Methodology for Calculating Skyshine Radiation

 

I.       Introduction

Radiation emitted in an upward direction within the accelerator enclosure can scatter off ceiling and air, and produce radiation exposure to personnel working inside or outside the building.  Both photons and neutrons must be considered.

 

 NCRP-51 [Ref. 14, p. 68] provides an expression for calculating the skyshine dose rate Ds,x  for x-rays for distances out to 250 m:

Ds,x  = 2.5 x 10-2 D0 W1.3 /d2    mrem/hr                                    (1)

where W (sr) is the solid angle subtended at the source by the periphery of the shielding walls, D0 is the x-ray source dose rate at 1 meter in the vertical direction calculated for each source (rad m2/hr) and d is the straight line distance (m) between the source and point where the dose rate is to be evaluated. 

 

The solid angle W subtended at a point within an enclosure bounded by shielding in the form of a polygon of L lines at height H above the point has been evaluated [19] by numerical integration of the solid angle increment dW = sinqdqdf and is summarized below for several points of interest within the enclosure.

 

                  Point                                                                                              W(Sr)

                  Beam Dumps (Normal full beam loss point)                         1.71

                  After 1st Bend Magnet  (Dump for failure of bend magnet)  3.90

                  Diagnostic Flag (upstream of 1st Bend Magnet)                               4.29

                  End of linac tank 4                                                              3.88

                  Compressor Flag (Energy selection slit)                                           3.81

            Electron Gun                                                                                  3.57

 

Using the value of W for the source being evaluated and the distance d to the control console (location of highest expected occupancy), we can obtain the X-Ray skyshine dose rate.

 

For neutron skyshine, NCRP-51 [Ref. 14, p. 69] provides a formulation for calculating the scattered neutron flux rate Fsn at any point within 20 m of the source point as:

Fsn = 5.4 x 10-4 F0 W /2P   n cm2 / s                             (2)  

where F0 is the fluence at one meter from the source and  W is the solid angle previously discussed.   In calculating the skyshine dose equivalent for neutrons within the building using this equation, we make two assumptions: a) the high energy neutron fluence will not appreciably contribute to the skyshine within the building and that the neutron spectrum does not appreciably soften in the scattering from the walls, ceiling, and floor.  We can then convert the fluence in equation 2 to:

H ss,n =  5.4 x 10-4 H0 W/2p                                                     (3)

where H0 is the calculated giant resonance neutron dose equivalent rate vertically at  one meter for the source.

 

For calculating skyshine at distances greater than 20 meters, NCRP-51 [Ref. 14, p. 69] provides the following formula:

Fsn(d) = 6.5 x 10-2 F0 W /2P d1.6  n cm2 / s                             (4)

 

where d is the distance in meters to the location being evaluated, and the other variables are as previously defined.

 

Another useful method for estimating neutron skyshine is provided by Alsmiller et al (Ref . 26).  In this paper, a series of importance functions are tabulated which permit evaluation of skyshine at various distances from the source.  To use the importance functions, the neutron fluence in various energy bins and the angle of emission relative to vertical must be determined.  With these values, the neutron dose equivalent at various distances can be directly calculated.

 

Both methods were used when skyshine was calculated, the higher value of the 2 methods was used.  There was good agreement between the methods is each calculation.

 

 

 

II.                 Sample  Calculations

 

A.     Neutrons

 

We have calculated the neutron emission rate from various sources in appendix 9. The values at 300 MeV for the faraday cup are summarized below:

 

Table I

 

Neutron Yields at 1 m at 90o from 20 nA beam loss in the Faraday Cup

Fluence [n/cm2- s (x 103)]

 

Energy [300 MeV]

GRN

HEN

F0 (90o)

24

1.3

 

 

Above the dump 12" of borated polyethylene is provided which will remove a considerable fraction of the GRN and a less significant fraction of the HEN.  Moe (Ref . 25) provides the attenuation lengths that can be used to re-calculate the neutron fluence at one meter taking into account the polyethylene.  The attenuation length (l) in borated polyethylene for GRN is 6.3 g/cm2 and for HEN is 62 g/cm2.  Calculating these attenuation for 12" of polyethylene, we get:

