.. _sec-wwbias: [ WW Bias ] section ================================================== In the **[ww bias]** section, minimum values of the weight window defined in **[weight window]** can be biased for certain regions. This option is useful when the **[weight window]** parameters for a certain region are biased after automatically generating the **[weight window]** section by **[t-wwg]**. :numref:`fig-wwbias` shows a flowchart of how to perform a transport calculation using **[weight window]** and **[ww bias]**. First, generate the **[weight window]** section by **[t-wwg]**. If the obtained parameters of **[weight window]** are enough to effectively use the variance reduction technique, the **[ww bias]** section is not needed. However, if they are not enough, the variance reduction technique can be used more effectively by biasing the **[weight window]** parameters for a certain region with **[ww bias]**. There are two methods to set the **[ww bias]** section. One is an automatic method using **[t-wwbg]**, which is a Weight Window Bias Generator, and the other is a manual method by a user, which is explained below. For details of **[t-wwbg]**, see :numref:`[t-wwbg]`. When performing a transport calculation with **[ww bias]** and **[weight window]**, set **icntl=0** and **iwwbias=1** in the **[parameters]** section. .. _fig-wwbias: .. figure:: ../assets/wwbias.png :width: 40em :align: center The flowchart of the connection calculation between **[weight window]** and **[ww bias]**. When more than one **[weight window]** section is defined, the combinations of **[weight window]** and **[ww bias]** are chosen in the order of appearance in the input file. Therefore, the same number of **[ww bias]** sections are required as the number of **[weight window]** sections. The format of **[ww bias]** is as follows. Note that you should set the same particle, energy mesh, and regions as in **[weight window]**. **mesh=reg** is selected as default if the **mesh** specification is skipped. When **mesh=xyz** is specified, **x-type**, **y-type**, and **z-type** must be defined in subsequent lines in the same way as for **[weight window]**. When **mesh=tet** is specified, the same cell number specification by **reg=** is required as in **[weight window]**. .. code-block:: text :caption: **[ WW Bias ]** section example (1) [ WW Bias ] part = neutron eng = 2 1e-3 1.0 reg wwb1 wwb2 1 0.25 0.25 2 0.50 0.50 3 1.00 1.00 4 2.00 2.00 .... ........ ........ In the first line, **part=** defines which particle is to be considered. When it is omitted, **part=all** is set. The expression of **part=** is the same as that in tally format. Note that only the expression as **ityp** can be set. Each nuclide cannot be specified. Next, the energy mesh should be defined. The line starting with **eng=** specifies the number of meshes. In the next line, energies, :math:`e_1, e_2, e_3, ...`, are defined. Furthermore, names of columns are given as **reg**, **wwb1**, **wwb2**, and so on. In the **reg** column, cell numbers are written. Bias values are given in the columns of **wwbi**. The skip operator **non** can be used. Each **wwbi** column corresponds to energies of :math:`e_{i-1} < E < e_i`. Here, :math:`e_0=0` is assumed. The format **( { 2 - 5 } 8 9 )** can be used, and the lattice and universe style **( 6 < 10[1 0 0] < u=3 )** can also be used. However, any value that is not a single numeric value must be enclosed by **( )**. By setting **iwwbias=1** in the **[parameters]** section, the **[weight window]** parameters multiplied by the inverse of the defined biases in **[ww bias]** are used. In this case, the products of the multiplication are output in the input echo of **[weight window]**, and **[ww bias]** with **off** is output. If an input file without **[ww bias]** is used, all values of **[ww bias]** in the input echo are set to **1**. An example of **[ww bias]** is as follows. .. code-block:: text :caption: **[ WW Bias ]** section example (2) :name: ex-wwbias-ex 1: [ WW Bias ] 2: part = neutron 3: eng = 1 4: 1.00000E+05 5: 6: reg wwb1 7: 1 1/7 8: 2 1/6 9: 3 1/5 10: 4 1/4 11: 5 1/3 12: 6 1/2 13: 7 1 14: 8 2 15: 9 3 16: 10 4 17: 11 5 18: 12 6 Here, neutron is considered as **part**. One energy region below 100 GeV is specified. Regions between 1 and 12 are gradually biased. The region with a larger number is biased more strongly than that with a smaller number. The xz cross-sectional view of a geometry, a concrete cylinder with a central axis on the z-axis and a radius of 100 cm, is shown below. Two results of neutron fluence obtained by transport calculations without and with **[ww bias]** are also shown below. Source particles of 14 MeV neutrons were generated at x=0, y=0, z=90 cm as an isotropic source. After generating a **[weight window]** section by **[t-wwg]**, the result without **[ww bias]** was obtained by performing the calculation with only the **[weight window]** section. The result of the calculation with both the **[weight window]** section and the **[ww bias]** section of :numref:`ex-wwbias-ex` is also shown below. The neutron fluence without **[ww bias]** was distributed in both regions of small and large cell numbers. On the other hand, the fluence with **[ww bias]** was distributed only in the large cell numbers, which were biased by **[ww bias]** of :numref:`ex-wwbias-ex`. As seen in this example, when focusing on a certain region, the calculation can be efficiently performed by **[ww bias]**. .. image:: ../assets/wwbias-geo.png :width: 30em :align: center (a) xz cross-sectional view of the geometry. .. image:: ../assets/wwbias-wo-bias.png :width: 30em :align: center (b) Result without **[ww bias]**. .. image:: ../assets/wwbias-with-bias.png :width: 30em :align: center (c) Result with **[ww bias]** of :numref:`ex-wwbias-ex`.