# Toward the Generation of an Isolated TW-Attosecond X-ray Pulse in XFEL
## 3 Methods with Current Modulation
### Regularly Spaced Multi-Current Spikes  
The number of current spikes in the method proposed in Zholents [20] can be as many as desired. If a many-cycle laser pulse is used, multiple current spikes are generated [37]. However, if a many-current spike electron beam is sent into undulator units, each current spike independently generates radiation. If a method is devised in which all current spikes contribute only to a single radiation pulse, the radiation power will be increased, so that an over 1 TW radiation pulse can be achieved.  
One idea is to introduce a large delay to the radiation pulses with respect to the current spikes at the initial stage of an undulator line [37]. X-ray pulses can be delayed by using a series of mirrors (see [PERSON] et al. [42] for the method of X-ray pulse delay): the first radiation pulse (\"Target Pulse\" in Figure 4a) is delayed to the tail current spike (\"Tail Peak\" in Figure 4a). This first radiation pulse is called the target radiation pulse (TRP). After a large delay, the TRP is amplified at the next undulator unit because this TRP is only matched with the tail current spike. Other radiation pulses are not matched with other current spikes. For the third amplification process, the electron beam is further  
Figure 3: Current modulation method introduced in [PERSON] [20]. The blue arrows represent the propagation of a laser pulse. The electric field of a few-cycle laser is shown in the inset (left part). The energy modulation of the electron beam through a wiggler is shown in the inset (the middle part). The shape of energy modulation is almost the same as the profile of the few-cycle laser field. The chicane turns the energy modulation into density modulation, as shown in the inset (right part). The number of current peaks is the same as the number of cycles of the laser field. The peak value of a current spike is determined by the amplitude of the energy modulation.  
delayed to match the amplified TRP with the second-last current to the tail current spike. During the radiation process in the third undulator unit, the TRP is amplified further due to the interaction with the current spike. This process is repeated until the first current spike (\"Head peak\" in Figure 4a) is matched to the TRP. From this method, [PERSON] [37] reported that the Spring-8 Angstrom Compact free electron LAser (SACLA) XFEL can generate an X-ray pulse with a radiation power of 6.6 TW and a pulse width of 53 as at a wavelength of 0.1 nm, as shown in Figure 4b.  
A drawback to this process should be pointed out. In the first step, all the current spikes radiate independently and generate many radiation pulses. In the subsequent steps, these unwanted radiation pulses may also be amplified by other current spikes because the spacing between the current spikes is the same as that between the radiation pulses. Of course, the amplification speed of the other radiation pulses is lower than the fresh current spike because the energy spread of the matched current spike is larger due to the amplification process of the TRP. However, the matched current spike still has the ability to amplify the radiation pulses. Thus, creating a truly isolated X-ray pulse using regularly-spaced current spikes is challenging. There would always be satellite radiation pulses beside the main TRP, as shown in Figure 4b, where two small (about few hundred GW) satellite radiation pulses are depicted.