## 2 Review of Efforts toward Attosecond Hard X-ray FEL
The duration of the spikes is expected to be in the range of 400 to 600 attoseconds. SLAC has recently tested out a self-seeding scheme by using the first half of the undulator to seed the second half through a diamond-based monochromator and has demonstrated self-seeding at angstrom wavelengths [31]. They noticed the reduction of a bandwidth by a factor of 40-50 with respect to SASE. Later, with the advent of a carrier-envelope-phase (CEP)-stabilized few-cycle laser, the interaction of such a laser with an electron bunch in a wiggler magnet of single or double period prior to an X-ray undulator in SASE FEL was considered. This interaction plays a vital role for the eventual generation  
Figure 1: (Color online). High gain harmonic generation (HGHG) attosecond free electron laser (FEL). Ultrafast X-ray pulses are produced through a sequence of undulators, which are resonant at different wavelengths [30]. of isolated attosecond X-ray pulses with FEL. The use of a few-cycle optical pulse laser in FEL was first recognized in 2004 [32], where an ultra-relativistic electron beam, a few-cycle optical laser pulse and a coherent X-ray radiation from harmonic cascade was used. The simulation showed the generation of a 100 attoseconds FWHM X-ray pulse with multi-megawatt power. In another simulation using a simpler layout, as shown in Figure 2[33], a femtosecond CEP laser and a wiggler magnet were used for energy modulation prior to entering into the SASE FEL to produce a train of 300 attoseconds X-ray pulses at 0.1 nm with GW power. The laser modulates the energy profile of an electron beam in a two-period wiggler resonant to the laser wavelength. This energy-modulated electron beam enters an X-ray undulator, which produces SASE radiation. A train of attosecond pulses was obtained in simulation (see Figure 2b). A crystal monochromator after the X-ray undulator was suggested for the selection of the single peak pulse. The scheme is supposed to produce 300 attoseconds-long single pulses with GW-level output power (a few hundred nJ) at a 0.1 nm wavelength. In a later proposal [34], instead of the monochromator, two undulators of different lengths were suggested, as shown in Figure 3. There is no monochromator between an X-ray undulator and a sample. The undulator is divided in two uneven parts, with the first part being a source for a seed signal, which is fed into the second part. Using an offset frequency resonance in the second undulator, the simulation showed the generation of a 300 attoseconds pulse with 100-GW output power. A magnetic chicane is used to allow the interaction between the seed signal and virgin electrons of the same electron bunch. The second undulator is tuned to an offset frequency of the radiation produced in the first undulator. Hence, a seed radiation at the offset frequency is exponentially amplified, while a seed radiation at reference-frequency remains the same. This scheme expects to deliver a 300 attosecond FWHM pulse with a peak power of 10 GW, which can be further increased to 100 GW using a tapered undulator. Figure 2: (Color online). Attosecond enhanced self-amplified spontaneous emission (SASE) (ESASE) scheme. (**a**) The layout of the scheme. (**b**) The single shot temporal structure of the central part of the radiation pulse. Dotted line represents the energy modulation of electron bunch [33]. The energy modulation of an electron beam at a low energy is more convenient than at a high energy, because a longer wiggler is required at a higher energy. Another advantage of the energy modulation at a lower energy is the small energy spread induced in an electron beam by a wiggler magnet itself. This energy modulation at low energy was studied in combination with another successive accelerator, prior to entering into a long SASE FEL undulator [35].The simulation resulted in the generation of X-ray pulses with a pulse width of \(\sim\)200 attoseconds with a perfect synchronization to a modulating laser pulse.