1. Achieving Required Peak Spectral Brightness Relative Performance for Four Undulator Technologies
Neil Thompson
WP5 – 20/03/19

2. FEL Brightness Have spec: B ≥ 1e33 ph/s/mm2/marad2/0.1%bw at 16keV
δ is the normalised degeneracy parameter - a correction factor to account for longitudinal and transverse coherence. The most dominant parameters are the peak current, the beam energy and the wavelength.

3. FEL Brightness
Required peak current to achieve FEL peak brightness 1033
Normalised emittance (mm-mrad) E
0.1
0.2
0.3
0.4
0.5
5GeV
4.6kA
5.2kA
5.6kA
5.8A
6.0kA
6GeV
3.7kA
4.2kA
4.5kA
4.7kA
4.9kA
7GeV
3.2kA
3.5kA
3.8kA
4.0kA
4.1kA

4. Relative Performance for Four Undulator Technologies

5. Undulator Comparison
Quick comparison of different undulator technologies to motivate discussions
Have determined, for beam energies from 4 – 9 GeV, for different undulators:
the period for the FEL to tune from 8keV at minimum gap (or max field) to 16keV
the aw parameter at 16keV
Have calculated, using simple 1D model (no corrections for emittance, energy spread, diffraction)
The 1D saturation length and saturation power at 16keV for a constant peak current
Not intended to provide absolute answers to the performance but to illustrate the relative differences we could expect between the different undulator types and how the technology would affect our choice of beam energy, for example
Achievable field: c1 c2 c3
REF
Cryogenic PMU
3.896
-4.022
0.529
EuPraxia Report D6.1, 2016
DELTA helical
1.45
-1.28
-2.24
A. B. Temnykh, PR-STAB 11, , 2008
Hybrid Planar
3.67
-5.08
1.54
P. Ellaume et al, NIM A455, 2000,

6. Undulator Comparison
Helical SCU data from 3D modelling at STFC (Vicky Bayliss + Mike Courthold)
4m SCU with 4mm gap and 11.5m period was built at STFC as prototype for the ILC positron source.

7. Undulator Comparison – 3mm gap
Period required for 8keV at minimum gap of 3mm
Corresponding aw at 16keV
1D saturation length for peak current 4kA, beam radius 25um
1D saturation power for peak current 4kA, beam radius 25um

8. Undulator Comparison – 4mm gap
Period required for 8keV at minimum gap of 4mm
Corresponding aw at 16keV
1D saturation length for peak current 4kA, beam radius 25um
1D saturation power for peak current 4kA, beam radius 25um

9. Parameter Set Adopted parameters at FEL: Parameter Value Comments
Energy
5.5GeV
Allows options for undulator technology
Lower than SwissFEL
Consistent with Peak Brightness 1033 ph/s/mm2/mrad2/0.1%bw
Peak Current
5kA
Achievable from LiTrack results
Normalised Emittance
0.2 mm-mrad
Consistent with Q < 100pC
Bunch charge
< 100pC
RMS Slice energy spread
1e-4
Slice length = one SASE spike length (2πlc ~ 0.3fs)
Max Photon Energy
16keV
FEL tuning range at fixed energy
X 2
Peak Spectral 16keV
1033 ph/s/mm2/mrad2/0.1%bw

10. Genesis Steady-State (single slice) @ 16keV (3mm gap)
Undulator Type
Period aw
CPMU Planar
12.87 mm
0.628
Delta Helical
13.78 mm
0.550
Hybrid Planar
14.12 mm
0.521
SCU Helical
9.85 mm
0.907
Beam radius optimised to 13um (β = 9m)
Module length = 2m
Intermodule gap = 0.25m

11. Genesis Time Dependent @ 16keV (3mm gap)
Flat-top bunch with full width = 5.45fs
Charge = 27pC
Same shot noise seed for each case.

12. Genesis Time Dependent @ 16keV (3mm gap) – Summary of results
CPMU
Delta
Hybrid
SCU
Saturation Power (mean over pulse) (GW)
9.1
8.9
7.6
9.8
Saturation Length (m)
24.5
26.5
29.1
15.6
Saturation Pulse Energy (µJ) 49 48 29 54
FWHM Bandwidth
9.87e-4
9.75e-4
9.96e-4
1.16e-3
Peak Brightness (mean over pulse) #ph/s/mm2/mrad2/0.1%bw
2.39e33
2.37e33
1.98e33
2.18e33
Notes
FWHM bandwidth is of a single spiky spectrum – needs averaging over many pulses
Brightness assumes full transverse coherence, so probably an over-estimate by factor ~2
No wakes included - Likely to reduce peak power and increase bandwidth.