Synthetic model of gamma-ray emission during DT experiments on the SPARC tokamak

This paper presents a synthetic model of gamma-ray emission for the SPARC tokamak's reference discharge, utilizing realistic plasma profiles and high-fidelity radiation transport simulations to evaluate detector performance, optimize spectrometer placement, and assess the feasibility of reconstructing fusion power via gamma spectroscopy amidst high neutron yields.

The Gist

Imagine the SPARC tokamak as a tiny, super-hot star trapped inside a giant magnetic bottle. Inside this star, atoms are smashing into each other so hard that they fuse, releasing a massive amount of energy. The scientists in this paper are trying to figure out how to "listen" to this star using a specific type of sound: gamma rays.

Here is a breakdown of their work, using simple analogies:

1. The Goal: Listening to the Star's "Voice"

When the atoms in the plasma fuse, they don't just release heat; they also shoot out invisible particles called gamma rays. Think of these gamma rays as the star's unique "voice" or fingerprint.

• Why listen? By analyzing the pitch and volume of this voice, scientists can tell exactly how much power the star is making, how fast the particles are moving, and how well the heating systems are working.
• The Problem: The star is also screaming very loudly with neutrons (another type of particle). The neutrons are so loud that they drown out the quieter gamma-ray "voice." It's like trying to hear a whisper at a rock concert.

2. The Microphone: The LaBr3 Detector

The team wants to use a special microphone called a LaBr3 detector (a crystal made of lanthanum bromide).

• Why this one? It's tough and can handle high temperatures, but it has a limit. If too many neutrons hit it at once, it gets "confused" and stops working properly (like a microphone that gets blown out by a speaker).
• The Challenge: In the SPARC experiment, the neutron "noise" is expected to be 10 times louder than anything ever heard before in similar experiments.

3. The Solution: The "Soundproof Wall" (Attenuator)

To hear the gamma rays, the scientists needed to build a wall to block the neutrons but let the gamma rays pass through.

• The Wall: They designed a thick slab made of High-Density Polyethylene (HDPE), which is essentially a very dense plastic.
• How it works: Imagine the neutrons are like heavy bowling balls and the gamma rays are like tennis balls. The HDPE wall is like a thick foam padding. It stops the heavy bowling balls (neutrons) dead in their tracks, but the lighter tennis balls (gamma rays) can still bounce through to the detector.
• The Catch: The wall has to be just the right thickness. If it's too thin, the neutrons get through. If it's too thick, it blocks the gamma rays too. They calculated that for the loudest experiments, they need a wall about 1.2 to 2.5 meters thick.

4. What They Can Hear (The Results)

The team ran computer simulations to see what the detector would actually "hear" once the wall is in place.

• The Main Song (DT Fusion): They found that the main gamma rays from the fusion reaction (the "DT" reaction) are loud enough to be heard clearly above the noise, provided they use the thick plastic wall.
  • The Result: They could measure the total power of the fusion reaction with about 5% to 10% accuracy. This is a big deal because it gives them a second, independent way to check their power numbers, separate from the neutron measurements.
• The Background Noise: Even with the wall, there is still a lot of "static" (background noise) caused by neutrons hitting the walls of the room and creating their own gamma rays. This static is so loud that it drowns out the quieter "songs" (other types of reactions).
• The Quiet Songs (Boron and Helium-3):
  • They tried to listen for gamma rays from Boron (used to clean the walls) and Helium-3 (used for heating).
  • The Verdict: With the current microphone (LaBr3) and the thick plastic wall, these signals are too quiet to hear. The static is just too loud. The paper suggests that to hear these, they might need a "super-microphone" (a different type of detector) that can handle even more noise.

5. The "Whisper" of the Future

The paper concludes that while the current setup works well for measuring the main power output, it's not sensitive enough to study the finer details of the plasma (like the Boron or Helium-3 signals) because the neutron noise is just too overwhelming.

In summary: The scientists built a computer model of a "noise-canceling" system for the SPARC tokamak. They proved that with a thick plastic wall, they can finally hear the main "voice" of the fusion power. However, the background noise is still too loud to hear the quieter, more complex "whispers" of the plasma, suggesting that future experiments will need even better technology to hear those details.

Technical Summary

Technical Summary: Synthetic Model of Gamma-Ray Emission During DT Experiments on the SPARC Tokamak

Problem Statement
The SPARC tokamak, currently under construction by Commonwealth Fusion Systems, is designed to achieve a fusion power ($P_{fus}$) of 140 MW and an energy gain factor ($Q$) of approximately 11. While the primary method for inferring fusion power involves redundant measurements of the 14.1 MeV DT neutron yield, the authors argue for the necessity of an independent diagnostic based on a different physical mechanism to reduce systematic errors. Gamma-ray spectroscopy is proposed as a candidate for this independent measurement. However, the high neutron flux expected in SPARC (significantly higher density than previous devices like JET due to its compact volume) poses a severe challenge for traditional inorganic scintillators, such as Lanthanum Bromide (LaBr$_3$), which are susceptible to saturation and neutron-induced background. The paper addresses the feasibility of measuring specific gamma-ray lines from DT, D$^3$He, DD, and $\alpha$+$^{10}$B reactions amidst this intense neutron background.

