5.25. [ Multiplier ] section

In the [multiplier] section, multiplier sets consisting of factors that depend on particle energies can be set as multipliers of [t-track], [t-cross], and [t-point] tally results. To use this function, multiplier subsections in the tally section must be defined. For example, this function can be used for dose estimation using any dose conversion factor.

Only one multiplier set can be defined per [multiplier] section. A maximum of 100 [multiplier] sections can be defined in an input file. The format of this section is given as follows.

Listing 5.25.1 [ Multiplier ] section example (1)
    [ Multiplier ]
      number = -201
      interpolation = log
      part = all
      lagrange = 2
      file = multiplier201.out
      epsout  = 1
      y-txt = Conversion coefficients (arb.)
      ne = 10
           20.0       2.678
           30.0       7.020
           50.0       18.50
           100.0      24.26
           200.0      16.13
           500.0      10.51
           1000.0     10.55
           2000.0     10.98
           5000.0     12.10
           10000.0    12.45

The ID number of each [multiplier] section can be set by a negative integer between -200 and -299. Particle type can be specified by the part parameter. part=all indicates that the data are applicable to all particles. There are six particles that can be defined in a [multiplier] section. The data interpolation method is defined by the interpolation parameter. Set it to log for log-log interpolation, lin for linear-linear interpolation, xlog or ylin for linear-log interpolation, and xlin or ylog for log-linear interpolation. If you want to use the given data as group constants without interpolation, set interpolation to glow or ghigh. The number of energy points or groups is given by ne, and data of each energy and factor should be defined in the subsequent lines. Note that the data should be listed in ascending order of energy. The coefficient of the minimum energy point is used at energies below the minimum energy, and the coefficient of the maximum energy point is used at energies above the maximum. If you want to avoid using values outside the defined energy range, adjust the e-type for each tally.

Since version 3.35, the interpolation method using the 4-point cubic Lagrangian interpolation formula is available. This interpolation method is also recommended by ICRP. The lagrange parameter is used to switch between the two interpolation methods. For the conventional 2-point interpolation, specify 2, which is the default, and for the 4-point Lagrange interpolation, specify 4. If you specify the output file name in file, the input data and interpolation data are output. epsout can be used to make the eps file. If you want to show the name of the coefficients defined in the [multiplier] section in the output file, use y-txt to specify the text displayed on the y-axis.

From version 3.03, conversion coefficients for several types of radiation dose and soft error rate on semiconductor devices are pre-defined. The multiplier IDs of pre-defined data are shown in Table 5.25.1. Those data are included in the phits/data/multiplier directory with the file name m+|ID|+.inp, for example m200.inp for \(k=-200\). The unit of conversion coefficients for radiation dose is pSv cm \(^2\), and that for soft error rate is (FIT/Mbit)/(/cm \(^2\)/s). You can add your own [multiplier] section in this folder. If you specify a [multiplier] section with the same ID number in your input file, the pre-defined data are overwritten by the specified data.

The conversion coefficients for SER are derived from the neutron-induced SEU cross section for a virtual semiconductor device calculated by PHITS and a device simulator. [1] The background SER [2] is about 400 (FIT/Mbit). Here, 1 FIT = 1e-9 error/hour. Generally, SEU cross sections depend on the device. Therefore, the conversion coefficients should not be used to estimate the exact SER. Please use them to estimate SER roughly or to compare SER in a radiation field and background SER.

Table 5.25.1 Pre-defined conversion coefficients

Multiplier ID

Data information

-200

\(H^*(10)\) [3]

-201

Effective dose based on ICRP60, AP irradiation [4]

-202

Effective dose based on ICRP103, AP irradiation [5]

-203

Effective dose based on ICRP103, ISO irradiation [5]

-204

New operational quantity \(H^*\), maximum effective dose among all irradiation conditions [5]

-210

Sex-averaged effective dose equivalent, ISO irradiation [6]

-211

Effective dose equivalent for male, ISO irradiation [6]

-212

Effective dose equivalent for female, ISO irradiation [6]

-213

Dose equivalent for male red-bone marrow, ISO irradiation [6]

-214

Dose equivalent for female red-bone marrow, ISO irradiation [6]

-215

Dose equivalent for male skin, ISO irradiation [6]

-216

Dose equivalent for female skin, ISO irradiation [6]

-299

Soft error rate on semiconductor device, ISO irradiation [1]

5.25.1. Multiplier subsection

The multiplier option of the tally section is used to define a multiplier set following the basic format \((C\ k)\), where \(C\) is a normalization factor and \(k\) is the ID number of the set. Note that \(k\) should be negative. The format of the multiplier subsection is given as follows.

Listing 5.25.2 Multiplier subsection example
    multiplier = all
          part = neutron
          emax = 1000
        mat   mset1        mset2
        all   ( 1 -201 )  ( 2 -202 )

In the first line, multiplier=all should be specified. In the second line, part= defines which particle is to be considered. A maximum of six particles can be entered here. all, which is the default, can also be used. Only the listed particles will be multiplied. In the third line, emax= defines the maximum energy of multiplication. If emax is omitted, it is automatically defined as the maximum energy given in the [multiplier] section. The first column in the following line should be mat, and its value should be all. Although this definition is meaningless, it cannot be omitted. The columns mset1 and mset2 define multiplier sets up to a maximum of six sets. The result of each set is printed out. Although several multiplier subsections can be defined in one tally section, the number of multiplier sets should be constant across subsections.

