In 1979, Tajima and Dawson proposed the concept of laser wakefield acceleration (LWFA). When a strong laser is incident on the plasma, the ponderomotive force dislodges the electrons in the background plasma and then excites a wakefield to accelerate the particles. Without the breakdown voltage limitation in the plasma, the acceleration gradient ofLWFA can reach 100 GV/m, which is three orders of magnitude higher than that of the conventional radio frequency accelerator. Therefore, it is of great significance for the development of miniaturized particle accelerators and being expected to be applied to table-top free electron lasers.

The nonlinear wakefield, called the bubble, has a microstructure, and the accelerated electrons usually have only an fs-level pulse length and a µm-level transverse size. Due to the non-uniform longitudinal acceleration field and the nonlinear transverse field in bubble, e beam based on LWFA has large energy spread and emittance. A research team from Shanghai Institute of Optics and Fine Mechanics has experimentally verified self-amplified spontaneous emission based on LWFA. However, higher requirements are still put forward for the quality of the e beam in order to application, and the optimization of quality depends on the accurate diagnosis scheme.

Drawing on conventional accelerators, the six-dimensional phase space brightness is generally used to characterize the comprehensive quality of the e beam, where and represent the horizontal and vertical emittance of the e beam, respectively. The quality of optimization depends on the accurate diagnosis scheme, and the instability of the wakefield leads to the shot-to-shot jitter. Thus, how to achieve a high-resolution single-shot measurement of the e beam emittance is of great significance for further optimization of emittance.

Recently, State Key Laboratory of High Field Laser Physics of Shanghai Institute of Optics and Fine Mechanics had made important progress in the diagnosis of e beam emittance based on LWFA. The research team proposed a single shot emittance diagnosis scheme for e beam slice emittance, which is published in the High Power Laser Science and Engineering, Volume 11, Issue 3 (Kangnan Jiang, Ke Feng, Hao Wang, Xiaojun Yang, Peile Bai, Yi Xu, Yuxin Leng, Wentao Wang, Ruxin Li. Measurement of electron beam transverse slice emittance using a focused beamline[J]. High Power Laser Science and Engineering, 2023, 11(3): 03000e36).

To solve the problems mentioned above, the research team designed a single diagnosis scheme for transverse slice emittance of beam. While accelerated in the nonlinear plasma wake, the electrons experience transverse oscillation, which causes the evolution of the beam emittance. Considering a relativistic electron accelerates and oscillates in the bubble, the transverse trajectory can be expressed as in a linear focus field. It is thereby obtained that an electron with energy γ rotates with a frequency of in the phase space (r, ), where is the betatron oscillation wave number and is the plasma wave number. The energy-dependent rotational frequency of electrons in the phase space results in different phase advances. Based on the correlation between energy and oscillation frequency, phase compensation of e beam relative to the center energy can be realized. When electrons with energy spread remain in the same phase, e beam presents slice information.

In the experiment, the beam is mainly composed of three quadrupole magnets and one dipole magnet. The distance between the quadrupole magnets and the magnetic field gradient is adjusted according to the energy and divergence of e beam to achieve the horizontal and vertical focusing ofe beam. For a given focused beamline, the position of the focus is related to energy. The focused electron is deflected by dipole magnet to show the correlation between energy and size on the spectrum. Based on phase compensation and the coupling relationship between transverse size and energy, transverse slice emittance of e beam can be calculated. The measurement accuracy of this scheme can reach the order of 10 nm, and the emittance measured by experiments is 0.27 mm🞌mrad after optimization.

In this paper, a method of slice emittance diagnosis based on phase compensation is proposed. According to the measured emittance, it can be used as the basis for quality optimization, and the matched beamline can be designed to ensure the long-distance transport of e beam. In the future, the research group will continue to develop accurate diagnostic schemes, optimize e beam parameters, and achieve the higher quality radiation output of tabletop free electron laser.

Figure 1 Transverse phase space motion trajectory of the low-energy part (a) and high-energy part (b) of the e beam; transverse phase space distribution of electrons before (c) and after (d) phase compensation

Figure 2 Experimental measurement results and compensated phase advance