THz Streaking Algorithm To Reconstruct Ultrafast X-ray Pulse

X-ray free electron laser is a well-developed new generation advanced light source with high brilliance.At present,there are a few giant free electron laser scientific facilities all over the world,e.g.LCLS in United States,European XFEL in Germany,SCALA in Japan,PALX in South Korea,Swiss-FEL in Switzerland,DCLS and SXFEL in China and etc.Free electron laser(FEL)is based on linear accelerator which generates relativistic electron bunches to pass through undulators to gain and achieve coherent radiation.One of the major advantages of FEL is a light source with tunable radiation wavelength,especially the high-power femtosecond FEL pulses in the extreme ultraviolet(XUV)to X-ray ranges have broad applications.The ultra-short radiation pulse duration of X-ray free electron laser make it an ideal light source for time-resolved experiments.In addition,the peak power density up to10~1 ~8W/cm~2 of the focused FEL beam could be used to study the X-ray nonlinear processes in various materials.Therefore,it is very important to measure the pulse width of ultrafast X-ray free electron laser radiation accurately.The techniques to characterize the FEL radiation pulse include the following:streak camera,autocorrelation method,and frequency resolved optical gating and etc.The streak camera has low temporal resolution.Even the most advanced commercial streak camera in the world can only achieve time resolution of a few hundred femtoseconds.So it is impossible to accurately measure the FEL radiation pulse whose pulse width spans only a few femtoseconds to few tens of femtoseconds.The auto-correlation methods include the intensity auto-correlation and field strength auto-correlation,mainly aiming to measure the time width of FEL pulse but not the phase.The FROG method could be used to retrieve the pulse duration and phase of femtosecond laser or attosecond pulses delivered by high order harmonic generation(HHG)of the laser.However,the algorithm of FROG is complex and requires large amount of computational resource.In order to measure the FEL pulse duration we developed a dynamic model of the photoelectron wave packet excited by the ultra-fast FEL pulse in noble gas then modulated by external terahertz electric field,and analyzed the energy modulation due to the variation of THz field intensity,electron initial kinetic energy and time delay in-between the FEL pulse and THz wave.The wave packet and spectrum of photoelectrons are modulated differently by THz field at different delays with respect to the zero crossing of the THz vector potential.The ultrafast FEL pulse width is calculated by comparing the boarding of photoelectron spectrum in final state and in initial state.Moreover,the photoelectron energy spectral broadening due to the THz modulation by different FEL pulse lengths and at different delays is further analyzed to evaluate the errors for charactering the FEL radiation pulse length by using this method,thus the acceptable time jitter in the measurement is accessed.Furthermore,according to the shift of the center energy of the modulated photoelectron spectrum at different time delays,we simulated the final photoelectron energy distribution of any arbitrary sequential double-pulse with variable mutual delays and calibrate the time interval of the FEL double-pulse.This result is potentially very usefully for the time-resolved FEL dynamic experiment and research,e.g.a two-color FEL experiment.