Physics of X‐ray radiation production and transport. Simulating photons and waves from the X‐ray sources to the samples Manuel Sánchez del Río AAM, ISDD, ESRF
PhysicsofXrayradiationproductionandtransport.
SimulatingphotonsandwavesfromtheXraysourcestothe
samples
ManuelSnchezdelRo
AAM,ISDD, ESRF
Outline
Evolutionofxrayscience Sources: singleparticles(easy)andsetsofparticles(bunches,materials)
Optics: whyXrayopticsisdifferent?Concepts Calculations
Example:ID20(UPBL6) Nextgenerationofsimulationtools
Atthebeginning
Rntgen1895 Revolutionaryrays
Xraysareonly light(optics)
Butalsoparticles (photons)
I could have done it in a much more complicated way"said the red Queen, immensely proud.Lewis Carroll
What I cannot create, I do not understand.
I calculate everything myself.
If you cannot calculate Just simulate it! It may be a good starting point.
Light(EMradiation)emissionbymovinge
E0=20 keV
E0=31 keV
E0=40 keV
E0
E0=20 keV
E=19 keV
E=8 keV
e-
E0
2
6 120000.511e
E GeVm c MeV
= =
2 2 2 2 '2 2 20
1 1 0
( ) sin ( ) cot ( )n nn n
P d P P e v d J J
= =
= + = +
This formula is valid for all values of the velocity v.
In the non-relativistic limit, v
1912:Schottsformula
1944IvanenkoandPommeranchucktheorizedthatmaximumattainableenergyislimitedbytheradiationlosses
1946BlewettattheGeneralElectricLabsobservedtheshrinkingoftheelectronorbitatthehighestenergyof100MeVinamannerconsistentwiththepredictionsofthetheory.Theyfailedindetectingtheemittedradiationbecausetheysearcheditintheenergyrangeclosetothefirstharmonic,whereasthemaximumofthefrequencyspectrumliesintheregionclosetothecriticalenergy.
1947,April24th,Pollock,Langmuir,Elder,andGurewitsch sawthebluishwhitelightemergingfromthetransparenttubeoftheirnew70MeV synchrotronatGeneralElectric'sLaboratory:Synchrotronradiationhadbeenseen.
SRFormulation(1e)Ivanenko and Sokolov (1948) derived an asymptotic formula for the spectral distribution of the radiation intensity. The same result was also obtained by Schwinger (1949)
320
620
2 533
3( ) ( )2 m cE
m cW W K x dxE
=
2 22 2 3/ 2 2 2 3/ 20
2/3 1/32 3( , ) ( ) cos ( )6 3 3cedW K K dR
= +
3max 0
1 12 2c
=
Today, we can implement these functions in one line of code, e.g., Mathematica
BM EmissionbyNincoherent e
MonteCarlo(SHADOW) Energy(andpolarisation)sampledfromspectrum AngularDistribution(1e,x,z) Geometry(alongthearc,x,z) Limitation:Computertimeandmemory
Typically:103 109 rays Desirable:onerayperphoton,i.e.,10141020
xy
x x
xy
z
Real Space (top) Phase Space (H)
Wiggler:LikeBM,butabitmorecomplex
Undulator:1e emissioninterfereswithitself
=K
For a single energy (odd harmonic)
Codes
XOP:Urgent(Walker),US+WS(Dejus),Xwiggler,BM SRW(ChubarandElleaume) SPECTRA(TanakaandKitamura) SynchrSim(Grimm)
http://flash.desy.de/sites/site_vuvfel/content/e403/e1642/e2308/e2310/infoboxContent2357/TESLAFEL200805.pdf
Lighemittedbytightbunchedbeams
Thesecondterm,duetotherandompositionoftheelectrons,itisrandomlypositiveandnegative,itsaveragevalueiszero.
Thisisnottrueiftheelectronbunchlengthisshorterthanthewavelength,andthepowerisproportionaltothesquareofthestoredcurrent. ThisisthebasisoftheFreeElectronLaser(FEL).Inpractice,thespectralfluxobservedisproportionaltoanumberbetweenNandN2.
Inpracticalcases,thecoherentradiationisweakandhiddenbytheincoherentemission.Tomakeitdominate,averylongundulatorofseveraltensofmetersmustbeinstalledinaspecialbypasssectionofthering.Thisisquitedemandingfromanacceleratorpointofview.Itrequiresthehighestpeakcurrent,thesmallestemittance,thesmallestenergyspread,andverylongundulators.ThespectralrangeoftheemittedradiationislimitedtoVUVorsoftxrays.
