For experiments requiring the longitudinal shaping of the beam at the exit of an electron linear accelerators, it is crucial to infer the initial beam profile at the entrance of the linear accelerator and key parameters. After passing through the dispersion section of beam bunch compressor, and the high-frequency system, the electron beam will undergo modulation on the longitudinal density. Based on the longitudinal dynamic process, this paper proposes to use automatic differentiation to provide the design of beam initial conditions and key parameters corresponding to a specific longitudinal profile of the beam at the exit of the linear accelerator. Finally, we implemented this method on a section of linear accelerator consisting of two L-band accelerating cavities, one S-band accelerating cavity, and a bunch compressor.

In electron linear accelerators, the improvement of the acceleration gradient of the acceleration structure has been a continuous research topic for scientists, which can reduce the construction cost of the entire accelerator by increasing the accelerating gradient. For the CEPC and HEPS projects at IHEP, S-band 3 meters long and C-band 1.8 meters long accelerating structure has been devel-oped. The operating frequencies are 2860 MHz, 2998.8 MHz and 5720MHz respectively. CEPC linac is 30 GeV with S & C-band structures in the TDR phase. The high-power test gradient of S-band accelerating structure reach the 33MV/m. The C-band structures also designed and waiting for high power test. HEPS is 500 MeV linac in-jector and already conditioning for one year. The maxi-mum gradient achieved with the beam during commis-sioning was approximately 26 MV/m with a beam current of 7 nC. During actual operation, it has been functioning at around 20 MV/m. The electron beam has remained stable up to the present time.

For experiments requiring the longitudinal shaping of the beam at the exit of an electron linear accelerators, it is crucial to infer the initial beam profile at the entrance of the linear accelerator and key parameters. After passing through the dispersion section of beam bunch compressor, and the high-frequency system, the electron beam will undergo modulation on the longitudinal density. Based on the longitudinal dynamic process, this paper proposes to use automatic differentiation to provide the design of beam initial conditions and key parameters corresponding to a specific longitudinal profile of the beam at the exit of the linear accelerator. Finally, we implemented this method on a section of linear accelerator consisting of two L-band accelerating cavities, one S-band accelerating cavity, and a bunch compressor.