PHITS has some built-in coefficients available for the [multiplier] section. If you set \(k=-1\), a value of 1/weight is used as the multiplication factor to obtain tally results of a Monte Carlo particle, that is, particles always having their weights as 1. For \(k=-2\), a value of 1/velocity is used. For \(k=-120\), material density is used. Therefore, you can obtain mass in the region by setting icntl=5. You can also set an ID number included in the /phits/data/multiplier/ directory without specifying the [multiplier] section in the input file. Currently, databases of conversion coefficients for several types of radiation dose are included in the directory. Please see Table 5.25.1 for details. The unit of dose conversion coefficients is pSv cm \(^2\). Thus, doses in units of pSv/s can be directly calculated when the calculated fluence is normalized to /cm \(^2\)/s. Note that the energy unit of dose conversion coefficients for heavy ions is MeV/n, and you have to set IMeVperN=1 in the [parameters] section when you use heavy-ion data in your simulation.

In addition to them, effective doses based on ICRP60 for AP irradiation from proton, neutron, electron, and photon can be separately calculated by specifying \(k=-101\), \(-102\), \(-112\), and \(-114\), respectively. However, this method is no longer recommended because the corresponding doses can be calculated by \(k=-201\). Note that the unit of these dose conversion coefficients is (\(\mu\) Sv/h)/(n/s/cm \(^2\)). That is, doses in units of \(\mu\) Sv/h can be directly calculated when the calculated fluence is normalized to /cm \(^2\)/s. It should be noted that the interpolation method of the conversion factor was changed in PHITS version 2.00 from linear-linear to log-log.

When settings use nuclear and atomic data libraries, excluding EGS mode, the contained cross sections and kerma factors can also be used as mset in the following format.

Listing 5.25.3 mset format using MT numbers
    ( C  m  MT1  MT2  ... )

Here, \(C\) is the normalization factor, \(m\) is the material ID defined in [material], and MT1, MT2 are MT numbers of cross sections to be multiplied with fluence. When more than one MT number is specified, the multiplied factor is the product of them except when the MT numbers are connected with :. Here, : indicates sum instead of product, in the same way as the [cell] section. The complete MT number list is available from https://wwwndc.jaea.go.jp/cgi-bin/ENDFfig?help=yes or Appendix B of https://www.oecd-nea.org/dbdata/data/manual-endf/endf102.pdf. Major MT numbers are shown below.

Table 5.25.2 Major MT numbers

MT number

Explanation

1

(z,total) total reaction cross section [barn]

2

(z,z0) elastic scattering cross section [barn]

3

(z,nonelas.) non-elastic scattering cross section [barn]

4

(z,n) production cross section of a neutron [barn]

16

(z,2n) production cross section of two neutrons [barn]

17

(z,3n) production cross section of three neutrons [barn]

18

(z,fission) fission cross section [barn]

22

(z,n:alpha) production cross section of a neutron and an alpha particle [barn]

27

(z,abs) absorbed cross section [barn]

28

(z,np) production cross section of a neutron and a proton [barn]

102

(z,gamma) radiative capture cross section [barn]

103

(z,p) production cross section of a proton [barn]

104

(z,d) production cross section of a deuteron [barn]

105

(z,t) production cross section of a triton [barn]

106

(z,3He) production cross section of a 3He particle [barn]

107

(z,alpha) production cross section of an alpha particle [barn]

108

(z,2alpha) production cross section of two alpha particles [barn]

109

(z,3alpha) production cross section of three alpha particles [barn]

When you multiply the result with part=neutron by the cross section of a reaction that produces charged particles, such as MT=103, set e-mode>0 in the [parameters] section. Note that reaction channel cross sections, for example MT=102-109, are included only in neutron cross-section libraries below 20 MeV. If you wish to refer to values from charged-particle libraries or neutron libraries above 20 MeV, use integral cross sections in the 200 series. For example, MT=203 corresponds to the (z,xp) cross section.

Negative MT numbers have special meanings as follows.

For part=neutron:

Table 5.25.3 Special MT numbers for neutron

Special number

Explanation

-1

Total cross section without thermal adjustment [barn]

-2

Absorption cross section [barn]

-3

Elastic cross section without thermal adjustment [barn]

-4

Average heating number [MeV/collision]

-5

Gamma-ray production cross section [barn]

-6

Total fission cross section [barn]

-7

Fission \(\nu\) [number/fission]

-8

Fission \(Q\) [MeV/fission]

For part=photon:

Table 5.25.4 Special MT numbers for photon

Special number

Explanation

-1

Compton, incoherent, scattering cross section [barn]

-2

Rayleigh, coherent, scattering cross section [barn]

-3

Photoelectric cross section [barn]

-4

Pair production cross section [barn]

-5

Total cross section [barn]

-6

Photon heating number [MeV/collision]

Examples of mset using MT numbers are shown below.

  • (100.0 5 1): 100 x total cross section of material ID 5

  • (1.0 3 1 -4): neutron kerma factor of material ID 3, part should be neutron

  • (1.0 4 -5 -6): photon kerma factor of material ID 4, part should be photon

  • (1.0 5 4:16:17): sum of the (n,n), (n,2n), and (n,3n) cross sections of material ID 5

  • (1.0 1 1 -4:-6 -8): fission heat, total fission cross section x fission \(Q\)

If you want to know the actual multiplier value used, define mtinfo=1 just after the part parameter in the multiplier subsection. Additionally, add the e-type subsection after mtinfo to specify energy points for the output. The multiplier value will be output in the output file of the tally in the format of the [multiplier] section. However, if the material number is set to 0, the coefficients are written out when the first material number among those set in [material] is used in the calculation. For example, if the first written material number is not used in [cell] or in any other way, the coefficients for this material number are not written.