## 3 Toward the Generation of Isolated Attosecond Hard X-ray Pulse
### Optimization of Current Profile by Manipulation of Energy Profile of Electron Bunch  
Another method to control the side peaks in an electron bunch current profile is to manipulate the electron bunch energy distribution. Three different energy distributions are generated by changing radio frequency (RF) phases in a photo-injector section, as well as in the accelerator part, and by adjusting the parameters of a bunch compressor in the acceleration section. These three different energy distributions are as follows: (1) \(\sim\)20 \(\upmu\)m (\(\sim\)66 fs)-long electron bunch with an average current of 3 kA (Figure 8a), (2) \(\sim\)16 \(\upmu\)m (\(\sim\)53 fs)-long electron bunch with an average current of 4 kA (Figure 9a) and (3) \(\sim\)12 \(\upmu\)m (\(\sim\)40 fs)-long electron bunch with an average current 6 kA (Figure 10a). The rest of the electron beam parameters are chosen to be the same as in the beginning of Section 3.2. These energy distributions are generated by using the ELEGANT code. The parameters of the laser under consideration for this study are as follows: laser power is 13 GW, laser wavelength 1200 nm and pulse duration 7.5 fs FWHM. The momentum compaction factor, R\({}_{56}\), is selected between the quality of electron beam and the size of chicane. Figure 8 shows the simulation results for a \(\sim\)20 \(\upmu\)m (average current 3 kA)-long electron bunch. Figure 8a-c shows the longitudinal energy distribution before wiggler, after wiggler and after chicane, respectively. In Figure 8a, the electron bunch has a slight uphill in the central part of the electron  
Figure 7: (Color online). The variation of the main peak current after chicane. (**a**) The effect of the wiggler field, B\({}_{0}\), for two different laser wavelengths, 800 nm and 1200 nm. (**b**) The effect of laser power for two different laser wavelengths, 800 nm and 1200 nm. (**c**) The effect of the bending angle and the length between dipole magnets (L\({}_{1}\)). bunch. The interaction of the electron bunch with the co-propagating laser (7.5 fs FWHM, 800 nm) duplicates the laser field oscillation in the energy distribution of the electron bunch, as shown in Figure 8b. In Figure 8c, the electron bunch is further compressed by the chicane, so that its profile becomes steeper. The energy spread is (\(\Delta\)_E/E_) always less than the FEL parameter (\(\rho=5.4\times 10^{-4}\)). Figure 8d-f shows the current profile; before wiggler, after wiggler and after chicane, respectively. The current profiles before wiggler and after wiggler are similar in shape and magnitude. As seen in Figure 8f, after chicane, the current profile contains two major current peaks of 5.6 kA and 5 kA in the central part, due to the density modulation in the chicane. This current enhancement in the central part of electron bunch is caused by the steepening of the \(\Delta\)_E/E_ profile in the energy spread of electrons (Figure 8c). Figure 8g-i shows normalized emittances (both longitudinal and transverse) of the electron bunches. No significant change is observed in emittance due to these interactions. Figure 9 shows the results for the case of the 4 kA, 16 \(\upmu\)m (\(\sim\)53 fs) electron bunch. Before a wiggler, the energy distribution looks as shown in Figure 9a. When this electron bunch goes through a wiggler, it interacts with the laser and consequently suffers from the change in the electron beam energy distribution (Figure 9b). After passing through a chicane, the energy distributions becomes steeper (Figure 9c). Figure 9d,e and f show corresponding current profiles of this electron bunch. One can notice that after chicane, the current profile contains two major peaks of 7 kA and 7.39 kA. Corresponding normalized emittance is also shown in Figure 9g-i, indicating no difference in magnitude and shape between these locations. Figure 8: (Color online). The change of the characteristics of the 3 kA, 20 \(\upmu\)m-long electron bunch. (**a**)–(**c**): the longitudinal energy distribution. (**d**)–(**f**): current profile.