5.3.19.6. Gaussian and Maxwellian energy distributions¶
5.3.19.6.1. e-type = 2, (12)¶
Differential spectrum dφ/dE(i) is given by Gaussian distribution. For 12 case, energy is given by wave length (A).
eg0 : center of Gaussian distribution [MeV/n].
eg1 : FWHM of Gaussian distribution [MeV/n].
eg2 : minimum cut off for Gaussian distribution [MeV/n].
eg3 : maximum cut off for Gaussian distribution [MeV/n].
5.3.19.6.2. e-type = 3¶
Differential spectrum dφ/dE(i) is given by Maxwellian distribution: \(f(E)=E^a\exp(-E/T)\).
nm : (D=-200) number of energy group. If it is given by positive number, linear interpolation is assumed in a bin. If negative, logarithmic interpolation is assumed in a bin.
et0 : Temperature parameter \(T\) [MeV] given by \(T=kt\). Here, Boltzmann constant is \(k=8.617\times10^{-11}\) [MeV/K] and temperature \(t\) is in units of [K].
et1 : minimum cut off for Maxwellian distribution [MeV/n].
et2 : maximum cut off for Maxwellian distribution [MeV/n].
et3 : (D=0.5) Power index of energy, i.e. parameter \(a\) in the equation above.
5.3.19.6.3. e-type = 7¶
The same energy distribution as in the case of e-type = 3 can be specified. Unlike e-type = 3, the number of source particles generated in each bin is the same for all energy bin, but integrated values of the weight of source particles are adjusted to be proportional to \(f(E)=E^a\exp(-E/T)\). The number of source particles generated in each bin can also be changed by specifying p(i).
nm : (D=-200) Number of energy group. If it is given by positive number, linear interpolation is assumed in a bin. If negative, logarithmic interpolation is assumed in a bin. In the default (p-type=0), equal numbers of particles are generated in each cell. The integrated number of source particles generated in each bin is proportional to p(i).
et0 : temperature parameter \(T\) [MeV].
et1 : minimum cut off for Maxwellian distribution [MeV/n].
et2 : maximum cut off for Maxwellian distribution [MeV/n].
et3 : (D=0.5) Power index of energy, i.e. parameter \(a\) in the equation above.
p-type = 0, 1 : (D=0) generation option.
For 0, p(i)=1 for all i is assumed without the following data.
For 1, p(i) must be given from the next line by the format (p(i),i=1,nm).
The energy distribution of Maxwellian with \(a=0.5\), \(f(E)=\sqrt{E}\exp(-E/T)\), corresponds to the ordinary velocity distribution \(f(v)\) through the relation \(f(E)\,dE \propto f(v)\,dv\). When \(f(v)=A v^2 \exp(-mv^2/kt)\) and \(mv^2/2 = E\), we obtain \(mv\,dv=dE\), and therefore \(f(v)\,dv = A(E/m)\exp(-E/T)\cdot(1/m\sqrt{E})\,dE = (A/m^2)\sqrt{E}\exp(-E/T)\,dE\). Here, \(T=kt\).