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I read at Super Kamiokande water is surrounded by many photomultiplers to detect neutrino interactions. I was wondering if water was stored into some container and yes then can I shoot a neutrio beam of high energy onto a water container with no damage?

Neutrino beam energy might be around 12-120GeV

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Super Kamiokande is so big because the neutrino interactions it looks for are so rare. They would be very rare indeed in a jug of water.

But then, what are they like? A high energy neutrino interaction yields a particle or a few, mostly relativistic leptons. That's very similar to secondary cosmic rays. Above ground, a few secondary cosmic rays will pass through your jug per second. So, your jug is already experiencing something close to the effect of neutrino interactions at a much higher rate than any practical neutrino beam can cause.

This is, of course, why experiments like this must be buried deep under ground to screen out the cosmic rays.

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Neutrinos have very little mass, and have no charge and are weakly interacting. Neutrinos therefore will not damage water molecules, if by damage you mean cause ionization. There is no list of ionizing radiation (one I've seen anyway) that includes neutrinos.

For very high energy neutrinos, it's possible in principle that one may knock an electron out of it's orbital, but this will not happen anywhere near often enough for "damage" even for neutrinos in the hundreds of GeV range.

And as Triatticus points out in the comments, this is also true for neutrinos in the TeV range as is evidenced from the IceCube neutrino observatory where neutrinos pass through the entire earth with little to no interaction with water molecules.

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