High resolution effective k measurements using spontaneous undulator radiation
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High-Resolution Effective K Measurements Using Spontaneous Undulator Radiation. Bingxin Yang Advanced Photon Source Argonne National Lab. Two Essential Elements for Far-Field Measurements. (Adapted from x-ray diagnostics planning meeting, Feb. 2004, SLAC) Roll away undulators

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High resolution effective k measurements using spontaneous undulator radiation

High-Resolution Effective K MeasurementsUsing Spontaneous Undulator Radiation

Bingxin Yang

Advanced Photon Source

Argonne National Lab

Two essential elements for far field measurements
Two Essential Elements for Far-Field Measurements

(Adapted from x-ray diagnostics planning meeting, Feb. 2004, SLAC)

  • Roll away undulators

    Spontaneous radiation is most useful when background is clean, with each undulator rolled in individually.

  • Adequate Far-field X-ray Diagnostics extracts the beam / undulator information

    • Electron trajectory inside the undulator (mm / mrad accuracy)

    • Undulator K-value (DK/K ~ 1.5 × 10-4)

    • Relative phase of undulators (Df ~ 10°)

    • X-ray intensity measurements (DE/E ~ 0.1%, z-dependent)

    • Micro-bunching measurements (z-dependent)


Relative measurements of undulator effective K using far-field spontaneous radiation (8 keV, 40 m to 60 m from undulator exit). Bonus: Wide bandwidth monochromator for z-dependent x-ray intensity measurement (DE/E ~ 0.1%).

  • Introduction: A simple feature of the spontaneous spectrum

  • Effect of beam quality: emittance, energy spread…

  • Simulated experiments (DK/K ~ 10-6?!)

  • Key components

  • Final remarks (conditional conclusion)


Main tools
Main Tools

  • Analytical work (back of an envelope)

  • Numerical simulations (MathCAD)

  • Undulator Radiation Modeling (XOP)

    • Angle integrated spectra: XOP/XUS

    • Undulator radiation intensity profile: XOP/XURGENT

    • Reference: M. Sanchez del Rio and R. J. Dejus "XOP: Recent Developments," SPIE proceedings Vol. 3448, pp.340-345, 1998.

A closer look at the spectral edge
A Closer Look at the Spectral Edge

  • Monitor the edge of angle-integrated spectrum

    • Shifts DE/E ~ – 2DK/K.

    • 50 – 100 data points, 5 – 15 minutes to acquire a spectrum!

  • Monitor the intensity at fundamental photon energy

    • Change DF/F ~ 400 DK/K  < 6% intensity change needed

    • Takes 1 – 2 seconds to acquire data?

Impact of aperture change size and center
Impact of Aperture Change (Size and Center)

  • Lower energy photons come in larger angles.

  • Spectra independent ofaperture size / location as long as the beam is fully contained.

  • Spectra independent of emittance for adequate aperture.

Impact of finite energy resolution
Impact of Finite Energy Resolution

  • Electron beam energy spread (0.06% RMS)

    • X-ray energy spread = 25 eV FWHM

  • Monochromator resolution (DE/E ~ 0.1% or 8 eV)

    Small effect on 70-eV wide edge!

Impact of electron energy jitter

Impact of Electron Bunch Charge Fluctuation

Impact of Electron Energy Jitter

  • X-ray intensity is proportional to electron bunch charge. Current monitor data (20% fluctuation) can be used to normalize the x-ray intensity data.

  • Location of the spectrum edge is very sensitive to e-beam energy change (0.1% jitter): Dw/w = 2·Dg/g

Most damaging instrument effect!

A look at the output intensity jitter
A look at the output intensity jitter

Intensity distribution depends strongly on photon energy!

Effect of multi shots integration
Effect of multi-shots integration

An acceptable spectrum needs integration of 256 – 1024

shots, resulting scan time = 7 – 18 minutes @ 120 Hz.

Summary of one undulator simulations
Summary of One-Undulator Simulations

  • Intensity noise (jitter) at the spectrum edge is largely due to electron beam energy jitter.

  • With sufficient integration time, the measured spectrum is accurate enough to resolve effective K change at a level of DK/K ~ 1.5 × 10-4.

  • Average will take longer if LINAC jitter has time structure.

  • A faster and more accurate technique is desirable.

Electricity 101
Electricity 101

  • DV/V ~ 0.001, DI/I ~ 0.001, R = 3.50xxx?

  • Compare two passive devices: (R-R0)/R ~ I

Differential measurements of two undulators
Differential Measurements of Two Undulators

  • Insert only two segments in for the entire undulator.

  • Kick the e-beam to separate the x-rays

Use one mono to pick the same x-ray energy

Use two detectors to detect the x-ray flux separately

Use differential electronics to get the difference in flux

Differential measurements signal
Differential Measurements: Signal

  • Select x-ray energy at the edge (Point A).

  • Record difference in flux from two undulators.

  • Make histogram to analyze signal quality

  • Signals are statistically significant when peaks are distinctly resolved

DK/K =  1.5  10-4

Summing multi shots improves resolution
Summing multi-shots improves resolution

  • Summing difference signals over 64 bunches (0.5 sec.)

  • Distinct peaks make it possible to calculate the difference DK at the level of 10-5.

Example: Average improves resolution for DK/K =  10-5

Simulation ii recap
Simulation II Recap

  • Use one perfect reference undulator to test another perfect undulator (two Perfect Periodic Undulators)

  • Set monochromator energy at the spectral edge

  • Accumulate difference count from the two undulators for ~64 bunches (0.5 second).

The signal is statistically significant in resolving undulators with

DK/K =  3  10-6

Is it still meaningful?

Can we detect minor radiation damage?

Key component reference undulator
Key Component: Reference Undulator

  • Last segment in the undulator

  • Period length and B-field same as other segments

  • Zero cant angle

  • Field characterized with high accuracy

  • Upstream corrector capable of 400 mrad kicks.

Key component monochromator
Key Component: Monochromator

  • Large acceptance aperture (30 mm  15 mm)

  • Wide bandwidth (DE/E = 0.1%)

    • Asymmetrically cut Ge(111) crystals (2 – 8 keV)

    • Multilayer reflectors (0.8 – 2.5 keV)

  • Low power only

  • Large dynamic range detector(s)

  • Low noise amplifier and 16-bit digitizers

Final remarks
Final Remarks

  • We proposed a differential measurement technique for effective K. It is based on comparison of angle-integrated flux intensity from a test undulator with that from a reference undulator.

  • Within the perfect undulator approximation, its potential resolution, DK/K =  3  10-6 or better, is sufficient for LCLS applications.

  • It is essential to have remotely controlled roll away undulators for this technique to be practical.

  • For not so perfect undulators, we need to extend the definition of Keff, or define a new figure of merit. The limitation of this proposed technique will need to be re-examined in that context.