serious error (re. radiation shielding) in 1975 Summer Study?

> I can't find any flaw in your reasoning process, but still can't bring
> myself to believe that the Summer Study could have been off by this much.
> ...
> Seems like if there was such a fundamental flaw in the work, its enemies
> would have torn into it with gusto. And this would have happened in the
> 1970's.

That's a reasonable argument.

OK, let's see, either I've screwed up or I haven't. If I have, it'd be
great to know where, so I can correct the simulation. If I haven't,
then it's important news that will change the way we design space habitats.

So, begging your patience, here's the reasoning laid out so we can pick
it apart. (All references at
https://www.assembla.com/spaces/high-frontier/wiki/Radiation; use
http://www.easysurf.cc/cnver24.htm or some other source for unit
conversions.)

1. GCR in free space at solar minimum is found from several sources:
a. Rapp 2006 says 0.5 - 0.7 Sv per year; this is 50 - 70 rem/yr.
b. TM104782 says 60 rem/yr.
c. OSIRIS calculates 874 mSv/yr; this is 87.4 rem/yr.
d. SP-368 claims 1.0 mrad/hr; this is 24 mrad/day, or 87.6 rad/yr.

So, we have general consensus from multiple sources that our starting
dosage is somewhere in the 50-87 range in free space.

2. Does L4 or L5 really count as free space? The magnetosphere extends
to about 90,000 km on the day side of the Earth, but L4 and L5 are at
the same distance as the Moon, about 384,400 km. On the night side, the
magnetosphere has a long tail that extends millions of miles, but it's
quite weak by that point. The Van Allen belts extend to about 63,000
cm, so again, this is well short of L4/L5. Finally, OSIRIS calculates
GCR exposure on the Moon as 47 rem/yr, and this is with the Moon
blocking half the sky. So, yeah, I think the free-space calculations apply.

3. OK then, the next big question is: how much is this GCR radiation
attenuated by shielding? We have to be careful here not to use
attenuation rates found for SPE or trapped particles, as those both have
much lower energies than GCR particles, and are much easier to stop.
I've found two references with figures on this:

a. JSC Tech Memo 104782 (see Figure 6):
http://srag-nt.jsc.nasa.gov/Publications/TM104782/techmemo.htm
This shows attenuation for three different materials (Aluminum, Water,
and liquid H2). Let's focus on water, the middle performer by mass
(though it'd be interesting to convert these to depth and see how they
compare). The chart only extends to 50 g/cm^2, which is 500 kg/m^2 or
half a ton per square meter. At that point, GCR dosage has been reduced
from over 60 rem/yr to about 22 rem/yr. But the curve has flattened out
quite a bit by this point, and we have a long way to go to the 0.5
rem/yr target.

b. Rapp 2006:
http://www.marsjournal.org/contents/2006/0004/files/rapp_mars_2006_0004.pdf
This paper provides a similar graph as Figure 1, showing the dose
equivalent rate in tissues 5 cm deep, with shielding of 6 different
materials from Al to Li hydride. Again water is in the middle, so let's
start there. At 50 g/cm^2 (half a ton per m^2), the limit of this
graph, our dose equivalent rate looks to be about 22 rem/yr (again).

So, these two sources agree, but either goes nearly far enough. So I
did an approximate curve fit and attempted to extend it out -- but this
is quite likely where I introduced an error.

I've just tracked down the source for that figure; it's from NASA
Conference Publication 3360:
http://www.kiss.caltech.edu/workshops/space-challenge2011/references/radiation/Shielding%20Strategies%20for%20Human%20Space%20Exploration_Wilson.pdf

This is a thick book, and I'll need time to go through it more
carefully. A quick skim finds several similar figures, where they're
concerned with getting the dosage down only to "astronaut" standards (50
rem/yr) rather than general-population standards (0.5 rem/yr). But I'll
keep digging.

I guess this is the key bit... if anybody can find a figure (or even
better, a formula) for estimating the GCR attenuation effect of LARGE
amounts of shielding, i.e. tons per square meter, please share.

Meanwhile, I see that a lot of the original research done on this topic
has been done by Lisa Simonsen at Langley. Once I've studied this book,
if still clueless, I'll write to her and see if she can help.

Thanks,
- Joe