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Based on numerical modeling, the dynamic characteristics of high-power ytterbium-doped double-clad fiber amplifiers during the amplification of nanosecond pulses with kilohertz repetition rates are comprehensively analyzed. The temporal pulse energy, power, upper-level population distribution, amplified spontaneous emission, stored energy, pulse waveform evolution, etc., are emphasized in this paper. Some practical issues in amplification processes, such as the impacts of reflected pulses from the external surfaces and the fluctuation of input pulse energy on the amplifier performance, are also discussed. The models and results are important for the design and development of high-power double-clad fiber amplifiers.