# Calculating radiation dose from flux

1. Aug 18, 2010

### 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!

Last edited: Aug 18, 2010
2. Aug 18, 2010

### 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,

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

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

3. Aug 19, 2010

### 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.

4. Aug 19, 2010

### 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

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Last edited: Aug 19, 2010