Re: Why do cosmic rays do so little damage?

Here is one reference to hopefully answer your question:
The Earth, and all living things on it, are constantly bombarded by 
radiation from outer space. This radiation primarily consists of 
positively charged ions from protons to iron nuclei derived from the sun 
and from other sources outside our solar system. This radiation interacts 
with atoms in the atmosphere to create secondary radiation, including X-
rays, muons, protons, alpha particles, pions, electrons, and neutrons. The 
immediate dose from cosmic radiation is largely from muons, neutrons, and 
electrons, and this dose varies in different parts of the world based 
largely on the geomagnetic field and altitude. This radiation is much more 
intense in the upper troposphere, c. 10km altitude, and is thus of 
particular concern for airline crews and frequent passengers, who spend 
many hours per year in this environment. Here, the radiation exposure is 
not primarily due to the cosmic ray interaction with the thin atmosphere, 
but with the dense fuselage of the aircraft, causing relatively high 
background radiation in the cabin while the aircraft is at high altitude. 
Similarly, cosmic ray interaction with spacecraft components produces 
secondary radiation that causes higher background exposure in astronauts 
than in humans on the surface of Earth. Astronauts in low orbits, such as 
in the International Space Station or the Space Shuttle, are at low risk 
because the magnetic field of the Earth shields out most cosmic rays. 
Outside low Earth orbit, as experienced by the Apollo astronauts who 
travelled to the moon, this background radiation is much more intense, and 
represents a considerable obstactle to potential future long term human 
exploration of the moon or Mars.
Cosmic rays also cause elemental transmutation in the atmosphere, in which 
secondary radiation generated by the cosmic rays combine with atomic 
nuclei in the atmosphere to generate different radioactive isotopes. Many 
so-called cosmogenic nuclides can be produced, but probably the most 
notable is carbon-14, which is produced by interactions with nitrogen 
atoms. These cosmogenic nuclides eventually reach the earth's surface and 
can be incorporated into living organisms. The production of these 
nuclides varies slightly with short-term variations in solar cosmic ray 
flux, but is considered practically constant over long scales of thousands 
to millions of years. The constant production, incorporation into 
organisms and relatively short half-life of carbon-14 are the principles 
used in radiocarbon dating of ancient biological materials such as wooden 
artifacts or human remains.

Another reference writes....
Cosmic rays may prevent long-haul space travel
The radiation encountered on a journey to Mars and back could well kill 
space travellers, experts have warned. Astronauts would be bombarded by so 
much cosmic radiation that one in 10 of them could die from cancer.
The crew of any mission to Mars would also suffer increased risks of eye 
cataracts, loss of fertility and genetic defects in their children, 
according to a study by the US Federal Aviation Administration (FAA).
Cosmic rays, which come from outer space and solar flares, are now 
regarded as a potential limiting factor for space travel. "I do not see 
how the problem of this hostile radiation environment can be easily 
overcome in the future," says Keran O'Brien, a space physicist from 
Northern Arizona University, US.
"A massive spacecraft built on the moon might possibly be constructed so 
that the shielding would reduce the radiation hazard," he told New 
Scientist. But even so he reckons that humans will be unable to travel 
more than 75 million kilometres (47 million miles) on a space mission – 
about half the distance from the Earth to the Sun. This allowance might 
get them to Mars or Venus, but not to Jupiter or Saturn.
Risky business
Helped by O'Brien, the FAA's Civil Aerospace Medical Institute in Oklahoma 
City investigated the radiation doses likely to be received by people on a 
2.7-year return trip to Mars, including a stay of more than a year on the 
planet. The study estimated that individual doses would end up being very 
high, at 2.26 sieverts.
This is enough to give 10% of men and 17% of women aged between 25 and 
34 lethal cancers later in their lives, it concludes. The risks are much 
higher than the 3% maximum recommended for astronauts throughout their 
careers by the US National Council on Radiation Protection and 
Measurements.
The risks are smaller for older people because cancers have less time to 
develop. But women are always in more danger than men because they live 
longer and are more susceptible to breast and ovarian cancers.
The study warns that cosmic rays would also increase the risk of cataracts 
clouding the eyes. Furthermore, men exposed to a solar flare might suffer 
a temporary reduction in fertility, and the chances that any children 
conceived by travellers to Mars will have genetic defects are put at 
around 1%.
Serious brain damage
The study's lead author, the FAA's Wallace Friedberg, highlights other 
work suggesting that heavy nuclei in cosmic radiation cause "serious brain 
damage" in mice, leading to memory loss. "Heavy nuclei exposure must be a 
serious consideration for space missions such as a trip to Mars," he says.
Improving spaceships' shielding by using water, hydrogen or plastics can 
protect astronauts to some extent. But this is limited by the 
constrictions of craft weight and design, Friedberg points out. 
"Increased speed would also reduce radiation exposure" by reducing journey 
times, he notes. "And drugs or food supplements that can reverse radiation 
damage are being considered."
Others suggest more radical solutions might be needed. "Radiation exposure 
is certainly one of the major problems facing future interplanetary space 
travellers," says Murdoch Baxter, founding editor of the Journal of 
Environmental Radioactivity. "Unless we can develop instantaneous time and 
space transfer technologies like Dr Who’s TARDIS."
Journal reference: Radioactivity in the Environment (vol 7, p 894)

Another reference is:
 http://www.sirr.unina.it/Asi/collegamenti/Introduction/introduction.ht
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