(3.5)
An informative discussion of air activation around electron accelerators is given by Swanson (1979b). Swanson details the various production processes and yields. In common with most accelerator activation, the radioactive products from air are rather limited in number and toxicity and also generally have rather short mean lives. The production of radionuclides by the CEBAF accelerator is discussed by Stapleton (1987b) and with regard to the end stations by May et al. (1997). The radionuclides that can be identified from photo-production and neutron activation are set out in Table 3.5a and 3.5b.
Table 3.5a - Radioactive Products Produced by Photoproduction in Air
Radio Decay Half life Dec Const DAC(a) Prod Term B Nuclide Mode (1/sec) (Bq/m3) (Bq/kW-m) ------------------------------------------------------------------------- H - 3b - 12.3 yr 1.79E-09 8.0E+05(b) 7.1E+06 Be - 7g EC 54 day 1.49E-07 3.0E+05 1.1E+06 C - 11b + 20.5 min 5.64E-04 1.0E+05 1.1E+07 N - 13b + 10 min 1.16E-03 1.0E+05 1.1E+08 O - 15b + 2.1 min 5.50E-03 1.0E+05 5.6E+07 Cl - 38b -,g 37 min 3.12E-04 1.0E+05 6.8E+05 Cl - 39b -,g 55 min 2.10E-04 not listed 8.5E+06
Table 3.5b - Radioactive Products Produced by Neutron Activation in Air
Radio Decay Half life Dec Const DACa Prod Term B Nuclide Mode (1/sec) (Bq/m3) (Bq/kW-m) ------------------------------------------------------------------------- H - 3(a) data from (FED 1993) - except for H-3 and Be-7, all the DAC's are for immersion in a semi-infinite cloudb - 12.3 yr 1.79E-09 8.0E+05b 1.5E+07 Be - 7g EC 54 day 1.49E-07 3.0E+05 4.5E+06 C - 11b + 20.5 min 5.64E-04 1.0E+05 4.5E+06 N - 13b + 10 min 1.16E-03 1.0E+05 4.9E+06 O - 15b + 2.1 min 5.50E-03 1.0E+05 4.2E+06 Ar - 41b -,g 1.83 hr 1.07E-04 1.0E+05 (c)
An obvious point of concern about occupational exposures to activated air is the derived air concentration (DAC) based on the immersion dose in a semi-infinite cloud. The first question one should ask is how big is a semi infinite cloud of radioactive gases and secondly how can a semi-infinite cloud be sustained by short half life radionuclides? The third question is, if a semi- infinite cloud is not a reasonably achievable model, what is a more likely basis for a DAC standard? These questions are addressed in May et al (1997), and a synopsis is given in this account.
A simple method of determining the dose rate at the center of an infinite cloud is to use energy balance, assuming that the object at the center has similar composition to tissue and the air. This is a reasonable approximation in this case. The theory is that in an infinitely homogeneous and uniformly radioactive medium, the energy absorbed per unit mass is equal to the energy emitted per unit mass. Thus if each gram of the medium emits S photons per second of energy E MeV, then the energy emission rate density is given by S x E (MeV g-1 s-1). As 1 MeV = 1.602 x10-13joule and 1 rad is 10-5 joule g-1 therefore:
(3.5)
For a semi-infinite cloud we take half this result (ignoring the effect of backscatter), to give Dsemi = 1.07 S E. Substituting the values of 0.0025 for D (5 rads per working year) and 2 x 0.51 MeV for the photons from positron annihilation we obtain 0.0023 mCi g-1 which gives 1.06 E+05 (Bq/m3).
For the case of Ar-41, which is not a positron emitter, the photon energy per disintegration is 1.28 MeV, thus we can scale the positron result to give the Ar-41 result in proportion to photon energy per disintegration: 1.02/1.28 x 1.06 E+05 = 8.45 E+04. The result for Ar-41 is also reasonably close to the 1.0 E+05 DAC value listed.
Thus using a simple method we have verified the DAC values given in reference FED 1993.
However, this does not tell us how large the semi-infinite cloud might be and what the dose rate
might be at the center of a much more realistically sized cloud. To do this we use a very
approximate shielding procedure illustrated by Figure 3.1, which shows the coordinates of an
elementary volume dV of a hemispherical cloud centered on point P.
