Steady state microbunching (SSMB) proposed by Alexander Chao and Daniel Ratner is a new concept of accelerator light source, which means to maintain the microbunching in storage rings for coherent radiation production. By combining the high coherence and high repetition rate, SSMB can provide very high average power radiation. And the radiation wavelength can cover THz to soft X-ray. To promote the SSMB physics research and develop a SSMB-EUV light source, a taskforce has been established in Tsinghua University since 2017. Recently, we are continuing the proof of principle experiment and have observed multi-turn coherent radiation by modulating the electron bunch with laser single-turn on MLS storage ring. The experiment results are in very good agreement with theoretical prediction, which proof this kind of mechanism (maintain micro-bunch in storage ring) can work well. We have also proposed a complete design for high average power EUV radiation based on SSMB. The proposal will provide kW EUV average power at the radiation wavelength of 13.5 nm within 2% bandwidth. We have done the start to end study for this proposal and the researches on the key technologies are also underway. This kind of EUV light source may open a new roadmap to meet the requirements of EUV lithography.

To describe longitudinal fine structure within a particle beam like microbunching, a classical approach is to define a bunching factor or form factor which is the Fourier transform of the particle density distribution in longitudinal dimension. Such a 1D definition of form factor can be generalized to 6D spectral form function (SFF) to describe more complicated structure in phase space. The complex SFF is another complete description of beam in spectral domain and can offer complementary and valuable insight in beam dynamics study which usually invokes the real particle density distribution. The basic property and Fokker-Planck equation of the SFF is presented, along with its solution in a general coupled linear lattice. The example applications of SFF in electron storage ring physics and laser-induced microbunching are presented.