The Free-Electron Laser LCLS

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Figure 7.1: Schematic layout of the LCLS FEL machine layout. The injector produces single electron bunches with a repetition rate of up to 120 Hz. The two magnetic chicanes (BC1, BC2) compress the electron bunch longitudinally and thereby increase the peak current from the injector by a factor of

~100 to ~ 3 kA at the end of the linac. A 132 m long fixed-gap undulator is used for the x-ray generation process through SASE. Note this figure represents the machine status in 2011/12, when the measurements presented in this work were performed. (Figure reproduced from reference [16])

Table 7.1: LCLS electron and X-ray beam parameters for the low charge mode at 20 pC and at the more routine setting of 250 pC, according to Ref [142].

Parameter 20 pC 250 pC Unit

Injector bunch length (rms) 1.3 2.5 ps

Initial peak current 5 30 A

Final bunch length (rms) ~3 ~30 fs

Final peak current ~3 ~3 kA

FEL pulse duration (FWHM)^a ~2 ~60 fs

FEL Peak power ~400 ~20 GW

aBased on simulations at 1.5 Å.

7.1.1 Principle of longitudinal compression

At FELs a high peak current (typically kiloampere level) is required to efficiently generate radiation at X-ray wavelengths in an undulator structure and to achieve saturation. High peak currents cannot be generated directly in the electron source, as repulsive forces between the electrons would lead to an increase in transverse emittance resulting in a significant deterioration of the FEL performance. These space charge effects largely cancel at relativistic electron energies. Therefore, low current electron bunches are created and accelerated to higher energies and then temporally compressed in the magnetic bunch compressor chicane, consisting of four bending magnets. The principle of the longitudinal bunch compression is illustrated in Figure 7.2. The bunch compressor consists of four

119 bending magnets. The trajectory of the electrons passing through the magnetic chicane varies with their kinetic energy. Electrons with higher energy travel along a shorter path than electrons with lower energy.

Longitudinal electron bunch compression is achieved in two steps: First, a negative linear energy chirp (∆E E/ ~ z, with z being the position within the bunch) is introduced by off-crest acceleration in the RF-fields prior to the chicane. In this case, as shown in Figure 7.2 in the upper left illustration, the energy of the electrons in the tail of the bunch is higher than of those in the head. In the second step, the electron bunch passes through the magnetic chicane. Due to the energy-dependent trajectories, the electrons in the tail take a shorter path and catch up with the electrons in the head of the bunch at the exit of the chicane, thereby compressing the longitudinal bunch length [33]. By adjusting the RF phase in the cavities prior the magnetic chicane, the compression ratio of the electron bunch is changed and thus the electron bunch length can be controlled. This allows to generate electron bunches with durations below 10 fs [142].

Figure 7.2: Longitudinal electron bunch compression and temporal shaping. To compress the electron bunch, first an energy chirp is imprinted on it, as depicted on the left. It is then sent to a magnetic chicane, comprising of four dipole magnets. The electron trajectories in the magnetic chicane are energy dependent. The higher energy electrons at the tail of the bunch travel a shorter distance than the leading lower energy electrons and are thus able to catch up with them. In the center of the magnetic bunch compressor chicane, where the electrons are maximally dispersed in transverse direction, a V-shaped slotted aluminum foil is inserted. The slots in the foil leave two narrow parts in the beam unspoiled to permit only in these parts lasing in the FEL undulator. At the exit of the chicane, where the transverse dispersion is zero, the two unspoiled parts are separated in time and will generate two subsequent X-ray pulses. The separation and duration of the X-ray double pulses is controlled with the slot geometry.

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The electron bunch properties determine the corresponding X-ray FEL pulse durations, which have similar or even shorter durations [143,144]. As can be seen in Table 7.1, the shortest pulse durations are achieved in the low charge mode at 20 pC, as only in this mode the transverse emittance is reasonably preserved, even near full compression. However, changing the charge requires additional accelerator tuning and X-ray optics alignment [14⁴].

Other methods that promise even shorter pulses, down to the attosecond regime, require significant changes in the design of the FEL, see for example Ref. [145,146,147]. A simple way to generate and to shape short FEL pulses, which requires no changes in the linac, is the emittance-spoiling foil [148].

7.1.2 Temporal shaping at X-ray FELS

Temporal shaping of the X-ray FEL pulse can be achieved by modifying the emittance, which is defined as the area occupied by the electrons in the position-momentum phase space, of the driving electron bunch. This scheme relies upon the fact that the SASE gain process is highly dependent on the transverse emittance of the electron beam. A simple and robust implementation is illustrated in Figure 7.2. Here, a thin slotted aluminum foil is inserted in the center of the bunch compressor (BC2 at LCLS, see Figure 7.1) chicane in the path of the beam [148]. At this position of the chicane the linear energy chirp of the electron bunch is mapped onto the transverse spatial coordinate x, resulting in a tilt of the bunch with respect to its direction of propagation. The emittance of most of the beam increases by Coulomb scattering of the electrons passing through the foil, leading to a strong suppression of the FEL gain in the undulator in these fractions of the bunch, while the FEL gain remains practically unaffected in the unspoiled (preserved emittance) slice passing through the slit.

By introducing a V-shaped double slotted foil in the chicane, two time slices of the electron bunch remain unspoiled, resulting in the emission of two, time delayed, collinear X-ray pules. The pulse duration can be controlled by different slot widths, while the separation can be regulated by variation of the insertion depth of the foil, which changes the transverse separation between the unspoiled parts of the electron bunch. For a slot distance of ∆x ^the temporal separation of the two pulses can be estimated from [144]:

t x ηhCc

∆ = ∆ , (7.1)

where η is the momentum dispersion at the middle of the chicane, h is the linear energy chirp introduced in L2, C is the bunch compression factor, and c the speed of light. The linear chirp h is defined with the electrons’ relative energy spread over the longitudinal bunch length coordinate z0 before compression by:

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0

E hz E

∆ = . (7.2)

Similarly, the pulse duration can be calculated from the slot width and can be found in Ref.

[148]. The main difficulty in these calculations is the accurate knowledge of the initial beam conditions, such as the energy chirp. Moreover, it is also hard to take account of the collective effects and high order optics in these simple calculations.

The X-ray pulses from the emittance-spoiling foil can be as short as few femtoseconds and even reach sub-femtosecond durations [149]. The duration of these ultrashort X-ray pulses was also measured with the photoelectron streaking technique and is reported in Ref. [150].