Composition of cosmic radiation:
93 % protons
6.4 % alpha-particles (He-ions)
0.6 % other ions like Li, B and Bi
Enegry of cosmic radiation:
100000000 eV to 100000000000000000000 eV
Due to their very high enery these ions create secondary radition when entering the earths atmosphere. From 4 km to 20 km this secondary radition does mainly consist of electrons, positrons and photons.
Shielding:
Alpha particles will be absorbed by a sheet of paper. Of course this depends on their energy. But I am confident that ions will be absorbed by all the metal around you.
Eletrons and positrons on the other way will not be entirely absorbed by a piece of paper. You would need some layers of metal. Most of them will probably be absorbed by all the stuff around you. So I would not worry too much about them too.
Unfortunately photons (also called gamma rays or x-rays) are more or less unimpressed by all the stuff around you. You would need massive shields (for example thick lead sheets) to get rid of them. So you will be bombarded by photons when flying around. These photons will produce tertiary radiation when colliding with other atoms (e.g. in you body) which then can create damage to you DNA. The amount on damage depends on the mass and energy and biologic material. A good indicator is the amount of energy these particles deposit in you body multiplicated by a factor depending on the particle. This will get you an energy in the unit Sievert (Sv).
Now you will get these photons when being on the ground. So the question is, how much more energy you will get when flying around in the stratosphere.
If you are sitting around (which means you are not working with nuclear materials) you will get 2.4 mSv in a year. These are 0.0024 Sv.
Now let's compare:
teaching nuclear physics one year 0.00001 Sv
sitting around one year 0.00240 Sv
x-ray stommach 0.00380 Sv
smoking one year 0.00880 Sv
Results in you body:
changes in blood 0.2500 Sv
temporary radiation sickness 1.0000 Sv
really serious radiation sickness 4.0000 Sv
death 8.0000 Sv
Of cours if you get 0.25 Sv in 10 years you will not get blood changes. But if you get them in a short time, you will probably get them. But it's not that easy to say how short the time should be. In any way you should think about adding the energies over time. At the moment we assume a linear relationship between energy dose (Sv) and the probability for cancer. Although this can probably change when looking at small amounts of energy.
Allowed exposure in one year:
people working in exposed areas 0.0200 Sv
anybody else 0.0100 Sv
Life long exposure limit for exposed workes:
0.400 mSv
Conclusion:
If I would be flying around professionally (I am not, I am just teaching around;-), I would make the following calculation:
Energy dose "available" for flying aournd, assuming that I want to become 100 years old:
0.400 Sv - 100 x 0.00240 Sv = 0.1600 Sv
Then I would take a look at the online calculator for energy doses:
http://jag.cami.jccbi.gov./cariprofile.asp
This gives me a dose of 0.0001 Sv for a 40.000 ft 12 hour flight from FRA to LAX in February.
Which means that I could do this flight
0.1600 Sv / 0.0001 Sv = 1600 times
That sounds a lot, but you know better than I how many flights you do in your professional life. And please beware, that energy doses can be much higher when...
...flying higher
...flying during solar activity
...flying northern (on northern hemisphere) or southern (on southern hemisphere)
Suggestion:
Take the FAA energy dose calculator (URL provided above) and log your exposure before each flight. You will then be able to know when you have exceeded the official lifetime limit.
I hope all of this made any sense... Greetings, DRDR.