⚛OpenMC Neutron Moderation Simulator

OpenMC Simulation

Moderator Material

Select the moderating material used for neutron scattering and thermalization in the simulation.

The moderator determines the average energy loss per collision, the thermalization rate, angular scattering behavior, ...

Geometry

Select the geometry that is used in the simulation.

The geometry determines if a neutron escapes or is absorbed/thermalizes in the chosen material. It can also be plotted. Each geometry has it's specific parameters that are displayed after selecting a geometry type.

Sphere radius:

Center geometry point (x, y, z):

Simulation Settings

Select the settings that are used in the simulation.

The settings determine where the neutron source is positioned, the starting energy of the neutrons, the number of neutrons used in the simulation and the seed number for the simulation. This number provides the repeatability of the simulation. The thermal energy slider is used for the whole simulation, change it after running the simulation and then plot the available graphs. You can find it in the toggleable sidebar on the left side.

Source point (x, y, z):

Energy [eV]:

Number of batches:

Neutrons per batch:

Seed:

Random seed

Create a new setup

Create and name a setup with the chosen parameters for the simulation.

First give your setup a unique name and click Create XML Configuration. If that name is already in use the website will give you a choice of overwriting the existing setup or creating a new version of it. The website adds a suffix to the name, describing the number of neutrons, moderating material and the geometry shape used in the simulation.

Setup name:

Available setups

Run the simulation for the selected setup.

Select a setup you created and run the OpenMC simulation. If the setup is already run you will see an annotation text ✅ besides the setup name in the Select setup dropdown. You do not need to resimulate already run setups, but it is possible to do so. If a setup is already run you can select it and plot a graph without resimulating the setup.

Cross Section Viewer

View cross sections for the material used in the selected setup.

Displays cross sections for the material of the currently selected setup. For custom materials the data is read directly from the generated HDF5 file. For standard materials the data is read from the OpenMC cross section library.

X axis:

Y axis:

⚠ No setup selected.

Particle track visualization

Visualize neutron moderation tracks. Visualizing one particle gives a color coded energy loss graph. You can also visualize the used geometry.

After selecting a setup plot the particle tracks. An option to select the desired particles is given through particle indices. Input your particle indices in the way shown in the example. For example, the input 1 shows the first particle, 1-10 shows the first 10 particles, 1-100-10 shows each 10th particle from 1 to 100. If you want to visualize the geometry tick the box Show Geometry. Remember you can also change the thermalisation energy with the sidebar on the left. Plotting more than 100 particles at once may be slow and plotting more than 1000 is not advised.

Plot options

Particle indices (comma-separated, e.g. 0, 1, 5-10, 1-100-10):

Show Geometry

Plot output

Energy Loss per Collision

Visualize neutron energy loss per collision.

After selecting a setup plot the energy loss per sollision graph. An option to select the desired particles is given through particle indices. Input your particle indices in the way shown in the example. For example, the input 1 shows the first particle, 1-10 shows the first 10 particles, 1-100-10 shows each 10th particle from 1 to 100.

Plot options

Particle indices (comma-separated, e.g. 0,1,5-10,1-100-10):

Plot output

Up/Downscatter Heatmap: ΔE vs. Initial Energy

Plot an up/downscatter heatmap for particle energy loss vs. initial energy before collision.

After selecting a setup plot the up/downscatter heatmap. An option to select the desired particles is given through particle indices. Input your particle indices in the way shown in the example. For example, the input 1 shows the first particle, 1-10 shows the first 10 particles, 1-100-10 shows each 10th particle from 1 to 100. There are also several plotting options: ΔE log scale, Collision counts log scale and Normalize by source energy. You can also select a energgy loss ΔE range. Note that if ΔE log scale is selected the range must be positive (0 is not included).

Plot options

Particle indices (comma-separated, e.g. 0,1,5-10,1-100-10):

ΔE log scale

Collision counts log scale

Normalize by source energy

ΔE range [min, max] (leave empty = auto):

Plot output

Probability of scattering from E to E'

Plot a probability of scattering histogram from the initial energy bin E to all possible enrgies.

After selecting a setup plot the scattering histogram. An option to select the desired particles is given through particle indices. Input your particle indices in the way shown in the example. For example, the input 1 shows the first particle, 1-10 shows the first 10 particles, 1-100-10 shows each 10th particle from 1 to 100. There is also an option to select the initial energy bin E (in eV) from which the scattering occurs and the bin number used in the historgam. The histogram also shows the theoretical probability of scattering form E to E', where $E^{'} = E \cdot (1 - α)$ . This is also the only graph where the thermal cutoff energy selected in the sidebar does not affect the graph.

