Fusion Neutronics Workshop

Why is neutronics useful

• Radioactivity - Neutrons activate material, making it radioactive leading to handling and waste storage requirements.​
• Hazardous - Neutrons are Hazardous to health and shielded will be needed to protect the workforce.​
• Produce fuel - Neutrons will be needed to convert lithium into tritium to fuel the reactor.​
• Electricity - 80% of the energy release by each DT reaction is transferred to the neutron.​
• Structural integrity - Neutrons cause damage to materials such as embrittlement, swelling, change conductivity …​
• Diagnose - Neutrons are an important method of measuring a variety of plasma parameters (e.g. Q value).​

Topics Covered Half Day Course

• Neutron and Photon interaction cross sections

• Material creation

• Particle sources

• Constructive Solid Geometry (CSG)

• Tallies (heat, tritium breeding ratio, damage, flux)

• Neutron activation

Getting started

• Install Docker

• Download the docker image

• Run the docker image

• Navigate to the URL in the terminal

Detailed instructions are on GitHub

Containers

Tasks

OpenMC

Getting started

Timetable

Microscopic Cross Sections

• Probability of interaction is characterised by the microscopic cross-section (σ). It is the effective size of the nucleus.

• Cross section data is key to the neutronics workflow and provide us with the likelihood of a particular interaction.

• Cross sections can be measured experimentally with monoenergetic neutrons.

Experimental data

Cross section reactions

Cross section evaluations exist for:

• different nuclides
• different interactions.

A list of reactions available in OpenMC is here

For example:

• Be9(n,2n)2He would be a neutron interaction with beryllium 9 which results in 2 neutrons and 2 helium nuclei.
• Li6(n,Xt) would be a neutron interaction with lithium 6 nuclei which results in a tritium and X is a wildcard.

Reaction rate

• The reaction rate () can be found by knowing the number of neutrons per unit volume (), the velocity of neutrons (), the material density (), Avogadro's number (), the microscopic cross section at the neutron energy () and the atomic weight of the material ().
• This reduces down to the neutron flux (), nuclide number density () and microscopic cross section\sigma_{e}.
• This can be reduced one more stage by making use of the Macroscopic cross section ().

Now complete tasks 1, 2 and 3 in the half day workshop

Making materials

Making materials - nuclides

Simple material construction from nuclides.

mat2 = openmc.Material()
mat2.add_nuclide('Li6', 0.0759*2)
mat2.add_nuclide('Li7', 0.9241*2)
mat2.add_nuclide('O16', 0.9976206)
mat2.add_nuclide('O17', 0.000379)
mat2.add_nuclide('O18', 0.0020004)
mat2.set_density('g/cm3', 2.01)

Making materials - elements

Simpler material construction from elements.

import openmc

mat1 = openmc.Material()
mat1.add_element('H', 2)
mat1.add_element('O', 1)
mat1.set_density('g/cm3', 2.01)

Making materials - enrichment

Simple enriched material construction from elements.

import openmc

mat1 = openmc.Material()
mat1.add_element('Li', 4, enrichment_target='Li6', enrichment=60)
mat1.add_element('Si', 1)
mat1.add_element('O', 4)
mat1.set_density('g/cm3', 2.01)

Now complete tasks 4 and 5 in the half day workshop

Making Geometry

import openmc

surface_sphere = openmc.Sphere(r=10.0)
region_inside_sphere = -surface_sphere
cell_sphere = openmc.Cell(region=region_inside_sphere) 

cell_sphere.fill = steel

Making Geometry

import openmc

surf_sphere1 = openmc.Sphere(r=10.0)
surf_sphere2 = openmc.Sphere(r=20.0)
between_spheres = +surf_sphere1 & -surf_sphere2
cell_between = openmc.Cell(region= between_spheres) 

cell_sphere.fill = steel

Edge of the model

import openmc 

surf_sphere = openmc.Sphere(r=10.0, boundary_type="vacuum")
between_spheres = -surf_sphere
cell_between = openmc.Cell(region= between_spheres) 

Surfaces available

More complex geometry

OpenMC also supports:

• boolean operations like union, intersection and complement.
• rotations and translations
• nested geometry with universes
• different surface types (e.g reflective for sector model)

For more complex 3D geometry DAGMC can be used which makes use of a meshed geometry to transport particles.

Now complete task 6 in the half day workshop

Plotting particles

Spatial distribution of MCF and ICF sources

The spatial distribution of MCF plasma covers a larger area compared to ICF'

.

Energy distribution MCF and ICF sources

Now complete tasks 7, 8 and 9 in the half day workshop

Tritium Breeding Ratio

Now complete task 10 in the half day workshop

Damage tallies

Now complete task 11 in the half day workshop

Neutron scattering

Neutron scattering angle

Path length

Energy loss

The average logarithmic energy decrement (or loss) per collision () is related to the atomic mass () of the nucleus

Collisions to thermalize

The average number of collisions required to reduce the energy of the neutron from to .

If is 14MeV and is 0.025eV

Moderating power

We should account for the likelihood of scattering.

The number density of the nucleus (ND) and the microscopic cross section (σ) combine to produce the macroscopic scattering cross section (Σ)

Now complete tasks 12 and 13 in the half day workshop

Mesh tallies

Mesh tallies

Mesh tallies geometry

Now complete task 14 in the half day workshop

Activation reactions

Activation pathways

Activation products

Activation products from fission

• Fission of large atoms (e.g. U235)
• Results in two fission products far from stability

Build up and saturation

Now complete task 15 in the half day workshop

Summary task

Replace the "your code here" sections to make the best reactor.

Chose the best options from a selection of materials.

Refine the design to:

• maximize Tritium Breeding Ratio (TBR)
• maximize blanket heating
• minimize damage to the conductor

Now complete task 16 in the half day workshop