Re: manned Mission to Mars discussion
The amount of radiation is well-known. The total amount of exposure expected for a 2.5 years manned mission is equivalent of about few hundred years here on Earth. It's the effect on human body that is not well-known i.e. how much is the increase in the risk of dying from cancer. The estimates vary widely and there is no good way to test it. In the end some sort of radiation protection will have to devised before any manned mission to account for the potential severe solar storm which we already know is lethal within the magnitude of hours. I admit NASA is very much conservative on this front. Actually they are very conservative on most fronts. But the risk is real and not some figment of imagination.
As for a type of protection, you'd be correct in that lead would be right out, due to mass.
Would it perhaps be possible for a ship to carry a device to replicate the effect of a planet's magnetosphere? I'll admit right off that I don't know enough geology to know how the Earth create's it's mangentosphere or if it's possible to replicate on a small scale, but something like that could reduce the amount of radiation absorbed by the craft and crew...
For the more instantly lethal radiation events like a massive dose of fast traveling protons from a solar ejection a modest amount of aluminum would be enough. Although I don't know precisely all the details.
The higher priority placed by NASA admin. is on the type of radiation (coined HZE) that would pose more long-term health risks. Most of the risk uncertainty and technical challenge comes from these radiations. There has not been any technical demonstration but theoretically it could be as you said magnetic based.
You can read this paper if you have AIAA membership or if you are at an university with AIAA subscription. It's an old one but it's good.
HZE particle shielding using confined magnetic fields
"Bennett & Meyer are obviously the Ceti Eels introduced into the collective brain of Trekdom, leading to easy manipulation (TWOK), impaired cognitive functionality (TSFS), drooling (TVH), agonized death (TFF) and extended post-mortem twitching (TUC).