Best hull composition to resist interstellar environment (radiation+cosmic rays) while keeping mass to minimum?

Question

Keeping in mind the necessary characteristics of an interstellar ark traveling upwards of 1/10 the speed of light (functioning biosphere with water and atmospheric cycles, some sort of nuclear propulsion, leading protective magnetic field, rotational gravity...just to name a few) are there any suggestions in the space exploration community for the optimum hull composition to maintain radiation and cosmic ray levels within multi-generational life-sustaining levels while minimizing upkeep and repair headaches and, above all, acceleration penalties due to sheer mass?

Answer 1

If you're not volume constrained, hydrogen-rich material is good shielding against protons. We used polyethylene to shield the CCD detectors on ASCA.

Answer 2

upwards of 1/10 the speed of light

That's somewhat underconstrained. The energy of incoming particles increases dramatically as you go upwards, especially once you go fast enough that relativistic effects cannot be ignored. As a sort of starting position though, you can have a look at some work people have done on stuff like Breakthrough Starshot, such as The Interaction of Relativistic Spacecrafts with the Interstellar Medium:

We find that gas bombardment can potentially damage the surface of the spacecraft to a depth of ∼0.1 mm for quartz material after traversing a gas column of $N_H \sim 2\times10^{18}\mathrm{cm}^{-2}$ along the path to α Centauri, whereas the effect is much weaker for graphite material. The effect of dust bombardment erodes the spacecraft surface and produces numerous craters due to explosive evaporation of surface atoms. For a spacecraft speed $v = 0.2c$, we find that dust bombardment can erode a surface layer of ∼0.5 mm thickness after the spacecraft has swept a column density of $N_H \sim 3\times10^{17}\mathrm{cm}^{-2}$, assuming the standard gas-to-dust ratio of the ISM.

That's a potential problem when your interstellar vehicle weighs a few grams and could get lost in a pocket, but not when dealing with something the scale of something that could host a bunch of humans for decades at a time. There's also stuff like Project Icarus: A Review of Local Interstellar Medium Properties of Relevance for Space Missions to the Nearest Stars by Ian Crawford:

we find that this interstellar dust density would be expected to erode of the order of 5 kg m^-2 of shielding material over a six light-year flight at 0.1c (or 20 kg m^-2 at 0.2c). Clearly these shielding masses are starting to become significant (although they might be ameliorated by a different choice of shielding material, or a different strategy for dealing with dust impacts...)

The paper references Bombardment by interstellar material and its effects on the vehicle from Project Daedalus Final Report which I don't currently have access to, but is potentially interesting (though much of the science is 45+ years old now). The Daedalus spacecraft project proposed a ~1cm thick beryllium frontal shield for a 50 year trip reaching 0.12c.

A millimeter thick layer of quartz that's a meter squared in area masses 2.65 kg. The same size slice made of beryllium masses 1.85 kg. There's a significant difference in predicted erosion rates between the two papers that I can't easily reconcile for you, so I'll leave that as an exercise for the reader.

One thing that does pop up often in discussions of fast spaceflight is stuff like "ooh, at .1c a one gram micrometeorite packs the energy of 100 tonnes of TNT" which is true, but that's a giant piece of space dust and if there was that much stuff out there there's a good chance we'd see it. Crawford's paper suggests the biggest things you might expect to meet are submicrogram in size. They still pack a bit of a bang... megajoules, equivalent to kilos of TNT, so some mitigation is probably required and simple ablative shields risk being seriously damaged and rendered at least partially ineffective. Daedalus suggested using fine dust clouds projected ahead of the spacecraft, shepherded by "dust bug" vehicles, but I can't find the details of that, and it seems like it was mostly intended to survive the "encounter" phase of the flight where it might meet much denser interplanetary dust at the target star system, rather than the more rarefied material in interstellar space.

Personally, I like the idea of light, thin foil lightsails pushed ahead of the spacecraft by laser which can be replaced once they get a bit torn up. I'm not aware of any research on such things, but if I can think of that I'm sure someone more knowledgeable has written about it. Deeply spaced Whipple shielding, possibly with water tanks to help soak up and dissipate impact energy without disintegrating, will probably also help. Speaking of water though:

leading protective magnetic field

is kinda pointless. At .1 or .2c, the stuff hitting you from the front has an energy of 4-20 MeV per nucleon. That's pretty small beans by the standard of radiation shielding, and can be stopped by a few millimeters of basically anything more substantial than tissue paper. Ice, aluminum, titanium... its all fine for that sort of thing. Your magnetic fields won't work against neutral particles anyway.

The biggest radiation threat isn't stuff ahead of you, its the 1 GeV+ galactic cosmic rays that are an everyday threat once you're outside of Earth's atmosphere. The sort of mature spacefaring civilization that can actually make a multigenerational self-supporting starship will have already come up with some mechanisms to deal with this radiation which might well not have been anticipated by current research which doesn't really have much better advice than "stick several tonnes of stuff between you and the radiation source" which to be honest isn't a bad suggestion. A thick layer of water around your spacecraft makes for good shielding but also supports food and material production via aquaculture and exercise and leisure via swimming and so on.

Wrap the water layer up with whatever an advanced spacefaring industry would use. I suspect it would look a little like what we use now (multiple layers for different kinds of protection, insulation, etc) only with significantly fancier materials because they're a magical future scifi people and one should not skimp on materials when fitting out a generation ship. It seems less useful to speculate here. Foamed or structured 3d-printed aluminium or titanium? woven boron nitride nanotubes? Who can say?

multi-generational life-sustaining levels while minimizing upkeep and repair headaches and, above all, acceleration penalties due to sheer mass?

If you're expecting your mission to be multi-generational then you don't get to skimp on radiation shielding. You either need breakthrough electromagnetic techniques which don't currently exist and I can't usefully speculate on, or you need a few meters of ice or water, and you need to be prepared to boost it up to speed regardless of what it masses because the alternative is everyone dying of cancer and/or being unable to reproduce. Bite the bullet and build yourself some million-tonne disposable fusion rocket stages.