We are trying to detect MeV ions with Time of Flight method with plastic scintillator detectors in a vacuum. We chose EJ200 for the fast time discrimination and we are looking forward to connect it with a PMT that is fast and can work in vacuum.
Practically all PMTs work in vacuum, since they are photo-electron multipliers that imply amplification via electron avalanches between the dynode stages. Usually PMTs carry their own vacuum inside their bulb (glass or quartz) envelope, with the photocathode on the inside of the "window". In the old days, "open" PMTs were produced in the laboratory by cutting open the bulb, which of course makes you lose the photocathode. Then you also have to provide a vacuum for the device to work. Open PMTs were largely succeeded by channel electron multipliers ("channeltron") in which a funnel at the entrance of a thin glass tube provides a target for photons, electrons, or ions, and an electric field moves the (external) photoelectrons into and along the inside of the tube to initiate a sequence of secondary electron avalanches (all inside high vacuum). The next step was the miniaturization of the channels into a dense array ("microchannelplate" MCP), which is also at the heart of night-vison devices. Here the electrons (after amplification) hit a phosphor surface and produce an image that a CCD camera can see. Channeltrons and MCPs have picosecond pulses, probably good enough for your fast timing. So many people have used such schemes as yours over several decades that even the vendors of PMTs (Hamamatsu, Philips, Burle, and (formerly) many others) must know, if you can't find any of the hundreds, if not thousands, of publications on the subject.
I connected a Hamamatsu one with our plastic into vacuum. And it is working well now! But its temperature will increase when it stays too long inside the vaccum. I just tested it for one hour. I will try to attach it with some heat conductor to cool it down. Thanks everyone.
The main heat source is not the PMT, but the (external) voltage divider stage. However, vacuum is a good thermal insulator, and thus your idea for a heat conductor from a shroud around the PMT to a cool reservoir is helpful.