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Why it is said that the Microchannel Plates can be operated in vacuum? What is the maximum pressure in which it can be operated? Also, while it is not operating, should it be kept in vacuum?

Is this because the semiconducting property of the channels can be affected by the atmospheric pressure? Or while operating the gas molecules can be ionized and burn the detector?

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The electrons need to get from the top to the bottom without any interference from any gas molecules that might be in the channels. If nothing else, collisions with gas molecules will degrade performance. At atmospheric pressure, I don't think the device would work at all. You can blow a hole through an MCP with over-voltage, but I'm not sure how this relates to residual gas in the channels. Also, it is certainly possible to generate a discharge (spark) between the bottom of the MCP and whatever comes next, so you want to keep gases out of there.

You can store them in air, preferably in a dry box.

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