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Neutronics Analysis of Fusion Systems |
Presentation slides for the fusion energy neutronics workshop |
Jonathan Shimwell |
fusion,neutronics,neutron,photon,radiation,simulation,openmc,dagmc |
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- Reactions
- Isotope chart
- Transmutation reactions
- Q values
- Threshold reactions
- Fusion fuels (DT,DD ...)
- Energy distribution from DT
- Microscopic cross sections
- Experimental data
- Libraries (ENDF, TENDL, FENDL ...)
- Cross section regions
- Multigroup / continuous energy
- Group structures
- Reaction rate equation
- Macroscopic cross sections
- Scattering / thermalisation
- Decay data
- Photons
- Energy distribution from radioactive material
Nuclear reactions notation
Target nuclei (incident projectile, resulting fragments) resulting nuclei
Be9(n,2n)2He4 Target Projectile Product Product- 999 reactions channels with unique reaction IDs (MT numbers)
- MT 3 is elastic scattering (n,'n)
- MT 16 is neutron multiplication (n,2n)
- MT 18 is neutron multiplication (n,f)
- MT 205 is tritium production (n,Xt) where X is a wild card
- MT 444 is damage energy
Reactions that result in a change of the isotope
- 1 stable isotope of gold Au$_{79}^{197}$
- 3 natural isotopes of lead
- Pb$_{82}^{204}$ ⚛ -3 protons, -4 neutrons
- Pb$_{82}^{206}$ ⚛ -3 protons, -6 neutrons
- Pb$_{82}^{207}$ ⚛ -3 protons, -7 neutrons
- Pb$_{82}^{208}$ ⚛ -3 protons, -8 neutrons
- 2 reactions for converting gold to lead
- Pb204 (n,3npa) Au197
- Pb204 (n,nta) Au197
- No cross section data found in ENDF
Amount of energy absorbed (-ve) or release (+ve) during the nuclear reaction
| Reaction | Energy release [MeV] | Threshold reaction |
|---|---|---|
| Be9(n,2n) | -1.6 | Yes |
| Pb208(n,2n) | -7.3 | Yes |
| Li6(n,t) | 4.8 | No |
| Li7(n,nt) | -2.4 | Yes |
Mass and Binding energy converted to kinetic energy
Online Q value calculator at NNDC
Q values of fusion fuel reactions
| Reaction | Energy release (MeV) |
|---|---|
| D + T -> He$^{4}$ + n | 17.6 |
| D + D -> He$^{3}$+n | 3.3 |
| D + D -> T + p | 4.0 |
| D + He$^{3}$->He$^{4}$+p | 18.3 * |
- No neutron emitted
- Neutrons are not emitted in the primary fuel reaction
- Neutrons can be emitted by reactions with the products
- Energy capture via direct conversion or divertor?
| Reaction | Energy release [MeV] |
|---|---|
| D + Li$^{6}$ -> 2He$^{4}$ | 22.4 |
| P + Li$^{6}$ -> He$^{4}$ + He$^{3}$ | 4.0 |
| He$^{3}$ + Li$^{6}$ -> He$^{4}$ + p | 16.9 |
| He$^{3}$ + He$^{3}$ -> He$^{4}$ + 2p | 12.86 |
| p + Li$^{7}$ -> 2He$^{4}$ | 17.2 |
| p -> B$^{11}$ -> 3He$^{4}$ | 8.7 |
| p -> N$^{15}$ -> C$^{12}$ + He$^{4}$ | 5.0 |
- A DT plasma has several fusion reactions.
- DT is the most likely reaction.
- DD and TT reactions also occur with lower probabilities.
- All reactions and emit different energy neutrons.
- Measured in Barns (1 barn =
$10^{-28}m^{2}$ ) - Energy dependant
- Cross section evaluations exist for:
- different incident particles
- different nuclides
- different interactions.
