N!S!N! Bunch The electron beam and its synchrotron N!S!N!S!N!S!N!S!N!S!N!S!N!S!N!S!N!S!N!S!N!S!N!S!N!S!N!S!N!S!N!S!N!S!N!S!N!S!N!S!N!S!N!S!N!S!N!S!N!S! radiation are so intense that the electron motion is modified by the electric and magnetic fields of its own emitted synchrotron light. Under the influence of both the undulator magnet and its own S!N!S!N!S!N!S!N!S!N!S!N!S!N!S!N!S!N!S!N!S!N!S!N!S!N!S!N!S!N!S!N!S!N!S!N!S!N!S!N!S!N!S!N!S!N!S!N!S!N! synchrotron radiation, the electron beam is forced to form micro-bunches, separated by a distance equal to the wavelength of the emitted radiation. c0-'"d&8&9$&["*?*/" BC0-&""5'FGHH''':4559' Self-Amplified Spontaneous Emission N!S!N!S!N!S!N!S!N!S!N!S!N!S!N!S!N!S!N!S!N!S!N!S!N!S!N!S!N!S!N!S!N!S!N!S!N!S!N!S!N!S!N!S!N!S!N!S!N!S! Undulator Magnet Electron S!N!S!N!S!N!S!N!S!N!S!N!S!N!S!N!S!N!S!N!S!N!S!N!S!N!S!N!S!N!S!N!S!N!S!N!S!N!S!N!S!N!S!N!S!N!S!N!S!N! Bunch N!S!N!S!N!S!N!S!N!S!N!S!N!S!N!S!N!S!N!S!N!S!N!S!N!S!N!S!N!S!N!S!N!S!N!S!N!S!N!S!N!S!N!S!N!S!N!S!N!S! S!N!S!N!S!N!S!N!S!N!S!N!S!N!S!N!S!N!S!N!S!N!S!N!S!N!S!N!S!N!S!N!S!N!S!N!S!N!S!N!S!N!S!N!S!N!S!N!S!N! N!S!N!S!N!S!N!S!N!S!N!S!N!S!N!S!N!S!N!S!N!S!N!S!N!S!N!S!N!S!N!S!N!S!N!S!N!S!N!S!N!S!N!S!N!S!N!S!N!S! These micro-bunches begin to radiate as if they were single particles with immense charge. The process reaches saturation when The micro-bunching process has gone as Coherent far as it can go. S!N!S!N!S!N!S!N!S!N!S!N!S!N!S!N!S!N!S!N!S!N!S!N!S!N!S!N!S!N!S!N!S!N!S!N!S!N!S!N!S!N!S!N!S!N!S!N!S!N! Synchrotron Radiation c0-'"d&8&9$&["*?*/" BC0-&""5'FGHH''':4559' Free Electron Lasers (FELs) 0%$2%D1<'9%$).' External signal or spontaneous radiation interacts with the e-beam resonantly at undulator !& & Energy modulation # density modulation (microbunching) # coherent radiation at ! # ._<"#.#?$5')2"L%&'R(ZS' Start-up Undulator Hall at the Linac Coherent Light Source (LCLS) at SLAC BC0-&""5'FGHH''':4559' Spectral Properties for X-ray Free Electron Lasers BC0-&""5'FGHH''':4559' Linac Coherent Light Source at SLAC X-FEL based on last 1-km of existing 3-km linac 'The future looks bright…… 1.5-15 Å (14-4.3 GeV) Existing 1/3 Linac (1 km) (with modifications) Injector (35º) at 2-km ' New e- Transfer Line (340 m) X-ray Transport Undulator (130 m) Line (200 m) Near Experiment Hall UCLA Far Experiment BC0-&""5'FGHH''':4559' Hall Advanced Photon Source Upgrade ! */0'-122.#%5='&$9'$'<2"<"9$5'%"'+"'$'O$J"2'1<)2$+.'"6'%&.'6$-454%='",.2'%&.'