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## Spontaneous Radiation at LCLS

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General Properties

- Resonant wavelength:
- Maximum signal when directions of observation and trajectory are parallel with a characteristic opening angle of
- Maximum angle in electron trajectory is K/
- Effective solid angle of radiation is = 1/x K/

The Signal in Time Domain

trajectory

For larger angle in x the

uni-polar signals move closer

together, merging into a bi-

polar signal for >K/

Above plane of oscillation

Angular distribution (Far Field)

- Only odd harmonics are visible on-axis
- All harmonics are present for off-axis angles.
- The nth harmonic has n-1 knots in the yz-plane.

fundamental

2nd harmonic

3rd harmonic

Intensity Spectrum

- LCLS-lattice with super period. Detector 113 behind exit of undulator.
- Rich harmonic content on-axis.
- Wider spikes for off-axis radiation due to red shift
- Reduced harmonic content for off-axis emission.

Full Spectrum

- Summing over all emission angles, the full spectrum resembles that of a bend dipole.

Simplified LCLS lattice (far field)

Power Consideration

- The total power is
- For LCLS the total power is 75 GW, 10x larger than the FEL signal at 1.5 Å.
- The effective solid angle is 1/2 =1.5•10-9 rad2, 3 orders of magnitude larger than for the FEL signal (~10-12 rad2)

At saturation the FEL intensity is about 100 larger

than the spontaneous background signal

Intensity Distribution

- Angular distribution, 113 m behind undulator exit, using real LCLS lattice:

The peak intensity

is 73 kW/mm2

The distribution is almost like in the far field zone.

Total energy 75 GW

Spectral Power Cut

- The opening angle for a single frequency is:
- For LCLS the angle is = 1.5 rad.
- The emitted power at the fundamental is about 1 MW per 0.1% bandwidth (the full FEL signal of about 10 GW falls within this bandwidth).
- Higher harmonics contribute less than 5% to the total background signal and are most likely filtered out by spatial apertures.

Spatial Power Cut

- Array detectors (e.g. X-ray CCD cameras) or spatial collimator improve the signal to noise ratio.
- For LCLS, any cut below 1 mm2 at the first detector position (113 m behind undulator) would reduce also the FEL signal.

Signal-Noise (Full Undulator)

The noise signal for spatial cuts can be lower,

depending on the spectral response of the detector.

Detecting the FEL Signal

Solid - electron beam mis-steered

Dashed - undulator modules removed

Spectral Cut: 0.1%

Spectral Cut: 1.0%

Spatial Cut: 1 mm2

Spatial Cut: 4 mm2

FEL Signal

Detecting the FEL Signal

- For LCLS no information can be obtained from the FEL signal for the first 20 m with respect to undulator alignment and field quality.
- Operating at longer wavelength reduces the distance but makes the FEL signal less sensitive to the field quality.
- Short pulse operation of the FEL (e.g. two-stage pulse slicing or slit in dispersive section) reduces the signal-noise ration by 1-2 orders of magnitude.
- Information on undulator modules can be obtained by the spectrum of the spontaneous radiation.

Module Detuning Tolerance

- Detuned modules yield a ‘local’ phase slippage of the radiation field with respect to electron beam, yield a degradation in the synchronization of the resonance condition.
- Simulations yield tolerance of K=9.10-4

Undulator Module Tuning

- Possible method to tune undulator modules with the spontaneous radiation.
- Following method, proposed by TESLA (thanks to Markus Tischer, Kai Tiedke - HASYLAB, DESY)
- Prerequisite set-up: Non-destructive measurement of X-ray path (e.g. X-ray BPM, resolution < 1 mm)
- To measure changes in K of 9.10-4 the orbit of the photon beam has to be stable by about 2.1 rad.

Gas

X-ray beam

+

+

+

+

+

+

+

+

+

Pick-up line

Single Module Spectrum

- Bandwidth of 1/Nu~1%
- Angular distribution

after monochromator

At 5th harmonic

Ideal case of zero energy spread and emittance

Detuned Module

- Monochromator selects frequency slightly above 5th harmonic (shift of about 6.10-4)
- Variation in detected power and width of distribution
- Works best for monochromator tuned to the half value point of the high-frequency side of the spectrum

K/K = 10-4

Same at 1st harmonic

Emittance and Energy Spread

- Line width and distribution size are dominated by emittance (energy spread is negligible) for the 10th or higher harmonics.
- At 5th harmonic no degradation by emittance and energy spread.
- No benefits by going to higher harmonics

K/K = 10-4

1st

5th

10th

20th

Machine Jitter

- Energy jitter of 0.1% has same wavelength shift as detuning of K/K=10-4, but can be eliminated by statistic
- Same argument applies to charge jitter
- Alternatively the radiation measurement can be binned by measuring charge and energy of the spent beam.
- Jitter in beam angle (0.12-0.24 rad) is sufficiently small for the measurement. Transferred jitter on the radiation beam might be detectable if a X-ray BPM is installed.
- Other machine jitter not of relevance for tuning the modules.

Tuning the Undulator

- After BBA the orbit must be straight enough to have a beam divergence less than 1 rad.
- X-ray BPM are complimentary measurement of the orbit straightness. Improvement in resolution when installed in far hall, but not necessary when BBA is successful.
- Tuning works only for one module per time. If tuned modules remain in beam line than line width and distribution are determined by emittance and change in signal is too weak.
- Emittance effects can be slightly suppressed by increasing the beta-function for tuning.

Micro-Taper

- The energy loss due to spontaneous energy radiation requires to taper the undulator.
- The required taper is K=1.7•10-4 per module.
- Defines the required precision for undulator alignment.
- Denies module detuning at lower energy.

Ideal Case

Tapered

Not tapered

Coherent Radiation

- Coherent radiation arises from
- Undulator radiation, emitted under large angles
- Transition undulator radiation in the forward direction
- The coherently emitted energy of 40.5 J for CUR and 1.3 J for CTUR are negligible with respect to the incoherently emitted radiation.
- Although CTUR emits although at the resonant wavelength and is proportional to the bunching factor, the emission is strongly suppressed due to the finite extend of the electron bunch.

Conclusion

- Strong background signal from spontaneous undulator radiation. Requires some spatial and/or spectral cut to select FEL signal.
- No information on the undulator quality can be obtained from the FEL signal for the first section of the undulator.
- Individual undulator modules can be tuned by spectral analysis of the 5th (or 3rd) harmonics.
- Tuning for multiple modules in the beam line somehow limited by emittance

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