longitudinal coherence - synchrotron radiation...

Longitudinal Coherence

Definition: Distance over which two waves from the same source pointwith slightly different wavelengths will completely dephase.

λ−∆λ

Two waves of slightly different wavelengthsλ and λ−∆λ are emitted from the samepoint in space simultaneously.

After a distance LL, the two waves will beexactly out of phase and after 2LL they willonce again be in phase.

2LL = Nλ2LL = (N + 1)(λ−∆λ)

Nλ = Nλ+ λ− N∆λ−∆λ

0 = λ−N∆λ−∆λ −→ λ = (N + 1)∆λ −→ N ≈ λ

∆λ−→ LL =

2∆λ

C. Segre (IIT) PHYS 570 - Fall 2010 September 02, 2010 1 / 8

λ−∆λ

2LL = Nλ2LL = (N + 1)(λ−∆λ)

0 = λ−N∆λ−∆λ −→ λ = (N + 1)∆λ −→ N ≈ λ

∆λ−→ LL =

2∆λ

λ−∆λ

2LL = Nλ2LL = (N + 1)(λ−∆λ)

0 = λ−N∆λ−∆λ −→ λ = (N + 1)∆λ −→ N ≈ λ

∆λ−→ LL =

2∆λ

λ−∆λ

2LL = Nλ

2LL = (N + 1)(λ−∆λ)

0 = λ−N∆λ−∆λ −→ λ = (N + 1)∆λ −→ N ≈ λ

∆λ−→ LL =

2∆λ

λ−∆λ

2LL = Nλ2LL = (N + 1)(λ−∆λ)

0 = λ−N∆λ−∆λ −→ λ = (N + 1)∆λ −→ N ≈ λ

∆λ−→ LL =

2∆λ

λ−∆λ

2LL = Nλ2LL = (N + 1)(λ−∆λ)

0 = λ−N∆λ−∆λ −→ λ = (N + 1)∆λ −→ N ≈ λ

∆λ−→ LL =

2∆λ

λ−∆λ

2LL = Nλ2LL = (N + 1)(λ−∆λ)

0 = λ−N∆λ−∆λ

−→ λ = (N + 1)∆λ −→ N ≈ λ

∆λ−→ LL =

2∆λ

λ−∆λ

2LL = Nλ2LL = (N + 1)(λ−∆λ)

0 = λ−N∆λ−∆λ −→ λ = (N + 1)∆λ

−→ N ≈ λ

∆λ−→ LL =

2∆λ

λ−∆λ

2LL = Nλ2LL = (N + 1)(λ−∆λ)

0 = λ−N∆λ−∆λ −→ λ = (N + 1)∆λ −→ N ≈ λ

−→ LL =λ2

2∆λ

λ−∆λ

2LL = Nλ2LL = (N + 1)(λ−∆λ)

0 = λ−N∆λ−∆λ −→ λ = (N + 1)∆λ −→ N ≈ λ

∆λ−→ LL =

2∆λ

Transverse Coherence

Definition: The lateral distance along a wavefront over which there is acomplete dephasing between two waves, of the same wavelngth, whichoriginate from two separate points in space.

If we assume that the two wavesoriginate from points with a smallangular separation ∆θ, Thetransverse coherence length is givenby:

2LT= tan ∆θ ≈ ∆θ

R= tan ∆θ ≈ ∆θ

LT =λR

2LT= tan ∆θ

≈ ∆θ

R= tan ∆θ

≈ ∆θ

LT =λR

Coherence Lengths at the APS

For a typical 3rd generation undulator source, such as at the AdvancedPhoton Source the vertical source size is D = 100µm and we are typicallyR = 50m away with our experiment. If we assume a typical wavelength ofλ = 1A, and a monochromator resolution of ∆λ/λ = 10−5 we have for thevertical direction:

LL =1× 10−10

2 · 10−5= 5µm

LT =(1× 10−10) · 50

2 · (100× 10−6)= 25µm

LL =1× 10−10

2 · 10−5= 5µm

LT =(1× 10−10) · 50

2 · (100× 10−6)= 25µm

LL =1× 10−10

2 · 10−5= 5µm

LT =(1× 10−10) · 50

2 · (100× 10−6)= 25µm

X-Ray Tube Schematics

Fixed anode tube

Rotating anode tube

• low power

• low maintenance

• high power

• high maintenance

X-Ray Tube Schematics

Fixed anode tube Rotating anode tube

• low power

• low maintenance

• high power

• high maintenance

X-Ray Tube Spectrum

• Characteristic energy ofelemental fluorescenceemission

• Minimum wavelength(maximum energy) set byaccelerating potential

• Bremsstrahlung radiationprovides smoothbackground

X-Ray Tube Spectrum

Synchrotron Sources

Bending magnet

• Wide horizontal beam

• Broad spectrum to highenergies

Undulator

• Highly collimated beam

• Highly peaked spectrumwith harmonics

Synchrotron Sources

Bending magnet

Undulator

Synchrotron Sources

Bending magnet

Undulator

Synchrotron Sources

Bending magnet

Undulator

Synchrotron Sources

Bending magnet

Undulator

Synchrotron Sources

Bending magnet

Undulator

Bending Magnet Spectra

0 20000 40000 60000 80000 1e+050

Lower energy sources, such as NSLS have lower peak energy and higherintensity at the peak.Higher energy sources, such as APS have higher energy spectrum and areonly off by a factor of 2 intensity at low energy.

0 20000 40000 60000 80000 1e+050

Lower energy sources, such as NSLS have lower peak energy and higherintensity at the peak.

Higher energy sources, such as APS have higher energy spectrum and areonly off by a factor of 2 intensity at low energy.

0 20000 40000 60000 80000 1e+050

Lower energy sources, such as NSLS have lower peak energy and higherintensity at the peak.Higher energy sources, such as APS have higher energy spectrum and areonly off by a factor of 2 intensity at low energy.

100 1000 10000 1e+051e+05

Logarithmic scale shows clearly how much more energetic and intense thebending magnet sources at the 6 GeV and 7 GeV sources are.

100 1000 10000 1e+051e+05

Logarithmic scale shows clearly how much more energetic and intense thebending magnet sources at the 6 GeV and 7 GeV sources are.

longitudinal coherence - synchrotron radiation...

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