Optimizing Alpha Yield Scoring and Reducing Statistical Error for Low-Energy p-11B Fusion

Physics, Transport and Magnetic Fields
1

Versions

Please provide the used software versions.

FLUKA:4-5.1
Flair:3.4-5.2

Description

Hello FLUKA Experts,

As a Chemical Engineer working on alternative energy research, I am currently modeling proton-boron (p-11B) nuclear fusion targets using FLUKA.

I am simulating a 675 keV monoenergetic proton beam striking a custom B4C-doped polyurethane foam target. My primary goal is to score the Helium-4 (alpha) yield accurately. I have attached my .inp and .flair files for reference.

My Current Setup:

  • Physics: EVAPORAT activated.

  • Biasing: LAM-BIAS applied to the B-FOAM region for protons (to artificially increase the interaction probability of this low cross-section reaction).

  • Scoring: RESNUCLE to evaluate the H4_YIELD The Challenge: Because the p-11B fusion cross-section is extremely narrow (centered around the ~675 keV resonance peak), getting statistically significant alpha yields without running astronomically high numbers of primary histories is challenging.

    My Questions:

    1. LAM-BIAS Tuning: Are there specific recommendations for setting the interaction length reduction factor in LAM-BIAS for such low-energy, highly specific resonance reactions to maximize efficiency without crashing the transport logic?

    2. Alternative Biasing: Besides LAM-BIAS, are there other biasing techniques (e.g., splitting/Russian roulette via BIASING cards) that are generally recommended for scoring extremely rare secondary particles (Alphas) in low-energy scenarios?

    3. Statistical Error: What is the most robust FLUKA methodology to drive down the relative statistical error percentage for the RESNUCLE outputs in this specific cross-section regime?

    Any insights or guidance on improving the scoring efficiency and reducing the statistical uncertainty would be greatly appreciated!

    Best regards, Uftadi Beyazit Gul

Input files

Please upload all

B_doped_foam.flair (145 Bytes) (input file)

boron_doped_foam.inp (2.3 KB)

boron_doped_foam_24_tab.lis (6.0 KB)

boron_doped_foam_24_sum.lis (11.3 KB)

relevant files. (FLUKA input file, Flair project file, user routines, and data files)

4

Dear @uftadibeyazitg ,

In my opinion, your approach to setting up the physics of your model is absolutely reasonable.

1 LAM-BIAS is a proper tool in the case of a thin target, which will improve your statistics.

2 Another biasing technique will be efficient in the case of complex geometry, but for the single interaction region in the vacuum and single source, your model is not overloaded with the calculation of irrelevant collisions with excessive statistics. So, in your case, other biasing methods will not improve computational time/statistics.

3 In general, not. Some good practices will be to reduce the number of bins and the scored region-energy range to the essential minimum, so you will improve the "primaries to the number of bins " ratio. As a result, you will have better statistics within the one bin. (Looking at your usrbin cards, I would say you are aware of it). You may also select “region of interest” for energy by cutting off particle transport at relatively high energies manually

Small comment out of the scope of your question:

Unfortunately, some tasks need more computing power even if it is optimally configured. Consider using a computing cluster if it is possible. From your flair file, it seems that you make your calculations with one core of your PC. Do you use multiple spawns when simulations run?

Kind regards,

Illia

5

Dear Illia,

Thank you very much for your detailed review and encouraging feedback regarding the LAM-BIAS and USRBIN setups. It is great to hear that the physics approach for the model is on the right track!

You completely hit the nail on the head regarding the computing power. I was actually running the simulation directly on a single core without using multiple spawns.

Since I have a multi-core processor, I want to optimize this. How would you recommend I configure the number of spawns and cycles to improve the statistics efficiently? What should be my exact next steps to run this properly?

Thank you again for your valuable time and guidance!

Best regards,
Uftadi

6

Dear Uftadi,

reasonable number of cycles is 5, as it is the default; it is sufficient for the standard deviation calculation. The higher number makes sense if your calculation runs for many hours, and there is a chance to lose results due to the crash. Results cannot be saved within one cycle so a high number will reduce the percentage of possible loss.

The optimal number of spawns is the number of physical cores of all CPUs in your system minus 1. It is good to have 1 free for the maintenance of the basic operations of your PC. Pay attention that it will proportionally multipy amout of the disk space needed to store temporary files.

Also, I would recommend reducing the lambda multiplier in LAM-BIAS to the moment when it do not improve accuracy anymore (probably 10-100 times).

Kind regards,

Illia

7

Dear Illia,

Thank you so much for your clear and insightful response. Your recommendations were exactly the missing pieces I needed to stabilize my simulation.

Adjusting the LAM-BIAS multiplier down to 0.01 (100 times) as you suggested, along with using 5 cycles and optimizing the spawns to N-1, completely resolved the statistical variance issues I was facing. Thanks to your guidance, my statistical error dropped from 99% to under 0.1%, and the alpha yield results for my target material are now perfectly consistent and physically meaningful.

I truly appreciate your time and the practical rules of thumb you shared, especially regarding CPU management and disk space limits. These hardware-software balance tips are incredibly valuable for my ongoing research.

Kind regards,

Uftadi