SOS#$#WORKSHOP# Simulang#Hard#Xray# beamline# …...Crystals# BRAGG or reflection LAUE or...
Transcript of SOS#$#WORKSHOP# Simulang#Hard#Xray# beamline# …...Crystals# BRAGG or reflection LAUE or...
SOS -‐ WORKSHOP
Simula/ng Hard X-‐ray beamline op/cs by ray-‐tracing using
ShadowOui
Manuel Sánchez del Río AAM, ISDD, ESRF
Oasys+ShadowOui
• Install Oasys+ShadowOui: – hKps://github.com/srio/oasys-‐installa/on-‐scripts/wiki
• Download Tutorial Examples: – hKps://github.com/srio/ShadowOui-‐Tutorial
BM – Emission by N incoherent e-‐
• Monte Carlo (SHADOW) – Energy (and polarisa/on) sampled from spectrum – Angular Distribu/on (1e-‐, σ’x, σ’z) – Geometry (along the arc, σx, σz) – Limita/on: Computer /me and memory
• Typically: 103 -‐ 109 rays • Desirable: one ray per photon, i.e., 1014 -‐1020
x y
x x’
x y
z
Real Space (top) Phase Space (H)
ex12_bendingmagnet.ows
Wiggler: Like BM, but a bit more complex ex13_insertiondevices.ows
Undulator: Much more complex: 1e-‐ emission interferes with itself
θγ=K
For a single energy (odd harmonic)
ex13_insertiondevices.ows
Onuki & Elleaume Undulators, Wigglers and their applica9ons, CRC press, 2002
' 0.692r L L
λ λσ = ≈
2
2.7044 2r
LL λσ λ
π π= ≈
'1.894 2r rλ λ
σ σπ π
= ≈
• Undulator beams have not Gaussian profiles (even at resonances) • BY NOW, WE APPROXIMATE UNDULATORS BY GEOMETRIC SOURCES WITH GAUSSIAN SIZES AND DIVERGENCES
ex13_insertiondevices.ows
Non-‐imaging system: BL as a concentrator: which shape (in reflec/on)?
q p
ρρ
1 1 2sinp q
θρ
+ =
1 1 2sinp q R θ
+ =
• Point to point focusing (ellipsoid) • Collima/ng (paraboloid) • Focaliza/on in two planes
– Tangen/al or Meridional (ellipse or parabola)
– SagiKal (circle) • Demagnifica/on: M=p/q • Easier manufac/ring:
– 2D: Ellipsoid => Toroid – Only one plane: cylinder Ellipsoid (ellipse)=> cylinder (circle)
– SagiKal radius: non-‐linear (ellipsoid) => constant (cylinder) or linear (cone),
• Aberra/ons
ex15_aberration.ows
Mirrors Geometrical model Physical model
22 21
2
1 cos sin 2 2c cnn
θ θ δ δ δ⎛ ⎞
= ⇔ = − ≈⎜ ⎟⎝ ⎠
Fresnel equations give the reflectivity as a function of angle and photon energy. As a consequence, one gets the critical angle:
ex15_aberration.ows
Crystals
BRAGG or reflection
LAUE or transmission
(ex23_crystal_laue.ows)
ex18_sagittalfocusing.ows OTHER_EXAMPLES/crystal_analyzer_diced.ows OTHER_EXAMPLES/crystal_asymmetric_backscattering.ows
Theory of the Use of More Than Two Successive X-‐Ray Crystal Reflec/ons to Obtain Increased Resolving Power
J W. M. DuMond Phys. Rev. 52, 872 – (1937) hKp://dx.doi.org/10.1103/PhysRev.52.872
ex17_crystalmono.ows
LENSE = TWO INTERFACES Geometrical model Physical model
CRL = n iden/cal Lenses TRANSFOCATOR = m different CRLs
absorption in media
I/I0 = exp(-µ t)
(OTHER_EXAMPLES/lens_elliptical.ows) OTHER_EXAMPLES/CRL_Snigirev_1996.ows ex24_transfocator.ows
Other
ex16_kb.ows
ex19_beamline.ows