CodeslikeGENESIS(http://pbpl.physics.ucla.edu/~reiche/)areusedtocalculateXFELemisison
22 *
1 1
N N N
i i i ji i i j
P E E E E= =
= = +
XOP(W,Mo,Rh,Booneetal.) MonteCarloparticletransport(MCNP,EGS,GEANT4,PENELOPE,)
Radiationscatteredfromopticalelements
E. Secco and M. Sanchez del Rio, SPIE Proc 8141, 81410Z (2011)
W. Salah and M. Sanchez del Rio JSR 18 (2011) 512
Plasmas 99%ofthevisiblematterintheUniverseisinformofplasma PlasmasemitXraysduetovariouseffects(thermal
radiation,acceleratedchargedparticles,transitionsinions,nuclearreactions)
OnEarthwefoundnaturalplasmas(e.g.,lightinginthunderstorms)
Artificialplasmas(electricdischarges[pinches],lasergeneratedplasmas)maybeusedasXraysource
Xraysareaveryusefuldiagnostictoolforartificialplasmas
ITER5s
NIF109 s
s
WMELTING POINT
T~20keV (200 million C). High densities, > 1020m-3, must be maintained to produce a sustainable reaction
XRAYPLASMADIAGNOSTICSATM.I.T.ALCATORCMODTOKAMAK
XRAYPLASMADIAGNOSTICSATM.I.T.ALCATORCMODTOKAMAK
21
195pixelsfor60m
348
7pixels17
2m
/pixel~25.13
cm
Ar16+
Crystal
[]
Courtesy: PPPL
CoherenceandIncoherence Ifthesourceisincoherent,weaddtheintensitiesoftheemissionofeache at
theobservationplane(typicallyinraytracing)(N)
Ifthesourceiscoherent(suchasapointmonochromaticsourceatinfinity=>Planewave)weaddEattheobservationplaneandsquareittogettheintensity=>Waveopticspropagation.E.g.,FresnelKirchhoffpropagatorinfreespace(N2)
Ifthesourceisincoherentbutsmall,thereisstillsomecoherenceobserved(vanCitterZernike)
Butonecannotseeasourcetoosmall,becausethereisalimit(diffractionlimit)
Moreover,fullycoherenceorfullyincoherencedonotexist=>partialcoherence
Thesourceiscomplicated,andthisisonlythebeginning.
PhotonMatterinteraction(beforeoptics)
For1e atEf0(q)=>Fh(E,q) Incoherentscattering(Compton)=>Shower Photoelectricscattering(absorption,fluorescence)
1n i = 2
;2
;
e Ar NK f KA
K fA
= =
=
0( , ) ( ) '( ) "( )f Q E f Q f E if E= + +
20
8 0.6652448 barn3T
r = =
222 1 cos( )
2ed r f d +=
2220 ' ' sin
2 '
KNCd r E E E
d E E E = +
'1 (1 cos )
EE
=+
Tabulations:DABAX,xraylib
Thesingleinterface(Fresnel)
Structures in depth => playing with the reflectivity
Structures along the surface =>playing with the direction
22 21
2
1 cos sin 2 2c cnn
= =
Multilayers
no reflection from the back of the substrate
compute recurrently the reflectivity of each layer from bottom (substrate) to top
Whathappenstothedirectioniftheinterfaceisnotplane?
Ki Kg
g
=>Dispersion in energy
Gratings
Zoneplates/Lens
Amplitude FZPalternate zones - opaque
Efficiency:10.1 % (1st harmonic)1.1 % (3rd harmonic)
Phase FZPalternate zones -phase shifting
Efficiency40.5%
Kinoform FZP(sawtooth profile)
efficiency Up to 100%
t rn
Crystals
BRAGG or reflection LAUE or transmission
( )
( )
22
22
1 for 1( ) 1 for 1
for 11
x x xR x x
xx x
= +
Darwin, Phil. Mag. 27 (1914) 315 & 675
Dire
ctio
nR
efle
ctiv
ity
ImagingvsCondensingOpticalSystems
Imaging
Optics
NON
Imaging
Optics
Demagnification M
=> Large objects (elephants) are more deformed than small objects (ants)
OK,butIalwaysseeGaussians!
Yes:(Theoremofcentrallimit)
No:(plotitinlogscale!)
