1. A. Introduction to FELs A.1 Photon Science A.2 X-ray light sources A.2.1 First and second generation A.2.2 Third generation A.2.3 Fourth generation: FELs A.3 FEL basics A.3.1 Low- and high-gain FELs A.3.2 High-gain FEL facilities

3. X-ray wavelength Beam wiggles with undulator wavelength λ u : Due to relativistic Doppler shift (next page), the X-ray wavelength λ l is compressed longitudinally Due to the wiggle motion. Using the correct expression for (see exercise) leads to the famous formula with Parameter choice: 1.K has to be around 1 for undulator radiation 2.λ u as small as technology allows. 3.Beam energy γ as high as necessary to reach targeted X-ray wavelength λ l.

4. Relativistic Doppler shift Electron emits one wavefront F each wiggler period. In wiggler period N, F N is emitted. In wiggler period N+1, F N+1 is emitted. But light has moved only a little bit faster than beam and F N is spatially very closely emitted to F N+1. Time light and particle need for λ u Time difference between wavefronts corresponds to a wave length via

5. X-ray power Small gain regime High gain regimeSaturation regime …Power gain length: length for X-ray power increase by e. … FEL parameter: allows estimates for many important properties: P sat, Δω/ω 0, η e

6. Two types of FELs FEL oscillators Produced light is trapped between mirrors (in pulsed form). At every beam passage, light is amplified Part of the light is coupled out through a semi-permeable mirror. Very weak micro-bunching (small gain regime). Single pass FEL Light is produced in one long undulator. Strong micro-bunching (high-gain regime). L SAT has to be small to be able to build undulator short enough (beam quality).

7. FEL oscillators (FELO) Saturation power: In each passage the light power P is amplified by a small amount G << 1 Light reaches after some time a high power between the mirrors. The light power reaches saturation when Advantages: Very high spectral purity High repetition rate High average power Energy efficiency several beam passages Application: Can be driven by beam from synchrotron, energy recovery linac, or linac. Used wherever possible, but … There are only mirrors available below the X-ray regime (IR, optical, UV). XFELO (not achieved): In the X-ray regime, normal mirrors cannot withstand the photon power. Crystals, e.g. diamond, are tested as Bragg reflectors (crystal lattice). Reflection only at certain angles.

8. Single pass FELs (high-gain FELs) For X-rays, light has to be created in a single pass. Since FEL power grows exponentially, the goal is to reach saturation. Hence, the main design goals for a single-pass FEL are (typical values for hard X-ray facilities) Small X-ray wavelength λ l (0.1nm) High P SAT (< 1GW) Small saturation length L SAT ≈ 22 L g ( 60-100 m) Also short beams are advantageous for the photon science. 1.X-ray wavelength: Given by the undulator parameters K, λ u and the beam energy γ. – The undulator with the smallest possible λ u (about 1.5cm) is chosen that still has a large enough K≈1. – Then the beam energy (typically 6-15GeV) is chosen to reach λ l as

9. Electron beam and undulator parameter choice for a single-pass FEL 2. Saturation power: mainly determined by the beam current (order of 1-5 kA) 3.Saturation length: The basic gain length (1D gain length L g0 ) is fixed by the already determined parameters and cannot be reduced (order of (50-100m)/22 ≈ 2-4m). But it is at least possible to increase L g0 not too much if also the effects of beam emittances ε x, ε y and energy spread σ η are taken into account (3D gain length L g ). This implies very small values for ε (< 1μm) and σ η (order of 10 -4 ) Linac vs storage ring: The necessary high beam current I and the low emittances correspond to a high beam brilliance The needed values for B e cannot be achieved in a storage ring, but in a linac.

10. A. Introduction to FELs A.1 Photon Science A.2 X-ray light sources A.2.1 First and second generation A.2.2 Third generation A.2.3 Fourth generation: FELs A.3 FEL basics A.3.1 Low- and high-gain FELs A.3.2 High-gain FEL facilities

11. Typical high-gain FEL layout Electron Gun creates low ε x, ε y beam. Relatively high charge. Bunch compressors Reduce bunch length. Increase of I 0. Shortening of X-ray pulse. Linac Bring beam to γ r. Preserve ε and σ η. Photon beam lines Transport and focusing. Steering to different experiments Undulators Creation of X-ray pulses. Dogleg to distribute to several undualators. Experiment Several experimental rooms to house photon science.