#._%'\DT'=.$29;'' ! N9?O$%.+'-"9%''49'fáb\G:K'$#+'L455'>24#)'%&.'6$-454%='%"'%&.'9%$%.D"6'%&.D$2%'6"2'$'b2+').#.2$?"#' 9%"2$).'24#)'9"12-.;' ! h..#'$<<2",.+'>='8dN;''X122.#%5='4#'%&.'+.94)#'<&$9.' ! 3429%'1<)2$+.9'L455'9%$2%'4#'%&.'3$55'"6'FGHb' • B.L'$#+'1<)2$+.+'>.$O54#.9' • a#-2.$9.'-122.#%'%"'H\G'O*;' ' • 8.54,.2'HGG'?O.9'>.E.2'%.O<"2$5'2.9"51?"#K'+"L#'%"'H'<4-"9.-"#+;' ' BC0-&""5'FGHH''':4559' APS-U Project Baseline Scope 10 Renovated Front Ends 11 New Front Ends 4 Long Straight Sections 5 Planar Undulators 2 Polarized Undulators 6 Revolver Undulators 3 Superconducting Undulators SPX SRF Cavities and Cryostats 6 New Beamlines 8 Beamline Upgrades *+, $#- .+' /&" %"#' 0"1 2-.' A<) 2$+ .' R*/ 0DAS' <2"J .-%' Appendix 0: Radiated Power from Charges at Relativistic Velocities The classical formula for the radiated power from an accelerated electron is: 2e2 2 P = 3 a 3c Where P is the power and , the acceleration. For a circular orbit of radius r, in the non-relativistic case, , is just the centripetal acceleration, v2/r. In the relativistic case: ! 1 dp 1 d#m v dv v 2 a = = # o = # 2 = # 2 m d" m dt dt r o o 2 2 Where - = t/% = proper time, % = 1/√1-# = E/moc and # = v/c ! 2 4 4 2 4 2e " v 2ce E Boxes with lines P = 3 2 = 2 4 8 like this indicate an 3c r 3r mo c important equation.! BC0-&""5'FGHH''':4559' ! Appendix 0: Dependence on Mass and Energy of Radiated Power 2e2 " 4v 4 2ce2 E 4 P = 3 2 = 2 4 8 3c r 3r mo c c&.2.'$2.'%L"'<"4#%9'$>"1%'%&49'.e1$?"#'6"2'%"%$5'2$+4$%.+'<"L.27' ' ! 'H;''0-$5.9'4#,.29.5='L4%&'%&.'O$99'"6'%&.'<$2?-5.'%"'%&.'W%&'<"L.2'R<2"%"#9'2$+4$%.' -"#94+.2$>5='5.99'%&$#'$#'.D'L4%&'%&.'9$O.'%"%$5'.#.2)=K'N;S' ' 'F;''0-$5.9'L4%&'%&.'W%&'<"L.2'"6'%&.'<$2?-5.`9'.#.2)=''R$'T'Z.U'9%"2$).'24#)'2$+4$%.9'FWGG' ?O.9'O"2.'<"L.2'%&$#'$'H'Z.U'24#)'L4%&'%&.'9$O.'2$+419S' BC0-&""5'FGHH''':4559' Appendix 0: Radiation Patterns When V << C ^&.#','ll'-K'R# m GSK'%&.'9&$<.'"6'%&.' 2$+4$?"#'<$E.2#'49'$'-5$994-$5'+4<"5.'<$E.2#;' ' P.-$55'%&$%'9<.-4$5'2.5$?,4%='9$=9'%&$%'$#)5.9' %2$#96"2O'$97' ' ' ' ' ' sin" ' tan"lab = At the APS with E = 7 GeV, ! ' ' #(cos" + $) 2 ! = E/moc = 7 GeV/0.511 MeV! *#+'9"'$9'="1'-2$#M'1<'#K'%&.'2$+4$?"#' <$E.2#'>.)4#9'%"'+.6"2O'R4#'%&.'5$>'62$O.S;' ! = 1.4 x 104! -6 1/! = 73 x 10 ! ! BC0-&""5'FGHH''':4559' Appendix 1: BM Spectral Distribution c&.'9<.-%2$5s$#)15$2'+49%24>1?"#'"6'Å9=#-&2"%2"#'2$+4$?"#Å'L$9'L"2M.+'"1%'>='!;'0-&L4#).2'4#'HVWV;' 0-&L4#).2'6"1#+'%&.'9<.