( / 2)
2 2ln(2) 2.35
RMS
CL erf n
FWHM
=
=
=
FWHM76.1%
Imagingsystems(grazingoptics) Inorderforanyopticalsystemtoformanimage,
itmustsatisfythe"Abb sinecondition", atleastapproximately
Two(ormore)surfacesareneeded
E.g.:Wolteroptics
KB(1948):Goodapproximation
Nonimagingsystem:BLasaconcentrator:whichshape(inreflection)?
qp
1 1 2sinp q
+ =
1 1 2sinp q R
+ =
Pointtopointfocusing(ellipsoid) Collimating(paraboloid) Notes:
Focalizationintwoplanes TangentialorMeridional(ellipseorparabola) Sagittal(circle)
Demagnification:M=p/q Easier:
Onlyoneplane=>cylinderEllipsoid=>Toroid Parabola/Ellipse=>circle Sagittalradius:constant(cylinder),linear(cone),nonlinear(ellipsoid)
Aberrations
ID20InelasticScattering
meVresolution(103 timeslessthanwhatyoureadinthespectraph/s/0.1%bw)=>USETHEWHOLEBEAM (REDUCETHELOSSESBYDIMENSIONS)
Highresolution=>Collimationindiffractionplane H orL?(L hashigherdivergence,H seemsfavourable) LBL(140m)orshorter?
energy in the 5 - 20 keV rangefocal spot size 10 mminimal beam lossesenough space (>20 cm) around the samplesub-eV resolution
Source
5
1
57x10
88x6
402x10
11x6.2
20keV
400x10
10x10
ROUNDED
57x10
88x4
402x10
11x3.2
e
mrad
57x10
88x7.2
57x10
88x12Low
m23(L)1/2
rad
mrad
69(L/)1/2
402x11
11x5.6
402x13
12x5.6High
10keV5keVRMS
15cm
19cm
20m
23cm
28cm
30m
30cm
38cm
40m
38cm
47cm
50m
61cm
75cm
80m
L(FWHM)
p
76cm
94cm
100m
=3.1mrad=2.5mrad
1mirror:Howfar?
M1xM2=100LBL
SagCylCollimator+Ellipsoid*,q2=75cm
92,40
94,4
70m
79,40
81,3
60m
66,40
66,2.5
50m
186,40
207,7
140m
M(H,V)
M(raytracing)
52,40
49,2
40m
Rsag TOO SMALL (NEED Rs>2cm e.g. q2=300 @ 70m) , BUT OK IN H
V
H
* Computed for point-to-point focusing, thus neglecting collimation
Towardsfinalconfig ShortBL Useofsecondarysource(M=M1*M2MA=3.1*16MB=2.4*23) FirstHighPowerCollimatingmirror(sag/tan) KB:goodopticalperformance(goodapproxtoimagingsystem),tunability
Mirroroptimisation(toroidM~3,distances,astigmatism) Slopeerrors(0.50.7radRMS) PowerLoad Tolerances Monochromator(s)optimization
(1.8 x 15 m2 without slope errors)
96%
BLtransmitivity
4 6 8 10 12 14 16 18 200
1
2
3
4
5
6
Si(111) + Si(311)
Inte
nsity
[ 1
013 p
hoto
ns /s
]Energy [ keV ]
The angular distribution along M4 (Long mirror) implies that part of the mirror is not working
6 8 10 12 14 16 18 200,4
0,5
0,6
0,7
0,8
R
Energy ( keV )
FM4: Rh 3.1 mrad FM4: Rh 2.5 mrad FM4: Pt 3.1 mrad
Si111@7keV or Si333@21keV
XROsoftwareroadmapR
AY
TR
AC
ING
SR
SO
UR
CE
SW
AV
E O
PTI
CS
KERNEL
GUITO
OLS
SHADOW 3.0
SRW
XOP
(ShadowVUI)SHADOW 2.0 New Tool
PANSOXTICS
OpenSource
Python+Qt?
Acknowledgements
mycolleagues SpecialthankstoGiulioMonacoandLinZhang)
ReferencesWikipediaX-ray Data BookletAls-Nielsen & McMorrow, Elements of Modern X-ray PhysicsAttwood, Soft X-rays and Extreme UV radiationMichette (ed), X-ray science and technologySpiller, Soft X-ray Optics SPIE Press, 1994 Handbook of Optics (3rd Edition Volume 5)
Credits(figuresandmore)http://www.nobelprize.org/http://xkcd.comPENELOPEmanual,A.BielajewMClecturehttp://wwwantenna.ee.titech.ac.jp/~hira/hobby/edu/em/dipole/N.A.Dyson:XraysinAtomicandNuclearPhysics(2nd ed)http://hasylab.desy.de/science/studentsteaching/primers/synchrotron_radiation/http://www.shimadzu.com/an/ftir/support/ftirtalk/letter9/mirror.htmlhttp://dx.doi.org/10.1107/S0021889806003232N.Pablant(PrincetonU)Vivalaciencia,Mingote&SanchezRon
Thankyou!