In the past decade, the fourth-generation light source based on the combination of Energy Recovery Linac (ERL) and Free-Electron Laser (FEL) using superconducting linear accelerators has garnered significant attention. It holds immense potential, particularly in generating high-power Extreme Ultraviolet (EUV) light sources. This article primarily focuses on the physical design of an injector for ERL-FEL, based on a Very High Frequency (VHF) electron gun with a charge of 100 pC. The beam energy is accelerated to 10 MeV using 3-cell superconducting cryomodule. The optimization of beam parameters is conducted through employment of BMad and ASTRA simulations, incorporating the concept of Merger optimization. The beam emittance is less than 0.6 mm mrad, and the peak current at the injector exit exceeds 18 A. We present a new method to evaluate the Longitudinal Space Charge (LSC) effects in merger sections, which can be readily applied in design work. Furthermore, we introduce a novel type of merger. The performance of this new merger is comparable to the previously known optimum, the zigzag merger, offering a potential alternative solution for injectors in ERLs.
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