12. Electron gun Cathodes: – Thermal cathodes: Heating of metallic cathode increases energy if unbound electrons. Part of the electrons can escape cathode into vacuum due to their thermal energy. – Photo cathodes: Short laser shot on cathode. Electrons are ejected from cathode due to photo-electric effect. Higher beam brightness compared to thermal cathodes. Acceleration: – Beam has to be accelerated as fast as possible, since SC effects reduce with increasing γ. – Guns with RF acceleration field produce higher gradients than DC guns. – Transverse focusing with solenoid magnets. Goal: beam of highest brightness: -High charge and low ε. -Two counteracting wishes, since high charge creates high space charge fields which increase the emittance.

13. RF acceleration Several RF structures mounted on one module and are powered by one RF station. NC and SC structures in use. Choice impacts e - -bunch structure and RF and linac design. The RF station consists of an klystron (RF source) and its power supply called modulator. Depicted case: power of two klystrons combined with hybrid coupler to power 10 structures. EM waves are transported with waveguides (cooper pipe). RF system of the X-band XFEL collaboration RF bunch compressor shortens and intensifies the RF pulse.

14. Linac Beam focusing: – Usually FODO lattice. – Quadrupoles in the gaps between RF structure modules. Main target is to preserve the small ε and σ η from gun. Some aspects: – Longitudinal wakefields cause energy chirp. Can be compensated with off- crest acceleration. – Mechanical element offsets can cause the beam oscillations and dispersion. Can be compensated with beam-based alignment (BBA) techniques. Linac of PAL-XFEL (Korea) Many other interesting beam physics topics: -Micro-bunching instability and laser heating. -Transverse wakefields -Sensitivity studies of element parameter.

15. Bunch compressors Principle (linear dynamics): Acceleration of bunch off-crest to create energy chirp. Chirped beam is send through chicane. Particles in bunch head have less energy and have longer path Particles in particle tail vice versa. This leads to reduction of beam size. Two stage compression is easier for “complications”. Complications (non-linear dynamics and collective effects): Energy chirp is not perfectly linear (sinusoidal RF wave). The magnets of the chicane have non-linear components. In the dipoles, CSR is emitted and can increase projected ε. Small charge variations in combination with long. SC can create energy modulation that can result in unwanted micro-bunching.

16. Undulator magnets In XFEL facilities permanent magnet (PM) undulators are used (best suited up today). High precision element: – To keep K in tolerances, the mechanical tolerances are very stringent. – In operation, temperature in hall must be constant to about +/- 0.1 degree. – During whole life time, temperature must stay within +/- 1 degree. Otherwise irreversible deformations. – https://www.youtube.com/watch?v=7Fk1A ysFkUg In- and Out- of vacuum undulators: -LCLS vs SACLA -In-vacuum undulator has better performance but causes problems. Fixed and variable gap undulators -No variable gap in-vacuum (too complicated). LCLS undulator

17. Undulator section Structure Undulators only fabricated to a length of 4-5 m, several undulator modules are added. About 12-20 modules: 60 to 120m length. Gaps between undulators house: -Quadrupole magnets. -Beam position monitors (BPMs). -Phase shifters. -Beam loss monitors. Beam guidance Beam has to be steered to centres of the undulators: use of BPMs and either steering dipoles or QP movers. The beam is focused with quadrupole magnets that form a strongly focusing FODO lattice. But weak focusing of the undulator has to be taken into account.

18. Phase shifters Phase shift between beam and X-rays in gaps is unavoidable: 360 o = 1 Å. Phase shifters (magnetic chicane) are used to shifty beam. Sometimes there are individual magnet designs, sometimes they are based on the magnets of the undulators. First and second field integral determine properties of phase shifter. Taken from: “A PERMANENT MAGNET PHASE SHIFTER FOR THE EUROPEAN X-RAY FREE ELECTRON LASER” by H. H. Lu et al.

19. Photon beam lines and experimental area Only crystal mirrors (Bragg reflection) can be used, but only small angle are possible (1- 3 deg. soft X-rays; 0.1 deg. hard X-rays). This causes long photon beam lines. Still directly after the undulator, the X-ray intensity is too large for any material to withstand it. Therefore the X-ray beam is widened by its natural opening angle. After 50m (SwissFEL), X-rays can be used on first steering mirror. Shortly before experiment there is a second mirror to focus the X-rays again. More complex optics exist for soft X-rays (including monochromator), but more elements reduce X-ray coherence. To supply several (usually 3) experimental rooms, X-rays have to be steered with deflector mirror.