  In order to develop a long-lifetime MCP-PMT under high rates of circumstance,
we investigated the degradation of the quantum efficiency (QE) of PMT's with a
multialkali photocathode. We found that not only positive ions, but also
neutral residual gases would damage the photocathode resulting in an
enhancement of the work function; their countermeasures were established in
newly manufactured square-shaped MCP-PMT's with 4 or 4x4 multi-anodes. The
performances of the PMT's were measured: QE was stable up to an integrated
amount of anode output charge of 2-3 C/cm^2, while keeping other basic
performances steady, such as the time resolution for single photons of ~40 ps,
a photoelectron collection efficiency (CE) of 60%, a multiplication gain (G) of
a few x 10^6, and dark counts of 20-300 Hz. The causes of QE degradation are
discussed.
