added second mdgxs ipython notebook

docs/source/pythonapi/examples/mdgxs-part-i.ipynb

@@ -23,7 +23,7 @@
    "cell_type": "markdown",
    "metadata": {},
    "source": [
-    "Many Monte Carlo particle transport codes, including OpenMC, use continuous-energy nuclear cross section data. However, most deterministic neutron transport codes use *multi-group cross sections* defined over discretized energy bins or *energy groups*. Furthermore, kinetics calculations typically separate out parameters that involve delayed neutrons by delayed groups. An example is the energy spectrum for prompt and delayed neutrons for U-235 and Pu-239 computed for a light water reactor spectrum."
+    "Many Monte Carlo particle transport codes, including OpenMC, use continuous-energy nuclear cross section data. However, most deterministic neutron transport codes use *multi-group cross sections* defined over discretized energy bins or *energy groups*. Furthermore, kinetics calculations typically separate out parameters that involve delayed neutrons into prompt and delayed components and further subdivide delayed components by delayed groups. An example is the energy spectrum for prompt and delayed neutrons for U-235 and Pu-239 computed for a light water reactor spectrum."
    ]
   },
   {
@@ -78,7 +78,7 @@
     "### Spatial and Energy Discretization\n",
     "The energy domain for critical systems such as thermal reactors spans more than 10 orders of magnitude of neutron energies from 10$^{-5}$ - 10$^7$ eV. The multi-group approximation discretization divides this energy range into one or more energy groups. In particular, for $G$ total groups, we denote an energy group index $g$ such that $g \\in \\{1, 2, ..., G\\}$. The energy group indices are defined such that the smaller group the higher the energy, and vice versa. The integration over neutron energies across a discrete energy group is commonly referred to as **energy condensation**.\n",
     "\n",
-    "The delayed neutrons created from fissions are created from > 30 delayed neutron precursors. Modeling each of the delayed neutron precursors is possible, but this approach has not recieved much attention due to large uncertainties in certain precursors. Therefore, the delayed neutrons are often combined into \"delayed groups\" that have a set time constant, $\\lambda_d$. Some cross section libraries use the same group time constants for all nuclides (e.g. JEFF 3.2) while other libraries use different time constants for all nuclides (e.g. ENDF/B-VII.1). Multi-delayed-group cross sections can either be created with the entire delayed group set, a subset of delayed groups, or integrated over all delayed groups.\n",
+    "The delayed neutrons created from fissions are created from > 30 delayed neutron precursors. Modeling each of the delayed neutron precursors is possible, but this approach has not recieved much attention due to large uncertainties in certain precursors. Therefore, the delayed neutrons are often combined into \"delayed groups\" that have a set time constant, $\\lambda_d$. Some cross section libraries use the same group time constants for all nuclides (e.g. JEFF 3.1) while other libraries use different time constants for all nuclides (e.g. ENDF/B-VII.1). Multi-delayed-group cross sections can either be created with the entire delayed group set, a subset of delayed groups, or integrated over all delayed groups.\n",
     "\n",
     "Multi-group cross sections are computed for discretized spatial zones in the geometry of interest. The spatial zones may be defined on a structured and regular fuel assembly or pin cell mesh, an arbitrary unstructured mesh or the constructive solid geometry used by OpenMC. For a geometry with $K$ distinct spatial zones, we designate each spatial zone an index $k$ such that $k \\in \\{1, 2, ..., K\\}$. The volume of each spatial zone is denoted by $V_{k}$. The integration over discrete spatial zones is commonly referred to as **spatial homogenization**."
    ]
@@ -92,7 +92,7 @@
     "\n",
     "$$\\nu_d \\sigma_{n,x,k,g} = \\frac{\\int_{E_{g}}^{E_{g-1}}\\mathrm{d}E'\\int_{\\mathbf{r} \\in V_{k}}\\mathrm{d}\\mathbf{r} \\nu_d \\sigma_{f,x}(\\mathbf{r},E')\\Phi(\\mathbf{r},E')}{\\int_{E_{g}}^{E_{g-1}}\\mathrm{d}E'\\int_{\\mathbf{r} \\in V_{k}}\\mathrm{d}\\mathbf{r}\\Phi(\\mathbf{r},E')}$$\n",
     "\n",
-    "This scalar flux-weighted average microscopic cross section is computed by `openmc.mgxs` for only the delayed-nu-fission and delayed neutron fraction reaction type at the oment. These double integrals are stochastically computed with OpenMC's tally system - in particular, [filters](https://mit-crpg.github.io/openmc/pythonapi/filter.html) on the energy range and spatial zone (material, cell, universe, or mesh) define the bounds of integration for both numerator and denominator."
