We have developed an ultra-line-narrowed, high-repetition-rate, high-power injection-locked F2 laser system for 157 nm dioptric projection systems under the ASET project “F2 Laser Lithography Development Project”. A spectral bandwidth of < 0.2 pm (FWHM), an output power of > 25 W, and an energy stability (3-sigma) of < 10 % at 5 kHz repetition rate was successfully obtained by using a low-power ultra-line-narrowed oscillator laser and a high-gain multi-pass amplifier laser. These parameters satisfy the requirements of exposure tools. A numerical simulation code that can simulate the spectral dynamics of the F2 laser under different operation modes such as free running operation, line-narrowed operation, and injection-locked operation, has also been developed. Using this simulation code, it is found that the instantaneous spectral bandwidth narrows monotonously during the laser pulse, and a narrower spectral output can be obtained by seeding the tail area of the line-narrowed F2 laser pulse. And the line-narrowing operation of the oscillator laser and the behavior of the injection-locked laser system can be predicted very precisely with this simulation code. The development of F2 laser for microlithography will be accelerated by this new simulation code.