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High-Resolution Effective K Measurements Using Spontaneous Undulator Radiation

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High-Resolution Effective K MeasurementsUsing Spontaneous Undulator Radiation

Bingxin Yang

Advanced Photon Source

Argonne National Lab

(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)

Contents

- 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.

- 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?

- 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.

- 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 Bunch Charge Fluctuation

- 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!

Intensity distribution depends strongly on photon energy!

An acceptable spectrum needs integration of 256 – 1024

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

- 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.

- DV/V ~ 0.001, DI/I ~ 0.001, R = 3.50xxx?
- Compare two passive devices: (R-R0)/R ~ I

- 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

- 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 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

- 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?

- 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.

- 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

- 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.