.. _sec-multiplier: [ 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. .. code-block:: text :caption: **[ 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 :numref:`tbl-DCC`. Those data are included in the ``phits/data/multiplier`` directory with the file name ``m+|ID|+.inp``, for example ``m200.inp`` for :math:`k=-200`. The unit of conversion coefficients for radiation dose is pSv cm :math:`^2`, and that for soft error rate is (FIT/Mbit)/(/cm :math:`^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. [#abe2014]_ The background SER [#parma]_ 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. .. list-table:: Pre-defined conversion coefficients :name: tbl-DCC :widths: 20 80 :header-rows: 1 * - Multiplier ID - Data information * - **-200** - :math:`H^*(10)` [#expacs]_ * - **-201** - Effective dose based on ICRP60, AP irradiation [#jaeri1345]_ * - **-202** - Effective dose based on ICRP103, AP irradiation [#icru95]_ * - **-203** - Effective dose based on ICRP103, ISO irradiation [#icru95]_ * - **-204** - New operational quantity :math:`H^*`, maximum effective dose among all irradiation conditions [#icru95]_ * - **-210** - Sex-averaged effective dose equivalent, ISO irradiation [#icrp123]_ * - **-211** - Effective dose equivalent for male, ISO irradiation [#icrp123]_ * - **-212** - Effective dose equivalent for female, ISO irradiation [#icrp123]_ * - **-213** - Dose equivalent for male red-bone marrow, ISO irradiation [#icrp123]_ * - **-214** - Dose equivalent for female red-bone marrow, ISO irradiation [#icrp123]_ * - **-215** - Dose equivalent for male skin, ISO irradiation [#icrp123]_ * - **-216** - Dose equivalent for female skin, ISO irradiation [#icrp123]_ * - **-299** - Soft error rate on semiconductor device, ISO irradiation [#abe2014]_ Multiplier subsection --------------------- .. _multiplier-sub: The multiplier option of the tally section is used to define a multiplier set following the basic format :math:`(C\ k)`, where :math:`C` is a normalization factor and :math:`k` is the ID number of the set. Note that :math:`k` should be negative. The format of the multiplier subsection is given as follows. .. code-block:: text :caption: 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 :math:`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 :math:`k=-2`, a value of 1/velocity is used. For :math:`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 :numref:`tbl-DCC` for details. The unit of dose conversion coefficients is pSv cm :math:`^2`. Thus, doses in units of pSv/s can be directly calculated when the calculated fluence is normalized to /cm :math:`^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 :math:`k=-101`, :math:`-102`, :math:`-112`, and :math:`-114`, respectively. However, this method is no longer recommended because the corresponding doses can be calculated by :math:`k=-201`. Note that the unit of these dose conversion coefficients is (:math:`\mu` Sv/h)/(n/s/cm :math:`^2`). That is, doses in units of :math:`\mu` Sv/h can be directly calculated when the calculated fluence is normalized to /cm :math:`^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. .. code-block:: text :caption: **mset** format using MT numbers ( C m MT1 MT2 ... ) Here, :math:`C` is the normalization factor, :math:`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. .. list-table:: Major MT numbers :widths: 15 85 :header-rows: 1 * - 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**: .. list-table:: Special MT numbers for neutron :widths: 15 85 :header-rows: 1 * - 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 :math:`\nu` [number/fission] * - **-8** - Fission :math:`Q` [MeV/fission] For **part=photon**: .. list-table:: Special MT numbers for photon :widths: 15 85 :header-rows: 1 * - 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 :math:`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. .. [#abe2014] The critical charge is assumed to be 0.6 fC. The neutron energies from 1 MeV to 1 GeV are considered. For details, please refer to S. Abe and Y. Watanabe, IEEE Trans. Nucl. Sci. 61, 3519-3526 (2014). .. [#parma] The background means on the ground at Tokyo. The cosmic-ray neutron flux is calculated by the PARMA model. The PARMA model can be downloaded from http://phits.jaea.go.jp/expacs .. [#expacs] Taken from EXPACS, http://phits.jaea.go.jp/expacs/. .. [#jaeri1345] Y. Sakamoto, O. Sato, S. Tsuda, N. Yoshizawa, S. Iwai, S. Tanaka, and Y. Yamaguchi, "Dose conversion coefficients for high-energy photons, electrons, neutrons and protons", JAERI-1345, (2003) etc. .. [#icru95] ICRU Report 95, 2020. .. [#icrp123] ICRP Publication 123, Ann. ICRP 42(4), 2013.