Plot options

Particle indices (comma-separated, e.g. 0,1,5-10,1-100-10):

E initial bin range [eV] (leave empty = auto):

Number of bins:

Plot output

Collisions Until Thermal Histogram

Plot collisions until thermal histogram graph. The simulated distribution is compared to a Poisson distribution.

After selecting a setup, plot the collisions-until-thermalisation histogram. An option to select the desired particles is given through particle indices. For example, the input 1 shows the first particle, 1–10 shows the first 10 particles, and 1–100–10 shows each 10th particle from 1 to 100.

The simulated distribution of collisions until thermalisation is compared to a Poisson distribution

P (n) = \frac{⟨ n ⟩^{n}}{n!} \exp (- ⟨ n ⟩)

where the mean number of collisions is

⟨ n ⟩ = \frac{\ln (E_{0} / E_{th})}{ξ} .

Here $E_{0}$ is the initial neutron energy, $E_{th}$ the thermal energy, and $ξ$ the average logarithmic energy decrement per collision. It can be computed as

\begin{aligned} ξ_{i} & = \frac{2}{A_{i} + \frac{2}{3}}, \\ ξ & = \frac{1}{N} \sum_{i = 1}^{N} ξ_{i} \end{aligned}

where $A_{i}$ is the atomic mass of the atom constituting the selected moderator. $N$ is the number of athoms the molecule of the moderator is consisted of. If the moderator isn't a single athom moderator we use tha average. You can also plot the statistical accuracy of the simulated distribution using the given slider.

Plot options

Particle indices (comma-separated, e.g. 0,1,5-10,1-100-10):

Statistical accuracy

None

1σ

2σ

3σ

4σ

5σ

Plot output

Mean Free Path vs. Initial Energy

Plot Mean free path vs. initial energy. The MFP for particles are shaded in the background while the average MFP is at the front in red.

After selecting a setup plot MFP vs. initial energy graph. An option to select the desired particles is given through particle indices. Input your particle indices in the way shown in the example. For example, the input 1 shows the first particle, 1-10 shows the first 10 particles, 1-100-10 shows each 10th particle from 1 to 100.

Plot options

Particle indices (comma-separated, e.g. 0,1,5-10,1-100-10):

Log x scale

Log y scale

Plot output

Scattering Cosine/Angle PDF

Plot the cosine of the scattering angle distribution or only the scattering angle distribution.

After selecting a setup and plot type, plot the graph. An option to select the desired particles is given through particle indices. Input your particle indices in the way shown in the example. For example, the input 1 shows the first particle, 1–10 shows the first 10 particles, and 1–100–10 shows each 10th particle from 1 to 100.

The average cosine of the scattering angle is defined as

⟨ \cos θ ⟩ = \int_{- 1}^{1} \cos θ p (\cos θ) d (\cos θ) .

For elastic scattering on a nucleus of mass number $A$ , assuming isotropic scattering in the center-of-mass frame, this reduces to

⟨ \cos θ ⟩ = \frac{2}{3 A} .

For moderator molecules with more than one atom, we compute the average as

⟨ \cos θ ⟩ = \frac{1}{N} \sum_{i = 1}^{N} ⟨ \cos θ ⟩_{i} .

It needs to be noted that the angle theoretical value is just an approximation, because there is no easily interpretable equation to describe it

⟨ θ ⟩ \neq \arccos ⟨ \cos θ ⟩ .

Plot options

Particle indices (comma-separated, e.g. 0,1,5-10,1-100-10):

Plot output

Angle θ histogram

Cosine cos(θ) histogram

Scattering Heatmap: Angle vs. Energy

Plot a scattering heatmap for the cosine of the angle vs. initial energy before collision.

After selecting a setup plot the angle vs. energy heatmap. An option to select the desired particles is given through particle indices. Input your particle indices in the way shown in the example. For example, the input 1 shows the first particle, 1-10 shows the first 10 particles, 1-100-10 shows each 10th particle from 1 to 100. There is also a plotting option for the logarithmic scale of counts for better visibility.

Plot options

Particle indices (comma-separated):

Log scale counts

Plot output

dN/dE or dΦ/dE for Energies

Plot a $\frac{d N}{d E}$ or $\frac{d Φ}{d E}$ vs. initial energy before collsion.

After selecting a setup plot and the graph type plot the $\frac{d N}{d E}$ or $\frac{d Φ}{d E}$ vs. initial energy graph. An option to select the desired particles is given through particle indices. Input your particle indices in the way shown in the example. For example, the input 1 shows the first particle, 1-10 shows the first 10 particles, 1-100-10 shows each 10th particle from 1 to 100. There are also several plotting options: $\frac{d N}{d E}$ or $\frac{d Φ}{d E}$ log scale, lethargy scale and Show theory.

