Modelling the photon transport system of the ALICE FEL using wavefront propagation

1. Modelling the photon transport system of the ALICE FEL using wavefront propagation Mark D Roper Accelerator Science & Technology Centre STFC Daresbury Laboratory

2. Talk Outline The Alice FEL & beamline The modelling code The propagation results Conclusion Questions

3. The ALICE FEL ALICE energy recovery linac with cavity FEL 26 MeV beam energy 60 to 80 pC bunch charge 27 mm undulator period, 40 periods, variable gap 5.5 to 9 µm wavelength 100 µs macro-pulse at 10 Hz 1625 pulses within macro-pulse (16.25 MHz) Pulse duration ~1 ps Pulse energy ~3 µJ

6. The FEL Beamline A complicated path dictated by the building M1, M2, M4, M5, M6 are plane mirrors, 45° AoI M3 is a toroidal collimating mirror, 75 mm diameter, 72.5° AoI.

9. The FOCUS Code Developed by Steven Higgins and Marion Bowler The Sommerfeld Propagation Integral is used for propagation from every position R on a surface to each point r on the next surface (mirror or image plane) where da is a surface element on an aperture (surface),  is the wavelength, n is the normal to the surface, and the dot product gives the obliquity factor.

10. The FOCUS Code The field at a set of points on a plane can be read in, or Gaussian sources can be generated internally. Input field files are either ascii files compatible with the PHASE code of Bahrdt, or binary files compatible with the FEL code Genesis1.3. Realistic surfaces can be generated by adding deviations to a perfect surface (toroid, ellipse, plane), or by reading in the surface positions at a set of points. The code is part of suite which can take input radiation field pulses, Fourier transform to obtain the field as a function of frequency, propagate individual frequencies and inversely transform the fields to generate the output field pulse as a function of time. The code is written in C++ and runs under Windows. Simple text I/O is used. The visualisation is carried out using small stand-alone IDL codes.

11. The Propagations - Source A field file at the position of the out-coupling hole was generated with Genesis and was used as the source of the propagations

12. At the position of the diamond window 3.5 mm out-coupling hole 1.5 mm out-coupling hole

13. Halfway between M2 and M3 3.5 mm out-coupling hole 1.5 mm out-coupling hole

14. At the position of M3 3.5 mm out-coupling hole 1.5 mm out-coupling hole

15. At the position of M5 3.5 mm out-coupling hole 1.5 mm out-coupling hole

16. 12 m after the position of M3 3.5 mm out-coupling hole 1.5 mm out-coupling hole

17. Conclusions Wavefront propagation has been used to demonstrate the diffractive effects when mirrors are overfilled The cavity out-coupling hole needs to be considered as part of the optical design. The FEL output shows a near-perfect Gaussian TEM00 mode. The value of wavefront propagation in FEL beamline modelling is clearly demonstrated.

18. Thank you for your attention