**7. Some advanced single-pass FEL schemes**

Perhaps, the most common development of the basic SASE FEL scheme, where the amplifi‐ cation starts from noise with random phase, is represented by SASE FEL with seeding. In this case, already at the beginning of the undulator, unbunched electrons with random phase interact with coherent laser seed radiation, which bunches them accordingly. This scheme has the advantage of the stability of the phase, because the process is controlled by the seeding laser.

**Figure 12.** HGHG FEL with laser seed, harmonic generator, buncher, and amplifier.

To achieve extremely high frequencies, for example, those of the X-ray band, the following modification of SASE FEL with high-gain harmonic generation (HGHG) is sometimes employed (see schematic drawing in **Figure 12**).

It consists of the seed laser, harmonic generator, and the amplifier. The coherent seed laser radiation first passes the short undulator, called modulator, which is tuned to the seed frequency. The interaction with the electron beam gives the latter small longitudinal energy modulation. The following section of the installation converts this energy modulation into a beam density modulation in a magnetic dispersion unit. Then the modulated electron beam and the UR pass the second undulator, which is tuned to the *n*th harmonic of the modulator. When they pass the second undulator, the *n*th harmonic of the UR is fully amplified to saturation levels in this second undulator, frequently called radiator. At the exit the pulses with <20 fs duration can be obtained.

represents the simulation in the middle of the undulator length, and the right picture demon‐

**Figure 11.** Simulation of the density modulation of the electron beam along the undulator: undulator beginning—left

The transverse structure of the electron bunch is much larger than its longitudinal substructure. Note the length between the slices can be of the order of nm, and there can be up to

Perhaps, the most common development of the basic SASE FEL scheme, where the amplifi‐ cation starts from noise with random phase, is represented by SASE FEL with seeding. In this case, already at the beginning of the undulator, unbunched electrons with random phase interact with coherent laser seed radiation, which bunches them accordingly. This scheme has the advantage of the stability of the phase, because the process is controlled by the seeding

To achieve extremely high frequencies, for example, those of the X-ray band, the following modification of SASE FEL with high-gain harmonic generation (HGHG) is sometimes

It consists of the seed laser, harmonic generator, and the amplifier. The coherent seed laser radiation first passes the short undulator, called modulator, which is tuned to the seed frequency. The interaction with the electron beam gives the latter small longitudinal energy modulation. The following section of the installation converts this energy modulation into a

strates the electron density in the bunch at the end of the undulator.

picture, undulator middle—middle picture, undulator end—right picture.

**7. Some advanced single-pass FEL schemes**

**Figure 12.** HGHG FEL with laser seed, harmonic generator, buncher, and amplifier.

employed (see schematic drawing in **Figure 12**).

hundreds of thousands of slices in a bunch.

216 218High Energy and Short Pulse Lasers

laser.

One of the most important advantages of the mirror FEL is the possibility to select optical modes with the help of the mirrors. SASE FEL in its classical scheme is lacking this ability: there are no mirrors, which, in turn, gives other advantages. Together the advantage of the cavity-based mirror design with those of SASE FEL, the magnetic chicanes (small blocks in **Figure 13**) can be introduced between a sequence of undulators (big blocks in **Figure 13**) to impose a sort of mode locking in mirrorless single-pass FEL. The proper scheme is given in **Figure 13**.

**Figure 13.** SASE FEL design with chicane mode-locking (big blocks are undulators, small blocks are chicanes).

**Figure 14.** SASE output power after the undulator without (left) and with (right) chicanes.

The magnetic chicanes introduce an extra slippage of the radiation with respect to the electron bunch. Only those radiation wavelengths that have an integer number fit into the relative slippage of the radiation with respect to the electron bunch in one module will remain phasematched. Only they will constructively interfere over many such modules. In this way form the modes of the radiation field, which create a comb of equally spaced modes in the output frequency spectrum. Such a mode locking can be achieved by the beam energy modulation or by a beam current modulation of the same period. The result is similar to that created by the optical mode locking. We present the example of the power output and the spectrum of a common SASE FEL (see **Figures 14** and **15** left, respectively) to compare it with the example of the power output and of the spectrum of a FEL with chicane mode locking (see **Figures 14** and **15** right, respectively). Note that instead of the relatively broad SASE FEL spectrum, we now see the series of sharp equidistant peaks. The same regards the output power. At the end of the undulator-chicane line we achieve higher spectral power from the FEL.

**Figure 15.** SASE spectrum after the undulator without (left) and with (right) chicanes.

**Figure 16.** Schematic design of a self seed FEL.

Eventually, we touch on the functioning of the so-called self-seed FEL scheme, demonstrat‐ ed in **Figure 16**. The advantage of this type of FELs consists in that they are independent of any external radiation source, which must be otherwise very stable and precisely matched to the electron beam in space and time. Both undulators in the self-seed design are tuned to the same frequency. First undulator is in essence a short SASE FEL, which operates in the linear gain regime far from the saturation level. It produces the radiation in the form of typical SASE FEL pulses at the power level approximately 1000 times below the saturation level. Then the electron beam is fed through a magnetic chicane, which eliminates the density modulation, introduced in the first undulator, and delays the electron bunch to match the UR pulse at the next undulator. The radiation from the first undulator, which works in linear regime, is spectrally filtered by a narrow-band grating monochromator. The latter stretches the radia‐ tion pulse, where the coherence length now exceeds that of the electron bunch. After all, the reshaped radiation pulse and the delayed electron bunch meet. The filtered UR becomes the seed for the second undulator—radiator—which amplifies the UR to saturation level.

