If water is the cheapest, and most usable radiation shield material for human space travel, how do we get large amounts of it to orbit?
Water is only cheap on Earth. See related What is the current cost-per-pound to send something into LEO? (spoiler 1 Liter = 1KG, 3.78Liters = 1 gallon; very cheapest is more than 15,000USD to get 1 gallon of water to LEO)
Water is not the most effective shield. But it will work See related What thickness/depth of water would be required to provide radiation shielding in Earth orbit?
The effectiveness of a shielding material in general increases with its atomic number, called Z, except for neutron shielding which is more readily shielded by the likes of neutron absorbers and moderators such as compounds of boron e.g. boric acid, cadmium, carbon and hydrogen respectively.
Graded-Z shielding is a laminate of several materials with different Z values (atomic numbers) designed to protect against ionizing radiation. Compared to single-material shielding, the same mass of graded-Z shielding has been shown to reduce electron penetration over 60%. It is commonly used in satellite-based particle detectors, offering several benefits:
- protection from radiation damage
- reduction of background noise for detectors
- lower mass compared to single-material shielding
The cheapest shield for space will have the least amount of mass, for the greatest protection. So some kind of 'Graded-Z shielding' is going to be cheapest.
There is already lots of water in space near Earth
the team calculated a basic estimate for how much water could be trapped inside near-Earth asteroids. According to that estimate, there may be between 100 billion and 400 billion gallons (400 billion to 1,200 billion liters) of water spread among these space rocks. Source