- Important neutron reactions plotted
- Tritium breeding
- Neutron multiplication
- The reaction rate (
$RR$ ) can be found by knowing the number of neutrons per unit volume ($n$ ), the velocity of neutrons ($v$ ), the material density ($p$ ), Avogadro's number ($N_{a}$ ), the microscopic cross section at the neutron energy ($\sigma_{e}$ ) and the atomic weight of the material ($M$ ). - This reduces down to the neutron flux (
$\phi$ ), nuclide number density ($N_{d}$ ) and microscopic cross section$\sigma_{e}$ . - This can be reduced one more stage by making use of the Macroscopic cross section (
$\Sigma_{e}$ ).
- Lithium metatitanate has a material density of 3.4 g/cm3
- When plotting materials the Macroscopic cross section accounts for number density of the different isotopes
- Units for Macroscopic cross section are cm$^{-1}$
- Discretize a continuous distribution
- Histogram of average cross section in each energy bin
- Continuous cross section has rules for interpolation that can be accounted for.
- Groups are not equally spaced.
- Structures are optimized for different energy ranges (fission, fast fission, fusion etc)
Reactions have characteristics
- 1/v section
- resolved resonance
- unresolved resonance
- thresholds
- scattering
- The scattering angle varies depending on the energy of the incident neutron
- Low energy neutrons have isotropic scattering (even probability in all directions)
- High energy neutrons are more likely to have a low deflection angle and are forwards bias.
- There is also data on neutrons released in reactions such as (n,2n).
- The (n,2n) reaction is a threshold reaction and requires energy.
- No run away chain reaction possible.
-
Availability of experimental data varies for different reactions and different isotopes.
-
Typically the experimental data is then interpreted to create evaluation libraries, such as ENDF, JEFF, JENDL, CENDL.
Source IAEA nuclear data services
There are several groups that produce and distribute nuclear data
- TENDL 2023 🇪🇺 2850 neutron
- JENDL 5 🇯🇵 795 neutron
- ENDF/B-VIII.0 🇺🇸 557 neutron
- JEFF 3.3 🇪🇺 562 neutrons
- BROND 3.1 🇷🇺 372 neutrons
- FENDL 3.2b 🌐 191 neutron
- CENDL 3.2 🇨🇳 272 neutron
- Path length = 1 /
$\Sigma_{T}$ - A 14MeV neutron will lose energy via scattering interactions
- As the neutron energy decreases the path length also decreases
- Path length at thermal energy is more constant
The average logarithmic energy decrement (or loss) per collision (
| Hydrogen | Deuterium | Beryllium | Carbon | Uranium | |
|---|---|---|---|---|---|
| Mass of nucleus | 1 | 2 | 9 | 12 | 238 |
| Energy decrement | 1 | 0.7261 | 0.2078 | 0.1589 | 0.0084 |
- Lithium has a particularly high cross section for tritium production
- Li6 has a very high cross section at low neutron energies
- Li7 has a reasonable cross section at high neutron energies
- Other reaction channels are relativity low
- Often alloyed with Si or other elements to improve material properties (e.g. flammability)
- Elements up to Iron plotted
- Beryllium has the lowest threshold energy for any isotope with a n,2n reaction.
- This means even low energy 3MeV neutrons can undergo (n,2n) reactions.
- Often alloyed with Ti or other elements to improve material properties (e.g. swelling due to retention)
- Lead is also a popular choice for a neutron multiplier
- Elements up to Iron plotted
-
High atomic number = good gamma attenuation
-
High neutron capture resonances = good neutron attenuation
- High hydrogen content = excellent neutron moderator
- Low interaction cross sections and low density = transparent to neutrons and gammas
By knowing the materials present can you identify which blanket results in which spectrum
- FLiBe, Molten salt, typically 90% enriched Li6
- HCPB, helium cooled pebble bed, typically 60% enriched Li6
- HCLL, helium cooled lithium lead, typically 90% enriched Li6
- WCCB, Water cooled ceramic breeder, typically 60% enriched Li6
- WCLL, water cooled lithium lead, typically 90% enriched Li6
- Liquid Lithium, typically natural enrichment
