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Reactor fuel's power distribution plays a vital role in designing the new generation thermionic Space Reactor Power Systems (SRPS). In this paper, the 1/12th SPACE-R's full reactor core was numerically analyzed with two kinds of different axial power distribution, to identify their impacts on thermal-hydraulic and thermoelectric characteristics. In the benchmark study, the maximum error between numerical results and existing data or design values ranged from 0.2 to 2.2%. Four main conclusions were obtained in the numerical analysis: a) The axial power distribution has less impact on coolant temperature. b) Axial power distribution influenced the emitter temperature distribution a lot, when the core power was cosine distributed, the maximum temperature of the emitter was 194 K higher than that of the uniform power distribution. c) Comparing to the cosine axial power distribution, the uniform axial power distribution would make the maximum temperature in each component of the reactor core much lower, reducing the requirements for core fuel material. d) Voltage and current distribution were similar to the axial electrode temperature distribution, and the axial power distribution has little effect on the output power.