## 2 Review of Efforts toward Attosecond Hard X-ray FEL  
Hard X-ray FEL machines are either in operation or under construction [1; 2; 3; 4]. In the early 1980s, the basic concept of the current SASE-FELs was developed [5]. Even though SASE-FEL has been always a favorite choice as a potential source for sub-femtosecond X-ray pulses, its inherent problem limits the temporal coherence of the output radiation of a SASE-FEL. Moreover, this radiation consists of many sub-femtosecond peaks, whose arrival time varies randomly from shot to shot. This makes the use of SASE-FEL in pump probe experiments in the attosecond time scale very difficult. Exploiting the SASE scheme, several experiments and simulation work have been done for the generation of picosecond, femtosecond and attosecond X-ray pulses. SASE-FEL radiations in the vacuum ultraviolet (VUV), extreme ultraviolet (EUV) and soft X-ray regions have been demonstrated successfully [6; 7; 8; 9; 10; 11; 12; 13].The efforts towards the generation of hard X-ray pulses in a femtosecond time domain have been made. In the hard X-ray region, the linac coherent light source (LCLS) at the Stanford Linear Accelerator (SLAC) [14] is the first hard X-ray FEL machine, which has been in operation since 2009. This facility has tunable radiation wavelengths from 2.2 to 0.12 nm by varying the electron energy from 3.5 to 15 GeV. Since March 2012, scientists have also an access to the second hard X-ray FEL: The Spring-8 Angstrom Compact Free Electron Laser (SACLA). The shortest wavelength attained is 0.06 nm, with a maximum power of 10 GW, with a pulse duration of 10 fs [15]. Many applications, including spectroscopic studies of correlated electron materials and imaging studies, demand an excellent temporal coherence. Such a demand has resulted in various high gain seeded FEL schemes, including external seeding [16; 17; 18; 19; 20; 21; 22; 23] or self-seeding [24; 25; 26]. The Free ElectronLaser for Multidisciplinary Investigations (FERMI) at Elettra is a seeded FEL, which has been designed for producing high quality photon pulses in the EUV and soft X-ray spectral range [22]. The first undulator line, named FEL-1, was successfully operated to produce coherent radiation in the spectral range from 65 nm to 20 nm [23]. The second undulator line FEL-2, currently under commissioning, will cover the spectral range between 20 nm and 4 nm. Among these schemes, echo-enabled harmonic generation (EEHG) shows a great promise for producing a fully coherent short wavelength FEL. A classic high gain harmonic generation (HGHG) scheme [16] has suffered from the low up-frequency conversion efficiency. Consequently, this led naturally to a multistage approach for X-ray production seeded at an ultraviolet wavelength [27]. The beam echo effect has remarkable frequency up-conversion efficiency and allows for the generation of high harmonics with a relatively small energy modulation [20]. Using an EEHG scheme, coherent soft X-rays at 5 nm with GW peak power was calculated, starting from a 240 nm seeding laser [28]. Later, the EEHG scheme with an additional electron bunch compression has been proposed [29]. The calculation showed that X-ray pulses at 1 nm with a peak power of a few hundred megawatts and a pulse duration of 20 attoseconds full width at half maximum (FWHM) is expected. For the radiation at an even shorter wavelength, a four-stage HGHG-FEL scheme has been proposed, for which a train of attosecond pulses at 0.1 nm wavelength was expected in simulation [30]. This concept was realized by the generation of the eighth harmonic of SASE radiation using a single electron bunch and a four-stage HGHG configuration, as shown in Figure 1. The electron bunch passes through a sequence of four relatively short undulators. The first undulator is a SASE FEL undulator tuned at 0.8 nm, which operates in the high gain linear regime. The 0.1 nm wavelength radiation is achieved by a successive division of 0.8 nm to 0.4 nm to 0.2 nm and to 0.1 nm in a sequence.