The spatial dependence of the timing performance of the R3809U-50 Micro-Channel-Plate PMT (MCP-PMT) by Hamamatsu was studied in high energy muon beams. Particle position information is provided by a GEM tracker telescope, while timing is measured relative to a second MCP-PMT, identical in construction. In the inner part of the circular active area (radius r$<$5.5,mm) the time resolution of the two MCP-PMTs combined is better than 10~ps. The signal amplitude decreases in the outer region due to less light reaching the photocathode, resulting in a worse time resolution. The observed radial dependence is in quantitative agreement with a dedicated simulation. With this characterization, the suitability of MCP-PMTs as $text{t}_text{0}$ reference detectors has been validated.
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