 

12" x 2.54 cm/in x 0.95 g/cm3 = 28.95 g/cm2     of borated polyethylene               (5)

 

which is 4.6 l for GRN and 0.47 l for HEN.  Using the expression:

 

F = F0e-x/l                                                                                        (6)

 

we obtain the reduced fluences shown in following table:

 

Table II

 

Neutron Yields  through 12" of polyethylene at 1 m at 90o from 20 nA beam loss in the Faraday Cup     Fluence [n/cm2- s (x 102)]

 

Energy [300 MeV]

GRN

HEN

F0 (90o)

2.4

8.2

 

 

 

We can now calculate the neutron skyshine within the building using these source terms and the two different methodologies.  Using equation (2) where F0 = 2.4 x 102 n/cm2- s and W = 1.7 SR

 

Fsn = 5.4 x 10-4 x 2.4 x 102 x 1.7 /2P  = 3.5 x 10-2   n cm2 / s                (7)  

 

Assuming that the scattered neutrons have an energy of  about 1 MeV and using 7 n/cm2- s = 1 mRem/hr, we get

Hsn = 5  x 10-3   mRem/hr                                             (8)

 

Assuming 2000 hours per year of operation, skyshine would result in an annual dose equivalent from neutrons of 10 mRem/year.

 

As a separate check, the internal skyshine dose can also be calculated using the importance functions provided by Alsmiller (Ref. 26). Using these values, we calculate a total neutron skyshine dose equivalent rate = 5.5 x 10-3 mRem/hr from the dump, in good agreement with the previous calculation.

 

We can use the same formulation to calculate the skyshine dose in near-by buildings.  The nearest non- NSLS buildings are Building 535, Building 480, and Building 356; all of which are greater than 100 meters.  Using equation (4) we can calculate the neutron dose equivalent rate to be:

 

Fsn(100 m) = 6.5 x 10-2 x 10.6  x 102  x 1.71 /2P 1001.6  n cm2 / s                  (9)

 

Fsn(100 m) = 1.18 x 10-2 n cm2 / s                                     (10)

 

Hsn(100m) = 1.7  x 10-3   mRem/hr                                           (11)

 

Using Alsmiller's importance functions for this source, we obtain

Hsn(100m) = 0.87  x 10-3   mRem/hr                                         (12)

 

in good agreement with the previous calculation.  Assuming 2000 hours per year operation of the dumps, and using the higher value, we would expect the total neutron dose equivalent to be less 3.4 mRem/year at distances beyond 100 m.              

 

B.     X-rays

 

We can calculate the x-ray shine using equation (1) and source terms calculated using the methodology of appendix 9.  For the FEL stop, we have Do =  11.6 mR/hr, W = 1.71 SR,  and d= 9.75 meters to the desk area at the west end of the building.  Therefore,

Ds,x  (9.75m) = 2.5 x 10-2 x 11.6 x (1.7)1.3 /(9.75)2    mrem/hr   (13)

 

Ds,x  = 6.1  x 10-3   mRem/hr                                                     (14)

 

The skyshine at 100 m from this source would be:

Ds,x  (100 m) = 2.5 x 10-2 x 11.6 x (1.7)1.3 /(100)2    mrem/hr                (15)

 

Or                          Ds,x  (100 m) = 0.58 x 10-3  mrem/hr                                   (16)

 

We can now calculate the total skyshine dose within the building and at 100 m by adding the x-ray and neutron source terms:

(at 9.75 m) HT = 5.5 x 10-3  mrem/hr + 6.1  x 10-3  mRem/hr = 11.6 x 10-3   mRem/hr   (17)

 

Assuming 2000 hours a year, we get an annual skyshine dose from this source of  23 mRem per year.

(at 100 m) HT = 1.7 x 10-3  mrem/hr + 0.58  x 10-3   mRem/hr = 2.3 x 10-3   mRem/hr   (18)

 

Assuming 2000 hours a year, we get an annual skyshine dose at 100 m from this source of  4.6 mRem per year.

 

Website maintained by Laura Miller.  Revision date: 12/06/2002