Mars trip to use astronaut poo as radiation shield

Indefinitely. The kind of radiation that causes breeding of hazardous isotopes in local materials is neutron radiation, which is comparatively rare in interplanetary space because free neutrons have a half-life of only 15 minutes. The biggest source of danger in space is high energy proton radiation. Neutrons can, and are, produced in secondary reactions from particle radiation but the flux isn't a sufficient concern to worry about "activation" of materials like water.

Exposure to ionizing radiation can cause formation of free radicals as well as peroxides which could be a concern but the particle fluxes are too low to be a serious concern. At the levels of radiation where it would be a concern the crew would have been exposed to lethal levels of radiation many times over, even with meters worth of water shielding.

Exposure to radiation does not make it radioactive.

It's possible to preserve food with radiation: http://en.wikipedia.org/wiki/Food_irradiation It kills all the living beings inside, but don't make the food radioactive. (It's not exactly the same radiation, but it's very similar.)

There are two kinds of radiation in space: cosmic rays, and solar flares.

The water and food, and "the stuff water and food turns into over the course of a trip" as the joke goes, are very useful as a "storm shelter" against a solar flare. If one comes up and the crew is not shielded like this against the solar flare, they will die within a day or two.

Cosmic rays are very hard to effectively shield against. They don't stop for much, including people, but there are so many of them that you are bound to take a dose. Right now the best way to deal with it, for temporary trips in space, is probably just to deal with it: accept the 1% or 2% rise in cancer risk, and make up for it with superior health care once they are back on Earth.

The normal method isn't terribly adequate AFAIK, at least for the weight. The ISS crew has a pretty substantial increased cancer risk, and they're still partially protected by Earth's magnetic field.

Over a long term interplanetary voyage, the chances of cancers developing would probably approach 100%.

I think the idea is, you're going to have to carry all that water to Mars anyway, and it just happens to be the best form of shielding around.

I think their idea is that you start with water as your shielding and as you consume it over time you replace it with waste products. Stuff that's high in hydrogen makes excellent radiation shielding.

The "normal" method of radiation shielding is almost none.

All of our manned spaceflights except for Apollo have been in low Earth orbit. Nestled deep down inside of Earth's magnetosphere protects you from a lot of radiation. Being above the ozone layer means that you are exposed to more ultraviolet light, but this isn't a big deal because it's not like you "go outside" much, you'll always have a window or a helmet between you and the Sun and those will always have a UV filter. The real issue is particle radiation, which comes from the Sun, the galaxy, and from parts of Earth's magnetosphere (the van allen belts). In low Earth orbit a lot of the solar and cosmic particle radiation is blocked, and as long as you steer clear of the van allen belts at high altitudes you'll be alright. The aluminum skin of spacecraft will protect you from some radiation, and you can add additional mass, especially water, to add more radiation protection. Overall in Earth orbit the radiation environment is fairly mild though a bit on the concerning side if you were to live there for decades.

If you have to travel through the van allen belts or outside Earth's protective magnetospheric bubble then things get much more difficult. In the case of the Apollo program they were careful to ensure that the thickness of the spacecraft's skin was enough to block a goodly amount of particle radiation and they designed the mission profile such that the spacecraft passed through the van allen belts as quickly as possible (spending as little time exposed to their radiation as could be managed). And in terms of operations in orbit around or on the Moon the main advantages was again one of time. Astronauts only spent at most a few days up there, limiting their radiation doses. However, they were extremely vulnerable to solar flares, which could have subjected them to extremely high doses of radiation that they had no way to protect against. In that they just got lucky.

A Mars mission, however, will spend months in interplanetary space and the chance of the crew being subjected to the radiation from a solar flare are very much higher. Additionally, they'll be subjected to much higher accumulated doses of radiation just by being in interplanetary space for so long. The thin aluminum skin of a spacecraft won't be sufficient protection for these conditions, so they'll need both a greater level of day to day protection and also an area of heavy protection that they can use to ride out solar flares and CMEs. Generally large masses of water or organic material work the best in protecting from the high energy protons that are the most concerning source of radiation in interplanetary space.

P.S. There's another option for shielding which is to generate a miniature magnetosphere around a spacecraft. This has a lot of advantages but the biggest disadvantage is that it would require additional equipment (weight is the biggest constraint on any Mars mission) as well as a significant amount of power and the technology hasn't been proven yet. Here's a neat paper on the subject: http://www.ess.washington.edu/Space/M2P2/rad.shielding.pdf

This would be a great Start Trek episode.

"Shields are down to 10%, Captain!"

"All hands report to the poop deck!"