Calculating radiation dose from flux

[Walternate]

Hi!
Hopefully I'm not being too stupid, but I'm trying to work out the radiation dose received at a particular point in space being subjected to a high rate of proton flux.

I think.. that I am right in working it out this way so far, for instance if the flux rate of Protons >100Mev is 10^7 cm3 s-1

(100*10^6 ev) * (10^7 cm3 s-1) * (1.602×10^−19 Joules) = 1.602*10^-4 Joules cm3 s-1

Based on 1cm3 of body mass being 1g then:

(1.602*10^-4)*1000g = 0.1602 Joules/Kg (s-1)

= 0.1602 Gy (s-1)

0.1602 * 5 Proton Q.F. = 0.801 Sv (s-1)

So would the calculations be correct in stating that if you were suspended in an area of space with a Proton flux of 10^7 cm3 s-1 with proton energies of 100Mev you would be receiving an effective dose of 0.801 Sv / Second ?

It's probably all garbage, but if anyone can help I would be most grateful :)

Thanks!

 

[Bob S]

Here is a very rough calculation of the radiation dose from 100 MeV protons.

First, the proper unit of radiation dose is rads or Grays (energy deposited). 1 rad = 100 ergs per gram, and 1 rad = 0.01 gray. For 100 MeV protons, the entire dose is due to ionization (protons colliding with atomic electrons). See Equation 27.3 (Bethe Bloch equation) in

http://pdg.ihep.su/2009/reviews/rpp2009-rev-passage-particles-matter.pdf

Figure 27.2 shows dE/dx as a function of βγ. For a 100-MeV proton,

βγ = [(100 + 938)² - 938²]/938² = 0.22.

Note the Bragg peak on the left.

So for carbon in Fig.27.2, dE/dx = ~10 MeV per gram/cm² = 10⁷ eV per gram/cm²

So if we have a proton flux of 10⁷ protons per cm² per sec,

the radiation dose is

dose = [10⁷protons/(cm²sec)][10⁷eV-cm²/proton-gram][1.6 x 10^-12 ergs/eV][1 rad-gram/100 ergs]=

= [10⁷[STRIKE]protons[/STRIKE]/([STRIKE]cm²[/STRIKE]sec)][10⁷[STRIKE]eV[/STRIKE]-[STRIKE]cm<sup>2[/SUP[/STRIKE]]/[STRIKE]proton[/STRIKE]-[STRIKE]gram[/STRIKE]][1.6 x 10-12 [STRIKE]ergs[/STRIKE]/[STRIKE]eV[/STRIKE]][1 rad-[STRIKE]gram[/STRIKE]/100 [STRIKE]ergs[/STRIKE]] = 1.6 rads/sec

I don't have the dE/dx for tissue at 100 MeV, but it is close to carbon. I am also not aware of how quality factors are applied to protons in this calculation, because it is usually included in dE/dx. I hope this helps.

Bob S</sup>

 

[Walternate]

Thank you Bob :) I can see I was way off with what I was trying to do then. I'm not sure where I got cm3 for flux either, I should have spotted that really! I imagine flux is measured through a 2 dimensional plane?
I will have a read of what you posted for me so thank you! But I think I am a little way off being able to calculate what I was trying to do in all honestly.

 

[Bob S]

Note error in my previous post for the equation and value of βγ at 100 MeV.

the correct equation and value is βγ = sqrt{ [(100 + 938)² - 938²]/938²} = 0.47.

This reduces dE/dx of 100 MeV protons in carbon to about 6 MeV per gram/cm², and the rad dose at 100 MeV to about 1 rad per second..

I attach a thumbnail of proton dE/dx in water (similar to tissue). dE/dx = 7.28 MeV per gram/cm² at 100 MeV.

Bob S