  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.
