Depletion Results vs TBR in fusion source

User Support
1

Hi all,

There seems to be a large difference between the Li6 depletion and TBR results. The amount of atoms depleted do not match the amount of TBR produced, or tritium produced by a Li6 + n _> Tritium reaction. I get a reduction in Li6 atoms of the range of 10^18 atoms over the range of 12 years. Though when simply calculating the amount of neutrons per second for a 2GW fusion source I get the around 10^20 neutrons produced per second. Then when finding the TBR I get a TBR of 1.3. Now this implies that I would lose about 13^20 neutron per second, an order of 2 magnitudes larger than the loss over 12 years. This was a simple check and there maybe a simple misunderstanding on what depletion actually represents here. A description of my model and code used follows:

I have created a simple sphere with a isotropic fusion source in the centre (14.1MeV). Picture is added below. It contains a small layer of Tungsten (Purple) and a 100% Li lithium breeding section (Green). When calculating the Depletion a Volume is found using 4/3pir**3. The Operator and integrator are found below.

plot_1
plot_12000×2000 28.6 KB

operator = openmc.deplete.CoupledOperator(
    model = model,
    chain_file = chain,
    dilute_initial=0,
    reduce_chain=True, 
    reduce_chain_level=5,
    normalization_mode= "source-rate",
)
# Time steps and source rate
time_steps = [24*60*60*365] * 12
source_rates = [float(2e9)]* 12 

integrator = openmc.deplete.PredictorIntegrator(operator, time_steps, power=source_rates, timestep_units='s')

The depletion results and LI6 atoms are found using

results = openmc.deplete.Results("depletion_results.h5")

time, Li = results.get_atoms("6", "Li6",nuc_units= "atoms", time_units = "d")

Any help or information about potential oversights would be useful

2

There could be a few things going on. Could you share which chain file you used and the script to build your model (the one that produces this image)?

One thing I was unsure of from your description is the volume (which could be causing an issue). Each region that is tagged as depletable needs to have the correct volume. What is the region inside the tungsten made of? Is yellow-green inside the purple also Li-6?

Since there are three regions, you probably can’t use that volume formula unless it is only the inner region. Define r_{source}, r_{tungsten}, and r_{breeder} as the radii for the outer position of the source, the outer position of the tungsten, and the outer position of the breeder. The volume of the source is given by \frac{4}{3}\pi r_{source}^{3}. The volume of the tungsten is given by \frac{4}{3}\pi(r_{tungsten}^3-r_{source}^{3}). The volume of the breeder outside the tungsten is given by \frac{4}{3}\pi(r_{breeder}^{3}-r_{tungsten}^3).

Hope that helps and looking forward to the extra info.

3

Hi Lewis,

Yes the volumes are calculated as you suggested using the correct radius and deducting it from the previous radius. In terms of chain files I used ‘chain-endf-b8.0.xml’ but I have also tried with the ‘chain_endfb71_sfr.xml’ and ‘chain_endfb71_pwr.xml’ files from the openmc data page: all three get similar results.

Composition from the centre outwards are DT-plasma (Yellow), Tungsten (Purple), Lithium 6 (Green) and Lead (light green). Only Lithium-6 is depletable. The source is a point source at 0,0,0.

I have added my python script that runs the above code

CSG_geometry_test.py (3.9 KB)

4

@Adam2304 Please take a look at this post:

5

Hi @paulromano

Thanks I had already added the (n,t) reaction for tritium production in to the chain files but I think I may have found the cause. In the Predictor integrator there seems to be a problem when using the power input parameter. I originally used this as fusion output power i.e. 2GW. Though this gave extremely small depletion of the Li6 atoms. Though when I converted this using to neutrons per second using 17.6MeV (The energy from a single D-T reaction) and eV to joule conversion. You approximately get 10^20 Neutron per second. Substituting this in to the source_rates argument rather than the power argument of the Predictor integrator seems to fix the issue.

I dont know if I am using the power input incorrectly or if it is incorrectly converting the units. For reference my source was in eV.

source.energy = openmc.stats.muir(e0=14080000.0, m_rat=5.0, kt=20000.0)

Adam

6

The power option is intended for fission reactors and won’t work for a fusion system since we don’t track D-T fusion reactions. As you’ve discovered, you’ll have to use the source_rates argument instead.

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