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!