-%2$5'+49%24>1?"#'62"O'$#'$--.5.2$?#)'<$2?-5.K'1#+.2'%&.'4#u1.#-.'"6'$' -"#9%$#%'O$)#.?-'@.5+K'L$9'$'9O""%&5=',$2=4#)'61#-?"#'"6'<&"%"#'.#.2)='$#+'%&$%'%&.'9<.-%21O' -"15+'>.'<$2$O.%.24Q.+'>='$'-24?-$5'.#.2)=K'N-;' '''''''''''' b '''''''N-'k'b&-% sW'2;' ' I.2.'&'49'/5$#-M`9'-"#9%$#%'$#+'. /0 %&.'2$+419'"6'-12,$%12.'"6'%&.'%2$J.-%"2=;''B"%.'%&$%'%&.'-24?-$5' .#.2)='9-$5.9'$9'%b;''In practical units, the critical energy can be written as:' ' ' N {M.U|'k'F;FH]'Nb{Z.U|s'.{O|'k'G;GYY\H'h{MZ|'NF{Z.U|! - ' At the APS the bending magnets have a field strength of 5.99 kilogauss and the ring operates at E = 7 GeV . The critical energy of the radiation emitted from the BM is:! ! 2 Ec[keV] = 0.06651 B[kG] E [GeV]! or! 2 Ec = 0.06651(5.990)(7 ) = 19.5 keV or 0.64 Å.( BC0-&""5'FGHH''':4559' Appendix 1: BM Angular Distribution and Flux ! The opening angle of the entire radiation field (i.e., the power) is approximately:' $x = $y ) 1/%,& where $x is the horizontal angle and $y is the vertical angle. ! The collimation in the horizontal direction is lost and what is observed is just the vertical opening angle. ! Flux from a bending magnet is usually quoted as flux per unit horizontal angle (integrated over the vertical angle). There are no "simple" closed- form solutions for the photon flux, F, as a function of wavelength from a bending magnet however there are numerous series approximations that can easily be evaluated with a calculator/computer. From a bending magnet (B = 5.99 kG) at the APS operating at E = 7GeV and I = 100 mA (at the critical energy, integrated over all vertical angles) we get:! $ QN $$$ BC0-&""5'FGHH''':4559' Appendix 2: Where did “K” come from? ! ! & 2$z ) Fx = max = "m0v˙x = ev # B = ecB0 sin( + Ne1$?"#'"6'O"?"#'6"2'$' ' %ID * 2.5$?,49?-'-&$2).+'<$2?-5.' & ) 4#'$'O$)#.?-'@.5+' ecB0 2$z v˙x = sin( + z = ct "m0 ' %ID * & ) & ) ecB0 %ID 2$ct eB0 %ID 2$ct vx = , cos( + = , cos( + "m0 2$c ' %ID * "m0 2$ ' %ID * 2 & ) - 0 & ) & ) eB0 - %ID 0 2$ct eB0 %ID 1 - %ID 0 2$z 1 - %ID 0 2$z x = / 2 sin( + = / 2 / 2 sin( + = K / 2 sin( + "m0c . 2$ 1 ' %ID * . m0 2$c1 " . 2$ 1 ' %ID * " . 