Methodology
The authors developed a synthetic modeling workflow to estimate gamma-ray signals and neutron backgrounds at the proposed diagnostic location: the SPARC Neutron Camera (NCAM).

• Plasma Modeling: Realistic plasma profiles (densities and temperatures) for a Primary Reference Discharge (PRD, $P_{fus}=140$ MW) and a $Q>1$ scenario ($P_{fus} \approx 10$ MW) were generated using the TRANSP code. Fast ion distributions for Ion Cyclotron Resonance Heating (ICRH) were simulated using CQL3D and TORIC.
• Gamma-Ray Source Calculation: Gamma-ray emissivity was calculated by solving the reaction rate integral using velocity distributions and reactivity data (Bosch-Hale functions and interpolated cross-sections). Reactions of interest included T(D,$\gamma$)$^5$He, D($^3$He,$\gamma$)$^5$Li, D(D,$\gamma$)$^4$He, and $^{10}$B($\alpha$,p$\gamma$)$^{13}$C.
• Transport and Detection:
  • Optical Transport: The ToFu ray-tracing code was used to calculate photon fluxes reaching the detector through collimated lines of sight (LOS), assuming axisymmetric sources and negligible scattering in the collimators.
  • Radiation Transport: High-fidelity Monte Carlo simulations using OpenMC and MCNP were employed to model neutron transport, prompt gamma production from (n,$\gamma$) reactions in the torus hall and collimator structures, and the interaction of radiation with the detector and attenuators.
  • Detector Response: A 3-inch $\times$ 6-inch cylindrical LaBr$_3$ detector response was modeled, including energy deposition from neutrons (converted to electron-equivalent energy) and gamma-rays.
• Attenuation Strategy: High-Density Polyethylene (HDPE) attenuators were scoped to reduce the total particle rate hitting the detector to the spectroscopic limit of LaBr$_3$ ($\approx 5 \times 10^5$ counts/s).

Key Results

• DT Gamma-Ray Signal: The T(D,$\gamma$)$^5$He reaction produces gamma-rays at 16.7 MeV and 13.5 MeV. For a 3 cm collimator in the central LOS, the unattenuated rate is $\approx 8 \times 10^5$ $\gamma$/s. With a 124 cm HDPE attenuator (required for the PRD scenario), the detector efficiency above 11 MeV is reduced to $\approx 6\%$. Despite this, the signal remains detectable.
• Background Dominance: The neutron-induced background, primarily from prompt gammas generated by (n,$\gamma$) reactions in the torus hall materials, dominates the spectrum below 11 MeV. Direct neutrons are largely mitigated by the HDPE, but the prompt gamma background remains the limiting factor.
• Feasibility of $P_{fus}$ Reconstruction:
  • For the PRD scenario (140 MW), a 124 cm HDPE attenuator allows for a statistical uncertainty of $\approx 3\%$ over a 10-second integration.
  • For the $Q>1$ scenario (10 MW), a thinner attenuator (64 cm) could achieve $\approx 3\%$ statistical uncertainty over 10 seconds.
  • The authors note that achieving a total uncertainty of 10% on $P_{fus}$ requires reducing the uncertainty on the DT gamma-to-neutron branching ratio, which is currently known with only $\approx 20\%$ precision and significant variance between experiments.
• Other Reactions:
  • D($^3$He,$\gamma$)$^5$Li: The background from this reaction during DT operations is negligible ($<0.8\%$). However, the hollow emissivity profile suggests potential for diagnosing ICRH power deposition in DD plasmas.
  • $^{10}$B($\alpha$,p$\gamma$)$^{13}$C: The signal from fusion-born alphas interacting with boron impurities is extremely weak. Even with a 3 cm collimator, the signal-to-noise ratio is insufficient for a LaBr$_3$ detector behind an attenuator, as the prompt gamma background swamps the 3–4 MeV peaks.
  • DD Gamma: The 23.8 MeV gamma from DD reactions is orders of magnitude weaker than other signals and requires integration over many discharges.

Significance and Claims
The paper claims to provide the first comprehensive synthetic study of gamma-ray spectroscopy on SPARC, specifically addressing the unique challenge of high neutron flux density.

• Diagnostic Viability: The study concludes that gamma-ray spectroscopy using a LaBr$_3$ detector behind the NCAM is feasible for measuring DT fusion power in both PRD and $Q>1$ scenarios, provided a substantial HDPE attenuator is used.
• Independent Measurement: This diagnostic offers a method to infer $P_{fus}$ independent of neutron yield, which is critical for validating performance metrics on future power plants like ARC.
• Limitations and Future Work: The authors modestly state that while DT gamma measurement is viable, measuring the $\alpha$+$^{10}$B reaction or reconstructing the full DT spectral shape is currently limited by background and detector response function uncertainties. They suggest that alternative technologies, such as the MERGS electron recoil detector, might be better suited for high-rate environments without heavy attenuation. The work highlights the need for improved branching ratio data and further study of impurity transport in high-field machines to fully realize the diagnostic potential.