# Toward the Generation of an Isolated TW-Attosecond X-ray Pulse in XFEL
## 3 Methods with Current Modulation
### Single Current Spike II: Single Pass Method  
To solve the stability problem in the above methods, the possibility of using a single current spike without electron or optical delay unit was pursued, as shown in Figure 8. To check this possibility,  
Figure 6: Single current spike method-recycling. (**a**) An electron beam is modulated by a single-cycle laser pulse to have a single current spike; (**b**) In the first long undulator unit, a single radiation spike (red peak) is generated from a single current spike (blue peak); (**c**) With a delay unit which is composed of magnets and X-ray mirrors, the radiation spike can be rematched to the current spike. See [PERSON] at al. [42] for more details of the X-ray pulse delay shown in (**c**); (**d**) This step is repeated to the end. Reproduced from [PERSON] et al. [42] with permission. Figure 7: Simulation results with single current spike method-recycle in Figure 6. (**a**) The radiation power growth in the undulator line. SASE (green line) means the simulation result without any tapering in the undulator line. In the tapering case (blue line), an optimal tapering is provided in the undulator line without the recycle of a single current spike. The result shows a radiation power of only 0.55 TW with a pulse duration of 300 attoseconds. In the tapering with radiation alignment case (red line), the method in Figure 6 is applied. With the recycle of a single current spike, we can obtain radiation power larger than 1 TW. (**b**) The temporal profile of the FEL radiation. The main peak (red line) is expanded in the inset (the red line in the right part with two arrows) to show the temporal structure. Reproduced from [PERSON] et al. [42] with permission. FWHM: full width at half maximum. the following open questions should be addressed [44]: (1) How short should the current spike be? (2) How high does the current peak need to be and how can it be created? (3) How high does the power of a modulation laser need to be? (4) What is the best wavelength for a modulation laser? [PERSON] et al. [44] discussed these questions by using the two simulation codes: Elegant [46] and Genesis 1.3 [47]. To address the first and the second questions, a series of simulations for FEL radiation growth were completed for Gaussian current spikes with different widths and heights. It was found that a current spike with a 60 nm pulse width is appropriate to obtain an X-ray pulse with a duration less than 100 as with a sufficient chance of increasing the peak power of the radiation pulse. It was also shown that the peak current of a current spike has to be higher than 35 kA to obtain TW-level radiation power. Such a current spike can be generated by the method explained in Figure 3 with an appropriate power and wavelength of a modulation laser, as shown in Figure 8. The longer the wavelength of a modulation laser, the higher the peak current of a current spike. However, the power of a modulation laser and the magnetic field of the chicane were also increased simultaneously to maintain the width of the current spike at 60 nm. These realizations provide a clue to the answers to the last two questions. From the answers to the questions, it was concluded that a laser energy of 0.7 mJ at 2 \(\upmu\)m wavelength is needed to generate a current spike of 37 kA peak current for the generation of a TW-level X-ray pulse with PAL-XFEL parameters. In this case, there was no extra component between the undulator units. The simulation results are shown in Figure 9. An optimal tapering was applied to the undulator line. Due to the high peak current, the power of the FEL radiation grew very quickly in the early stage of the undulator line. In the middle part of the undulator line, the radiation pulse slipped out from the current spike. However, there was still a background current of a few kA. This small background level current still slowly amplified the radiation pulse.