Figure 3.1 Geometry for Estimating The Dose at P for Various Hemispherical Cloud Sizes
where:
S = activity per unit volume
SdV = activity in vol element dV
K = k factor (dose rate rem h-1 at 1 m per curie (Barbier 1969c)
analogous to G used in equation 3.3)
For positron emitters, K is 0.515 and for Ar-41 K is 0.645, now dose at P due to SdV is given by:
(3.6)
where m (mu) is a photon attenuation coefficient for air, and
(3.7)
hence:
(3.8)
(3.9)
Because of problems in the use of build up factors for deep penetration problems we derive an "effective" m (mu) by solving the above equation using [r approaching infinity], and Dp = 0.0025 rad h-1. This results in a value for m (mu) of 3.498x10-3 m-1 for positron decay photons and 4.381x10-3 m-1 for Ar-41 photons. At smaller distances this probably gives reduced dose rates but not unreasonably so in the context. Therefore, solution of this equation gives the dose rate corresponding to hemispherical clouds of different radii. The result is illustrated in Figure 3.2, which shows that to achieve the regulatory DAC value the cloud would have to be over a km in radius! For realistically sized clouds that could be contained by a building or hall of say 30 m radius the dose rate would only be 0.00025 radh-1 or 1/10 the dose rate for a semi-infinite cloud. Thus the immersion DAC would be much higher so that other limiting factors should be considered such as skin dose. Examples of DACs using hemispherical clouds of different radii are given in column 2 of Table 3.7.
Before leaving the discussion of a large cloud immersion dose let us consider by way of illustration the hypothetical case of a worker standing near an exhaust port from an accelerator vault containing air with radioactive gas concentrations at the level of 1 DAC (immersion in a semi-infinite cloud). Assuming still air and no mixing in the growing bubble of radioactive gas, we can take some account of the effect of radioactive decay on the radiation received by the worker.
Now because we assume that the radionuclides, at any given point within the hemisphere decay as the bubble expands, then
(3.10)
where
S(t) = volume specific activity at t after injection into the bubble
S0 = volume specific activity at time of injection into the bubble
Let L be the rate of air loss from the hall, then for a hemispherical volume:
(3.11)
hence:
(3.12)
substituting into equation (3.6):
(3.13)
(3.14)
(3.15)
With the other variables the same as before we can now solve this integral (3.15) over r numerically, for different values of L and mean life decay. We chose make up rates of 10 and 100 m3 min-1 to span what might be considered realistic numbers and further we include a make up rate of 1000 m3 min-1 to show what the result would be under absurdly extreme conditions. The results presented in Figure 3.3, using only the positron emitting radionuclides, show that for reasonable make up rates the equilibrium sized cloud would only be between 4 and 12 m radius giving dose rates between 2x10-5 and 8x10-5 rads per hour.
Having established the lack of realism in the use of immersion dose rates let us now examine the limits for skin and eye exposure. The equation derived earlier for an infinite cloud for photons can be used with caution for betas where is the mean beta energy: Db ~ 2.13 S (rad h-1 per mCi g-1). Converting to Bq/m3 and for an infinite cloud (which for betas is quite small), applying in this case a 0.5 factor for exposure to the skin being on one side only and a further correction for beta absorption in the basal layer of skin we obtain:
(3.16)
Now applying 70 mm as the approximate thickness of the basal layer of skin and m in the above equation which varies with mean beta energy, we calculate the DAC using an annual limit of exposure of 50 rem (0.025 rem/hour) for skin. For the lens of the eye we must apply the thickness of the cornea and aqueous humor which we take to be 3000 mm, we calculate the eye DAC using an annual limit on exposure of 15 rem. The data for both the skin and eye are given in Table 3.6. From this table we note that the skin dose is limiting.