+    "This scalar flux-weighted average microscopic cross section is computed by `openmc.mgxs` for only the delayed-nu-fission and delayed neutron fraction reaction type at the moment. These double integrals are stochastically computed with OpenMC's tally system - in particular, [filters](https://mit-crpg.github.io/openmc/pythonapi/filter.html) on the energy range and spatial zone (material, cell, universe, or mesh) define the bounds of integration for both numerator and denominator."
    ]
   },
   {
@@ -102,7 +102,7 @@
     "### Multi-Group Prompt and Delayed Fission Spectrum\n",
     "The energy spectrum of neutrons emitted from fission is denoted by $\\chi_{n}(\\mathbf{r},E' \\rightarrow E'')$ for incoming and outgoing energies $E'$ and $E''$, respectively. Unlike the multi-group cross sections $\\sigma_{n,x,k,g}$ considered up to this point, the fission spectrum is a probability distribution and must sum to unity. The outgoing energy is typically much less dependent on the incoming energy for fission than for scattering interactions. As a result, it is common practice to integrate over the incoming neutron energy when computing the multi-group fission spectrum. The fission spectrum may be simplified as $\\chi_{n}(\\mathbf{r},E)$ with outgoing energy $E$.\n",
     "\n",
-    "Computing the cumulative energy spectrum of emitted neutrons, $\\chi_{n}(\\mathbf{r},E)$, has been presented in the `mgxs-part-i.ipynb` notebook. Here, we will present the energy spectrum of prompt and delayed emission neutrons, $\\chi_{n,p}(\\mathbf{r},E)$ and $\\chi_{n,d}(\\mathbf{r},E)$, respectively. Unlike the multi-group cross sections defined up to this point, the multi-group fission spectrum is weighted by the fission production rate rather than the scalar flux. This formulation is intended to preserve the total fission production rate in the multi-group deterministic calculation. In order to mathematically define the multi-group fission spectrum, we denote the microscopic fission cross section as $\\sigma_{n,f}(\\mathbf{r},E)$ and the average number of neutrons emitted from fission interactions with nuclide $n$ as $\\nu_{n,p}(\\mathbf{r},E)$ and $\\nu_{n,d}(\\mathbf{r},E)$ for prompt and delayed neutrons, respectively. The multi-group fission spectrum $\\chi_{n,k,g,d}$ is then the probability of fission neutrons emitted into energy group $g$. \n",
+    "Computing the cumulative energy spectrum of emitted neutrons, $\\chi_{n}(\\mathbf{r},E)$, has been presented in the `mgxs-part-i.ipynb` notebook. Here, we will present the energy spectrum of prompt and delayed emission neutrons, $\\chi_{n,p}(\\mathbf{r},E)$ and $\\chi_{n,d}(\\mathbf{r},E)$, respectively. Unlike the multi-group cross sections defined up to this point, the multi-group fission spectrum is weighted by the fission production rate rather than the scalar flux. This formulation is intended to preserve the total fission production rate in the multi-group deterministic calculation. In order to mathematically define the multi-group fission spectrum, we denote the microscopic fission cross section as $\\sigma_{n,f}(\\mathbf{r},E)$ and the average number of neutrons emitted from fission interactions with nuclide $n$ as $\\nu_{n,p}(\\mathbf{r},E)$ and $\\nu_{n,d}(\\mathbf{r},E)$ for prompt and delayed neutrons, respectively. The multi-group fission spectrum $\\chi_{n,k,g,d}$ is then the probability of fission neutrons emitted into energy group $g$ and delayed group $d$. There are not prompt groups, so inserting $p$ in place of $d$ just denotes all prompt neutrons. \n",
     "\n",
     "Similar to before, spatial homogenization and energy condensation are used to find the multi-energy-group and multi-delayed-group fission spectrum $\\chi_{n,k,g,d}$ as follows:\n",
     "\n",
@@ -337,7 +337,7 @@
    "cell_type": "markdown",
    "metadata": {},
    "source": [
-    "Now we are ready to generate multi-group cross sections! First, let's define a 2-energy-group structure using the built-in `EnergyGroups` class. We will also create a 6-delayed-group structure using the built-in `DelayedGroups` class."