**Figure 17.** Spectrum after the first SASE FEL and after the second undulator-amplifier.

common SASE FEL (see **Figures 14** and **15** left, respectively) to compare it with the example of the power output and of the spectrum of a FEL with chicane mode locking (see **Figures 14** and **15** right, respectively). Note that instead of the relatively broad SASE FEL spectrum, we now see the series of sharp equidistant peaks. The same regards the output power. At the end

Eventually, we touch on the functioning of the so-called self-seed FEL scheme, demonstrat‐ ed in **Figure 16**. The advantage of this type of FELs consists in that they are independent of any external radiation source, which must be otherwise very stable and precisely matched to the electron beam in space and time. Both undulators in the self-seed design are tuned to the same frequency. First undulator is in essence a short SASE FEL, which operates in the linear gain regime far from the saturation level. It produces the radiation in the form of typical SASE FEL pulses at the power level approximately 1000 times below the saturation level. Then the electron beam is fed through a magnetic chicane, which eliminates the density modulation, introduced in the first undulator, and delays the electron bunch to match the UR pulse at the next undulator. The radiation from the first undulator, which works in linear regime, is spectrally filtered by a narrow-band grating monochromator. The latter stretches the radia‐ tion pulse, where the coherence length now exceeds that of the electron bunch. After all, the

of the undulator-chicane line we achieve higher spectral power from the FEL.

**Figure 15.** SASE spectrum after the undulator without (left) and with (right) chicanes.

**Figure 16.** Schematic design of a self seed FEL.

218 220High Energy and Short Pulse Lasers

Not only this FEL is independent on any external radiation source, but due to its design it also produces remarkably good radiation pulses with given characteristics.

In **Figure 17** we demonstrate the example of the output characteristics of such a self-seed FEL. Note that the spectral power distribution after the first (left) and the second undulator (right) differ from each other. The common SASE FEL spectrum (left) is rather broad and consists of many spectral lines even far below the saturation level. The output radiation on the contrary represents a narrow spectral line with only a small background of spontaneous radiation (right). Spectral brightness has increased by almost two orders of magnitude.

## **8. Challenges and future developments of X-ray FELs**

To conclude the review of some of the most prominent for X-FEL schemes, let us formulate main challenges for the X-ray FEL:


Note also that in the light of the above said the following requirements arise for the electron beam in transverse: low emittance of the beam and preservation of this low emittance; for the longitudinal dimension good compression and acceleration are required. The main negative factors, which affect the amplification, are the electron energy spread, the angular diver‐ gence, the transverse electron beam size, the diffraction of the wave and others. The electron energy spread has negative effect on both the amplification and FEL saturation level. Amplification mainly starts with the optimal electron energy, whose γ-factor determines the wavelength. As the energy is transferred from the electrons to the radiated electromagnetic wave, the energy ofthe electrons naturallydecreases. The wave emissions from allthe electrons differ from each other, because different electrons have different energies. After the waveelectron interaction, the electron beam energy spread increases and at a certain point it grows to a level, where no gain occurs. Moreover, well before the electrons loose a substantial portion of their energy, they slow down by emitting electro-magnetic energy and change their phase with respect to the wave. Thus they begin to take the energy from the wave rather than giving it.

In conclusion, let us state some areas, where the performance of the X-ray sources of coher‐ ent radiation can be further improved. First of all, the temporal coherence of SASE FELs can be improved. The improved temporal coherence would in turn improve the spectral bright‐ ness of the sources, which means the users will have more useful photons. The way to accomplish it could consist, for example, in seeding X-FEL from a radiation source with good temporal coherence.

An alternative approach to single-pass high-gain amplifier schemes is to use cavity feedback in a relatively low-gain system. The development of relatively high-reflectivity diamond crystal mirrors in the X-ray regime makes them feasible.

Reducing X-ray pulse durations to the attosecond regime will provide spatiotemporal resolution of atomic processes. Two techniques have so far been reported that can take pulse durations significantly below 100 as toward the atomic unit of time 24 as. The first technique employs a variation of an echo-enabled harmonic generation method and produces pulses of ~20 as duration at a wavelength of 1 nm with the power, which in peaks reaches ~200 MW. The second technique is based on mode-locking in conventional cavity lasers—oscillators. It could generate radiation at 1.5 Å wavelength in sequences of pulses with ~150 as intervals between them. The peak power in each pulse could reach ~5 GW and the duration of the pulse could be as short as ~20 as.

Eventually, γ-ray FEL would be extremely interesting for studying nuclear processes. This may be the future of X-FEL.
