Calculation of the Activation of Beam Dump Materials

B. Naumann and W. Neubert

The GEANT 3.21 program package allows to calculate the bremsstrahlung photon yields in electron-nucleus interactions [1] but not secondary reactions induced by photons like (g,n). In order to calculate the activation of different dump materials (e.g. C, Al, Cu, Cr, Ni, Mn, Fe) by such processes a special procedure explained in the following has been performed. In these calculations the corresponding (g,n)-cross sections are required. Most of these data are available in [2,3], the cross section of iron was taken from [4]. The saturation activity of a given radioactive nucleus is calculated by

dN
dt




  
  =  I ·NZ Eg,max


0 
Fg(Egsg,n(Eg) dEg, (1)

where I is the beam current and NZ is the number of stable nuclei in the probe irradiated by the photon fluence Fg. In a first approximation, the fluence Fg was calculated as the number of photons per energy bin which transmit the surface of the considered probe. The known half-life of the isotope allows to calculate the activity N(t) at a given time.

Furthermore, activation by radiative capture of the complementary produced neutrons has also been taken into account by using the (n,g) cross section data from [9]. The calculation of the neutron production in the graphite core of the beam dump are based on simulations with the MCNP program package ([5]), which were found to be in agreement with estimates in [6]. The obtained neutron yield was transformed into an energy spectrum (Watt distribution)

W(En) = C · e -a · En · sinh(b · En) 1/2.

The parameters a and b were obtained from fits to the photoneutron spectra of C, Cr and Au reported in [7].

Additionally, the production rate of radioactive nuclei induced by the radiative neutron capture was calculated in analogy to equation (1), where Fg(Eg), sg,n(Eg) and dEg were replaced by Fn(En), sn,g(En) and dEn, respectively.

We considered the activity of 60Co which is assumed to be produced in the energy domain of the ELBE accelerator mainly via the reaction 63Cu(n,a)60Co by photoneutrons. In the calculations we used cross sections available in [8,9]. A saturation activity of about 2.1 · 1012 Bq is expected for the 2 cm thick copper coating provided for cooling of the beam dump core as presented in [1]. The production of 24Na in the reaction 27Al(n,a)24Na calculated by the same method yields a similar activity.
A complete representation of the results is given in [10].

References

[1] B. Naumann et al., A Possible Beam Dump Design for Intense Electron Beams, this Report p. 36

[2] S. S. Dietrich and B. L. Berman, Atomic and Nuclear Data Tables, 38 (1988) 199.

[3] EXFOR Data basis, http://www.nea.fr./html/dbdata/x4.

[4] S. Costa et al., Nuovo Cimento 51B (1967) 199.

[5] H. Kumpf, FZR Internal report, Institute of Safety Research, 17.6.1998.

[6] W. P. Swanson , IAEA Technical Reports Series No.188, Vienna 1979.

[7] M. Barbier, Induced Radiactivity, North Holland Publishing Company, Amsterdam 1969.

[8] P. Jessen et al., Nuclear Data A1 (1966) 103.

[9] ENDF (evaluated nuclear data files) of the NDS online Data Service,
http://www-nds.iaea.org/.

[10] B. Naumann, W. Neubert and D. Pröhl, FZR Report FZR-267, Juli 1999.

FZR
 IKH 10/25/99 © B. Naumann