Table 3.6 - Estimated DAC for Beta Irradiation of the Skin and Eye Using Correction for
Basal Layer of Skin and a Correction for Cornea and Aqueous Humor for the Eye
Nuclide Eavg,b Approx. m (mu) DAC - Skin DAC - Eye
(MeV) (cm-1) (Bq/m3) (Bq/m3)
C-11 0.385 12 3.1E+06 3.1E+07
N-13 0.491 9 2.4E+06 1.0E+07
O-15 0.734 5.4 1.5E+06 2.2E+06
Ar-41 0.460 10 2.5E+06 1.4E+07
Table 3.7 Immersion DACs for Various Cloud Radii Together with DACs Where Skin
Dose is Limiting* (Positron Emitting Radionuclides)
Radius of DAC immers | Skin Dose DAC Crit Organ
Cloud r (m) WB only | (Bq m-3 per 25 mrad h-1)
(Bq m-3 per | C -11 N -13 O - 15
2.5 mrad h-1) |beta only beta+phot beta only beta+phot beta only beta+phot
1 2.9E+07 3.8E+06 3.8E+06 3.4E+06 3.4E+06 3.1E+06 3.1E+06
2 1.4E+07 3.2E+06 3.1E+06 2.6E+06 2.5E+06 2.1E+06 2.0E+06
3 9.6E+06 3.1E+06 3.0E+06 2.4E+06 2.3E+06 1.8E+06 1.7E+06
4 7.2E+06 3.0E+06 2.9E+06 2.4E+06 2.3E+06 1.6E+06 1.6E+06
5 5.8E+06 3.0E+06 2.9E+06 2.3E+06 2.2E+06 1.6E+06 1.5E+06
6 4.8E+06 3.0E+06 2.8E+06 2.3E+06 2.2E+06 1.5E+06 1.5E+06
7 4.1E+06 3.0E+06 2.8E+06 2.3E+06 2.2E+06 1.5E+06 1.5E+06
8 3.6E+06 3.0E+06 2.8E+06 2.3E+06 2.2E+06 1.5E+06 1.5E+06
9 3.2E+06 3.0E+06 2.8E+06 2.3E+06 2.2E+06 1.5E+06 1.5E+06
10 2.9E+06 3.0E+06 2.7E+06 2.3E+06 2.2E+06 1.5E+06 1.4E+06
11 2.6E+06 3.0E+06 2.7E+06 2.3E+06 2.1E+06 1.5E+06 1.4E+06
12 2.4E+06 3.0E+06 2.7E+06 2.3E+06 2.1E+06 1.5E+06 1.4E+06
13 2.2E+06 3.0E+06 2.7E+06 2.3E+06 2.1E+06 1.5E+06 1.4E+06
14 2.1E+06 3.0E+06 2.6E+06 2.3E+06 2.1E+06 1.5E+06 1.4E+06
15 2.0E+06 3.0E+06 2.6E+06 2.3E+06 2.1E+06 1.5E+06 1.4E+06
16 1.8E+06 3.0E+06 2.6E+06 2.3E+06 2.1E+06 1.5E+06 1.4E+06
17 1.7E+06 3.0E+06 2.6E+06 2.3E+06 2.0E+06 1.5E+06 1.4E+06
18 1.6E+06 3.0E+06 2.6E+06 2.3E+06 2.0E+06 1.5E+06 1.4E+06
19 1.6E+06 3.0E+06 2.5E+06 2.3E+06 2.0E+06 1.5E+06 1.4E+06
20 1.5E+06 3.0E+06 2.5E+06 2.3E+06 2.0E+06 1.5E+06 1.4E+06
Table 3.7 Cont. Immersion DACs for Various Cloud Radii Together with DACs Where
Skin Dose is Limiting* (Ar-41)
Radius of Cloud r (m) DAC immers WB only | DAC Skin Dose Crit Organ (Bq m-3 per 25 mrad h-1)
(Bq m-3 per 2.5 mrad h-1) | Ar-41 Ar-41
| beta only beta+phot
1 2.3E+07 3.6E+06 3.5E+06
2 1.1E+07 2.8E+06 2.7E+06
3 7.7E+06 2.6E+06 2.5E+06
4 5.8E+06 2.6E+06 2.4E+06
5 4.6E+06 2.5E+06 2.4E+06
6 3.9E+06 2.5E+06 2.4E+06
7 3.3E+06 2.5E+06 2.4E+06
8 2.9E+06 2.5E+06 2.3E+06
9 2.6E+06 2.5E+06 2.3E+06
10 2.3E+06 2.5E+06 2.3E+06
11 2.1E+06 2.5E+06 2.3E+06
12 2.0E+06 2.5E+06 2.2E+06
13 1.8E+06 2.5E+06 2.2E+06
14 1.7E+06 2.5E+06 2.2E+06
15 1.6E+06 2.5E+06 2.2E+06
16 1.5E+06 2.5E+06 2.2E+06
17 1.4E+06 2.5E+06 2.1E+06
18 1.3E+06 2.5E+06 2.1E+06
19 1.3E+06 2.5E+06 2.1E+06
20 1.2E+06 2.5E+06 2.1E+06
* the beta+photon dose is to the skin only - no whole body contribution included
From this data we can see the cloud size where the skin dose becomes limiting, the case for O-15
gives the smallest DAC and could represent the most conservative result.
Conclusions to be drawn from this simplified analysis is that for the radionuclides that are currently regulated on the basis of immersion in an infinite cloud, a more appropriate standard for accelerators is on the basis of the maximum size cloud that the accelerator vault can hold and then to consider whether the immersion dose is limiting or the skin dose. The tables provide some indication of the appropriate DAC to be used in given circumstances.
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