Basically, this is how the Earth protects us from solar flares.

Magentic fields do not work on neutrons, or electromagnetic radiation like gamma rays.

Long Answer:

The only thing that can stop ionizing radiation is matter, and the more matter you use the better. So several inches of lead shielding between you and the radiation source can stop the same radiation as several feet of iron shielding or maybe several yards of aluminum shielding, and so on. The more mass you use (i.e., the more pounds of stuff), the more radiation you can stop. But, in general, a pound of lead is just as effective as a pound of water, or a pound of air!

The only reason lead has such a good reputation as radiation shielding is that it is denser, that is, you can put the same number of pounds in a smaller space. So if you determine your spacecraft needs a thousand pounds of shielding to properly protect its crew, that’s what you’re going to need regardless of which material you choose. The only advantage of lead is that a thousand pounds of lead takes up a lot less room than a thousand pounds of aluminum. That is, lead is denser than aluminum.

There are other things you can do, though. For example, you can design your spacecraft so that more of its structural strength is provided by the external hull, as opposed to some internal framework of struts and supports. This means the hull does double-duty, it keeps the ship stiff and strong and keeps radiation out, and the weight saving can be made in reduced internal ribs and bracing. This may not be as efficient from an engineering standpoint, where the hull needs only be massive enough to keep the air in, and strength is provided by the frames and strakes, decks and bulkheads. To reduce the extra mass of a thick hull, it should be made as small in surface area as possible relative to the enclosed volume, and as much of the ship’s payload and structure as possible be mounted external to it.

Another strategy is to place the crew quarters in the center of the spacecraft, so that machinery, cargo, tankage, structural elements etc (which you have to carry anyway) can serve double duty as radiation shielding. The ideal spacecraft (from a radiation safety perspective) would be a sphere with the crew compartment at the very center, and the crew space most likely to be occupied would be at the center of that.

Radiation exposure will be time-variant, that is, you will get short but intense bursts of radiation from solar flares, passage through planetary radiation belts, etc, so you could rig a radiation shelter deep inside the spacecraft, surrounded by cargo, machinery, fuel, structure, less frequently used crew spaces, etc where the crew could retreat and take shelter for brief periods of extreme hazard. In other words, the control room or sleeping quarters should be placed deep inside the vessel, not near the external hull. Particularly radiation-sensitive material, such as biological samples and photographic film
could also be permanently stored there.

Deep space ships will probably not resemble aircraft or submarines. The generalized shape would be a roughly spherical object comprising the bulk of the ship’s payload, and equipage, with crew spaces deep inside. If the ship carries some radiation-generating source of its own (such as a fission reactor or fusion engine) it will probably be placed at the end of a long spar or truss as far from the rest of the ship as possible (radiation drops off rapidly with distance, by the inverse square law). A reactor or fusion chamber is made of massive materials, so paradoxically, it can serve for radiation shielding as well if its shape and distance is calculated properly to eclipse the radiation source! If the external point source of radiation is from one direction (say, from a solar flare), the engine or reactor module could be maneuvered to lie between the radiation and the ship, so the crew quarters would be exactly in it’s shadow. Cargo
and fuel storage bins could be mounted on the truss to provide additional radiation shielding from the engine or reactor and the occasional solar flare.

Real deep space craft will probably resemble the ship in Kubrick’s 2001: A Space Odyssey.

Quick question: Any light alternatives to lead? We’re going to need it if we’re going through the cosmos buffeted by THAT.

Surely, there could be something with the same density so as to block radiation, but light enough to not hinder spacecraft leaving celestial objects?