Plot options

Particle indices:

Log y scale

Show Theory

Use lethargy x scale

Plot output

dN/dE graph

dΦ/dE graph

N(E) survival graph

Analytic vs. Simulated ξ Comparison

Plot analytic vs. simulated $ξ$ comparison. You can plot a historgam of $\ln \frac{E}{E^{'}}$ or a $ξ$ vs. initial energy graph.

After selecting a setup and the plot type you can plot the graph. An option to select the desired particles is given through particle indices. Input your particle indices in the way shown in the example. For example, the input 1 shows the first particle, 1-10 shows the first 10 particles, 1-100-10 shows each 10th particle from 1 to 100. There are also several plotting options: Upscattering allowed and number of bins.

The theoretical $ξ$ is calculated using

\begin{aligned} ξ_{i} & = \frac{2}{A_{i} + \frac{2}{3}}, \\ ξ & = \frac{1}{N} \sum_{i = 1}^{N} ξ_{i}, \end{aligned}

where $A_{i}$ is the atomic mass of the atom constituting the selected moderator. $N$ is the number of athoms the molecule of the moderator is consisted of. In the energy dependent $ξ$ there is also a bin weighted theoretical $ξ$ value. This option is more accurate because it negates the effects of upscattering at lower initial energies.

Plot options

Particle indices:

Upscattering allowed

Number of bins:

Plot output

Energy-dependent ξ(E)

ln(E/E') histogram

ΔE/E for Energies

Plot the $\frac{Δ E}{E}$ vs. initial enrgies graph. The graph plots the maximum energy loss and the average energy loss.

After selecting a setup you can plot the graph. An option to select the desired particles is given through particle indices. Input your particle indices in the way shown in the example. For example, the input 1 shows the first particle, 1-10 shows the first 10 particles, 1-100-10 shows each 10th particle from 1 to 100. There are also several plotting options: Log y scale, Log x scale, Theory, E normalized and Include upscattering.

The relative energy loss per collision is defined as

\frac{Δ E}{E} = \frac{E_{in} - E_{out}}{E_{in}} .

For elastic scattering on a nucleus of mass number $A$ , the maximum possible relative energy loss occurs for head-on collisions and is given by

{(\frac{Δ E}{E})}_{max} = 1 - α, α = {(\frac{A - 1}{A + 1})}^{2} .

Assuming isotropic scattering in the center-of-mass frame, the average relative energy loss per collision is

⟨ \frac{Δ E}{E} ⟩ = \frac{1 - α}{2} .

If E normalized is selected $\frac{Δ E}{E}$ is relative and if that is not the case, the absolute values are displayed. You also have the choice of including upscattered collisions or not. This will affect the average energy loss values at lower initial energies.

Plot options

Particle indices:

Log y scale

Log x scale

Show Theory

E normalized

Upscattering allowed

Plot output

ΔN/Δt for times

Plot the $\frac{Δ N}{Δ t}$ vs. times or $N (t)$ graph.

The relative energy loss per collision is defined as

\frac{Δ E}{E} = \frac{E_{in} - E_{out}}{E_{in}} .

For elastic scattering on a nucleus of mass number $A$ , the maximum possible relative energy loss occurs for head-on collisions and is given by

{(\frac{Δ E}{E})}_{max} = 1 - α, α = {(\frac{A - 1}{A + 1})}^{2} .

Assuming isotropic scattering in the center-of-mass frame, the average relative energy loss per collision is

⟨ \frac{Δ E}{E} ⟩ = \frac{1 - α}{2} .

Plot options

Particle indices:

Log y scale

Log x scale

Differentiate

Show theory fit

Plot output

ΔN/Δt graph

ΔN/Δt difusion animation

OpenMC Simulation

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Welcome

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Controls

Set the desired thermal energy that will be used while plotting graphs.

Moderator Material

Geometry

Simulation Settings

Create a new setup

Available setups

Cross Section Viewer

Particle track visualization

Plot options

Plot output

Energy Loss per Collision

Plot options

Plot output

Up/Downscatter Heatmap: ΔE vs. Initial Energy

Plot options

Plot output

Probability of scattering from E to E'

Plot options

Plot output

Collisions Until Thermal Histogram

Plot options

Plot output

Mean Free Path vs. Initial Energy

Plot options

Plot output

Scattering Cosine/Angle PDF

Plot options

Plot output

Scattering Heatmap: Angle vs. Energy

Plot options

Plot output

dN/dE or dΦ/dE for Energies

Plot options

Plot output

Analytic vs. Simulated ξ Comparison

Plot options

Plot output

ΔE/E for Energies

Plot options

Plot output

ΔN/Δt for times

Plot options

Plot output