2$ 1 ' %ID * - 0 1 - %ID 0 - dx0 K eB0 %ID xmax = K and = where K = / 2 ./ 2 12 ./ dz12 2 m c " $ max " . $ 0 1 ! BC0-&""5'FGHH''':4559' Appendix 3: Wiggler Radiation Spectral Distribution Spectral Distribution: Wiggler radiation is the incoherent superposition of radiation from each pole of the wiggler. As with the bending magnet, the spectral distribution of the emitted radiation from a wiggler is smoothly varying as a function of photon energy and is characterized using the critical energy as a parameter. ' The APS has built a wiggler with a magnetic field, Bo , of 10 kilogauss, a period of 8.5 cm, and a length of 2.4 meters (N=28).! ! K = 7.9, Ec = 32.6 keV, $max = 577 microradians, xmax = 8 microns! Wiggler Flux: The flux from a wiggler can calculated by multiplying the bending magnet equations by 2N where N is the number periods (and by using the appropriate critical energy!). The APS Wiggler (Bo =10 kG, $ID = 8.5 cm, L = 2.4 meters; N=28, has a flux (at the critical energy integrated over all vertical angles) of:! ! 14 dF/d%x = 4.8 x 10 photons/sec - 0.1 % BW - mrad %x !! BC0-&""5'FGHH''':4559' Appendix 4: Undulator Flux To determine the flux from an undulator, we integrate over both the vertical and horizontal angular distributions of the central cone and so the flux will have units of: ' x-rays/sec-0.1% bw.' As with bending magnets, there is not a closed form expression for the flux, but it can be approximated by: 11 Fn = 0.72 x 10 N Qn I[mA] ph/sec-0.1% bw where: Qn(K) ) 1 for K >1. For APS Undulator A (N = 72) with the storage ring running at 7 GeV and 100 milliamps, typical flux values for the first harmonic (n=1) are:! ! a"e"TAY"K"NFNE""J-fD)(AF!Ng"<5!" BC0-&""5'FGHH''':4559' Appendix 5: APS Electron Beam Parameters EV BC6$&9#'$U(1. &H =$N$P$QR $:E&"<$"#<$"$*-9%+(#/$2&")-$-=$A0&)*"+$0:(W"#*0$1-$ .-&(;-#1"+$0:(W"#*07$-=$RIVS$X$1.0&0=-&0$$ $ EV &V M$RIRHY$P$QR $:E&" 'H$M H\R$:(*&-#'! 'H' M QQ$:(*&-&"<("#'! 'V M V$:(*&-#'! 'V' M N$:(*&-&"<("#'$ BC0-&""5'FGHH''':4559' Appendix 5: Comparison of Radiation & Electron Beam Properties ! a6'Z$1994$#'+49%24>1?"#9'$2.'$991O.+'6"2' #@/"C'$18&.02"#"-&D"&"8)',.-"0="O!E"L).)2D!"" a02"Nh"2&$+&;0'".-)"'&.12&8"0J)'+',"&',8)"+DR" >"%&'%&.'<$2?-5.'>.$O'$#+'%&.'2$+4$?"#' " 4%9.56K'2.915%$#%'9"12-.'94Q.'$#+'+4,.2).#-.'49' 02' = "[!/2L]"e""E!Y"L+(202&$+&'D!" %&.'e1$+2$%12.'91O'"6'%&.'%L"'-"O<"#.#%9K' " #$O.5=7' Z-)"(022)DJ0'$+',"D012()"D+U)"0=".-)"2&$+&;0'" +DR" ' " 2 2 2 2 '+i = 1 [0r + 0i ] and +I' = 1 [0r' + 0i' ].! O 02"e"ij!*fk' l"e"N!X"L+(20'D!" ! " ! ^.'-$#'#"L'-$5-15$%.'%&.'>.$O'>24)&%#.99' ?0LJ&2)".-+D"5+.-".-)"%)2;(&8"D+U)"&'$" 94#-.' $+%)2,)'()"0=".-)"#@/"<)&LR" " 2 'V' = *(+,-"."#/,#$%( B = Flux/4' +H +V +I`'+U`" 'V =(0(+,-".$%( ! BC0-&""5'FGHH''':4559' Appendix 6: Phase Space of the Charged Particles ! *'O"#"D.