+    "Now we are ready to generate multi-group cross sections! First, let's define a 100-energy-group structure and 1-energy-group structure using the built-in `EnergyGroups` class. We will also create a 6-delayed-group structure using the built-in `DelayedGroups` class."
    ]
   },
   {
@@ -389,7 +389,7 @@
     "* `ChiDelayed`\n",
     "* `Beta`\n",
     "\n",
-    "These classes provide us with an interface to generate the tally inputs as well as perform post-processing of OpenMC's tally data to compute the respective multi-group cross sections. In this case, let's create the multi-group chi-prompt and prompt-nu-fission cross sections with our 2-energy-group structure and multi-group chi-delayed, delayed-nu-fission, and beta cross sections with our 2-energy-group and 6-delayed-group structures. "
+    "These classes provide us with an interface to generate the tally inputs as well as perform post-processing of OpenMC's tally data to compute the respective multi-group cross sections. In this case, let's create the multi-group chi-prompt, chi-delayed, and prompt-nu-fission cross sections with our 100-energy-group structure and multi-group delayed-nu-fission and beta cross sections with our 100-energy-group and 6-delayed-group structures. "
    ]
   },
   {
@@ -402,7 +402,7 @@
    "source": [
     "# Instantiate a few different sections\n",
     "chi_prompt = mgxs.ChiPrompt(domain=cell, groups=energy_groups, by_nuclide=True)\n",
-    "prompt_nu_fission = mgxs.PromptNuFissionXS(domain=cell, groups=one_group, by_nuclide=True)\n",
+    "prompt_nu_fission = mgxs.PromptNuFissionXS(domain=cell, groups=energy_groups, by_nuclide=True)\n",
     "chi_delayed = mgxs.ChiDelayed(domain=cell, energy_groups=energy_groups, by_nuclide=True)\n",
     "delayed_nu_fission = mgxs.DelayedNuFissionXS(domain=cell, energy_groups=energy_groups, delayed_groups=delayed_groups, by_nuclide=True)\n",
     "beta = mgxs.Beta(domain=cell, energy_groups=energy_groups, delayed_groups=delayed_groups, by_nuclide=True)\n",
@@ -514,7 +514,7 @@
    "cell_type": "markdown",
    "metadata": {},
    "source": [
-    "The `Beta` object includes tracklength tallies for the 'nu-fission' and 'delayed-nu-fission' scores in the 2-energy-group and 6-delayed-group structure in cell 1. Now that each `MGXS` and `MDGXS` object contains the tallies that it needs, we must add these tallies to a `Tallies` object to generate the \"tallies.xml\" input file for OpenMC."
+    "The `Beta` object includes tracklength tallies for the 'nu-fission' and 'delayed-nu-fission' scores in the 100-energy-group and 6-delayed-group structure in cell 1. Now that each `MGXS` and `MDGXS` object contains the tallies that it needs, we must add these tallies to a `Tallies` object to generate the \"tallies.xml\" input file for OpenMC."
    ]
   },
   {
@@ -784,7 +784,7 @@
    "cell_type": "markdown",
    "metadata": {},
    "source": [
-    "Let's first inspect our delayed-nu-fission section by printing it to the screen."
+    "Let's first inspect our delayed-nu-fission section by printing it to the screen after condensing the cross section down to one group."
    ]
   },
   {
@@ -1043,7 +1043,7 @@
    "cell_type": "markdown",
    "metadata": {},
    "source": [
-    "The following code snippet shows how to export the chi `MGXS` to the same HDF5 binary data store."
+    "The following code snippet shows how to export the chi-prompt and chi-delayed `MGXS` to the same HDF5 binary data store."
    ]
   },
   {
@@ -1248,7 +1248,7 @@
     }
    ],
    "source": [
-    "# Set the time constants for the delayed precursors (in seconds^-1)\n",
+    "# Set the time constants for the delayed precursors (in seconds^-1) using some ficticious time constant data.\n",
     "precursor_halflife = np.array([55.6, 24.5, 16.3, 2.37, 0.424, 0.195])\n",
     "precursor_lambda = -np.log(0.5) / precursor_halflife\n",
     "\n",
@@ -1349,7 +1349,7 @@
    "cell_type": "markdown",
    "metadata": {},
    "source": [
-    "We can also plot the fission spectrum for the prompt and delayed neutrons."
+    "We can also plot the energy spectrum for fission emission of prompt and delayed neutrons."
    ]
   },
   {