10.4.9           Radiation background calculations

10.4.9.1          Energy deposition spectrum from direct ionization

a.              Under the conditions specified in requirement 10.4.2a.1, the energy deposition spectrum from direct ionization shall be calculated by using one of the following formulas:

1.              From direct ionization, by one of the following formulas:

o               Detailed calculation:     

o               Approximated calculation:        

where:

dY/de(e)          = energy deposition rate spectrum;

A                      = total surface area of the SV or detector;

dΦ/dE(E)        = differential incident particle flux spectrum expressed as a function of energy, E;

dPCL/dD(D)     = differential chord length distribution through the sensitive volume for an isotropic distribution;

dE/dx(E)         = stopping power for particles of energy E;

Emin                  = minimum energy for the incident particle spectrum;

Emax                  = maximum energy of the incident particle spectrum.

NOTE              This expression assumes the incident particle spectrum on the detector is or can be approximated to a isotropic angular distribution. Furthermore, it is assumed that the change in the stopping power of the particle through the sensitive volume and any multiple scattering can be neglected.

2.              For nucleon-nuclear collision-induced energy, by one of the following methods:

(a)            If the dimensions of the detector volume are 10 times (or more) smaller than the ranges and mean-free paths of the incident particles, by using the following formula:            

where:

dY/de(e), A, dΦ/dE(E), dPCL/dD(D), dE/dx(E), Emin, and Emax have the same meaning as in Clause 10.4.9.11, and:

M               =    mass of sensitive volume;

NA             =    Avogadro’s constant;

W              =    atomic or molecular mass of the material making up the detector;

σ(E)           =    nuclear-interaction cross-section for the material as a whole due to incident particles of energy E;

dP/de(E,e) =    energy deposition rate spectrum (or response function) for incident particles of energy E, and energy deposition, e .

(b)           Otherwise, by applying radiation simulation tools agreed with the customer.

NOTE 1      Examples of such tools are Geant4, MCNPX, and FLUKA. More examples can be found in Table 2 of ECSS-E-HB-10-12.

NOTE 2      For a rational and detailed discussion on energy deposition spectrum from direct ionization calculation and nucleon-nuclear interactions, see ECSS-E-HB-10-12, Section 9.2.

10.4.9.2          Nuclear interaction rates

a.              Under the conditions specified in requirement 10.4.4a.1, the nuclear interaction rates in the sensitive volume and surrounding material shall be calculated by the following formula:

where:

Ri(t)              = production rate for nuclide species i at time t;

M                  = mass of detector;

NA                 = Avogadro’s constant;

W                  = atomic or molecular mass of the material making up the detector;

dΦj/dE(E,t)  = differential incident flux spectrum expressed as a function of energy, E and time, t for particle species j (these are both primary and secondary particles);

σj®i(E)          = nuclear-interaction cross-section for the production of nuclide i in the detector material due to incident particle species j of energy E;

Ej,min              = minimum energy for the incident particle spectrum, j;

Ej,max             = maximum energy of the incident particle spectrum j.

NOTE              For a rational and detailed description, see ECSS-E-HB-10-12, Section 9.5.