#.2).?-K'-&$2).+'<$2?-5.K'1#+.2'%&.'$-?"#'"6'$'54#.$2'6"2-.'91-&'$9'49'6"1#+'4#'$' 9%"2$).'24#)K'%2$-.9'$'-"#%"12'4#'<&$9.'9<$-.'%&$%'49'$#'.554<9.;''' ! #' 0IKU(s) and 0IKU'(s) $2.'%&.'"#.D94)O$',$51.9'"6'%&.' %2$#9,.29.'<"94?"#'$#+'+4,.2).#-.K'2.9<.-?,.5=K'$%' [!$] 1/2 9"O.'<"94?"#K'9K'$2"1#+'%&.'9%"2$).'24#);' 2' = Arctan( 2 % /( $&" ) ) ! c&.'$2.$'"6'%&.'.554<9.'49'<2"<"2?"#$5'%"'$'<$2$O.%.2' # "6'%&.'>.$O'-$55.+'%&.'.O4E$#-.'R1#4%9'$2.'5.#)%&'_' [!"] 1/2 $#)5.S;' ! (4"1,455.9'c&."2.O'9%$%.9'%&$%'6"2'$'9=9%.O'91-&'$9' +.9-24>.+'&.2.K'%&.'<&$9.'9<$-.',"51O.'9&"15+' 2.O$4#'$'-"#9%$#%;'''a#'"%&.2'L"2+9'%&.'$2.$'"6'%&.' <&$9.'9<$-.'.554<9.'R.O4E$#-.S'49'-"#9%$#%'.,.#'46'%&.' 9&$<.'"6'%&.'.554<9.'-&$#).9'R<.24"+4-$55=S'$9'"#.')".9' a#'%&.'$>",.'+4$)2$OK ('49'%&.'.O4E$#-.'$#+',, #, ' $#+'%'+.9-24>.'%&.'9&$<.'"6'%&.'.554<9.'$%'$#=' $2"1#+'%&.'<$2?-5.`9'%2$J.-%"2=; <"4#%'4#'%&.'9%"2$).'24#);',, #, '$#+'%'$2.' 9"O.?O.9'-$55.+'%&.'cL499'<$2$O.%.29;' BC0-&""5'FGHH''':4559' Diffraction Limited Source Size and Divergence ! c&.'.y.-?,.'<&$9.'9<$-.'"6'%&.'2$+4$?"#'9"12-.'R+4'$#+'+4`S'&$9'-"#%24>1?"#9'62"O'94Q.'$#+' +4,.2).#-.'"6'%&.'<$2?-5.'>.$O').#.2$?#)'%&.'2$+4$?"#'$#+'%&.'4#%24#94-'9"12-.'94Q.'$#+'+4,.2).#-.' "6'%&.'2$+4$?"#'4%9.56;'BD".-)2)"&2)"8+L+.".0"-05"DL&88".-)")m)(;%)"J-&D)"DJ&()"&2)&"3+!)![")L+\&'()4" (&'"<)^''[.9K'="1'$2.'9?55'>"1#+'>='%&.'I.49.#>.2)'A#-.2%$4#%='/24#-4<5.;''P.-$557' "x"px # !/2 px "px = $x or = "$x and pz = !k = !(2% /&) pz pz so : "x"px = "x"$x pz = "x"$x[!(2% /&)] # !/2 "x"$x # & /4% !' c&49'49'%&.'9"D-$55.+'+4y2$-?"#'54O4%;'3"2'-.#%2$5'-"#.'"6'%&.'1#+15$%"27' ! 02' or (*2) = "[!/2L]'$#+'9"'' O 02'"2'R*x) k'Ö{!(s]' |' BC0-&""5'FGHH''':4559' Brightness vs. Photon Energy for Various SR Facilities ! c&.'&4)&'>24)&%#.99'>.$O9' $%'b2+').#.2$?"#'9"12-.9' R*(0'$#+'*/0K'6"2'._$O<5.S' 2.915%9'4#'$#'_D2$='>.$O'L4%&' <$2?$5'%2$#9,.29.'R"2'9<$?$5S' -"&.2.#-.;'' ! c&49'>.$O'<2"<.2%='-$#'>.' $#'4O<"2%$#%'<$2$O.%.2'4#' 9"O.'._<.24O.#%9'91-&'$9' <&"%"#'-"22.5$?"#' 9<.-%2"9-"<=K'_D2$=' &"5")2$<&=K'4O$)4#)K'.%-;' BC0-&""5'FGHH''':4559' The Linac Coherent Light Source (LCLS) at SLAC c&.'(X(0'19.9'%&.'5$9%'M45"O.%.2' "6'$#'._49?#)'b'MO'(aB*X'$%'%&.' 0%$#6"2+'(4#.$2'*--.5.2$%"2' c&.'CD2$='62..'.5.-%2"#'5$9.2'RC3N(S'2.54.9'"#' X.#%.2'R$%'0%$#6"2+'A#4,.294%=K' $'&4)&'.#.2)='54#.$2'$--.5.2$%"2'R(aB*XS'$#+' X*S #"%'"#'$'9=#-&2"%2"#s9%"2$).'24#);" BC0-&""5'FGHH''':4559'