Multiscale Assessment of Tritium Behavior in Preliminary Fusion Pilot Plant Design Using Surrogate Models in TMAP8

This study utilizes the open-source TMAP8 code to integrate component-level surrogate models with system-level fuel cycle modeling, enabling a computationally efficient multiscale assessment of tritium transport and retention in Tokamak Energy Ltd.'s preliminary fusion pilot plant design to optimize safety, economics, and design iterations.

The Gist

Imagine you are trying to build a massive, self-sustaining campfire that never goes out. This isn't just any fire; it's a fusion power plant, the kind that could give us limitless clean energy. To keep this fire burning, you need a special kind of wood called Tritium.

Here's the problem: Tritium is rare, it's radioactive, and it's like a piece of wood that slowly turns into dust on its own (it has a short "half-life"). You can't just buy it at the store in large quantities. So, your power plant has to make its own Tritium while it runs.

But there's a catch: Tritium is sticky. It loves to get trapped in the walls of the fire chamber, hiding in the cracks and pores of the metal, just like dust getting stuck in the crevices of a sofa. If too much gets stuck, you run out of fuel. If you can't track where it is, you might lose it or create a safety hazard.

This paper is about building a super-smart, fast-tracking system to figure out exactly how much Tritium is hiding in the walls of a future power plant and how to get it back out.

Here is how they did it, explained simply:

1. The Problem: The "Slow and Expensive" Way

Imagine you want to know how long it takes for a drop of water to soak through a thick sponge.

• The Old Way: You build a giant, perfect replica of the sponge, pour water on it, and wait. Then you change the sponge's thickness, the water temperature, or the pressure, and you have to build a new replica and wait again.
• The Issue: In a real fusion plant, the "sponges" (the walls) are huge, the conditions are extreme (super hot, bombarded by particles), and you need to test thousands of different designs. Doing this one by one would take years and cost a fortune. It's like trying to find the perfect recipe for a cake by baking a new one every time you change the oven temperature by one degree.

2. The Solution: The "Cheat Sheet" (Surrogate Models)

The researchers decided to stop baking every single cake. Instead, they baked a few hundred cakes with different ingredients and temperatures. Then, they wrote a super-fast "Cheat Sheet" (a mathematical model called a Surrogate Model) based on those results.

• How it works: Instead of waiting hours for a real simulation to run, the Cheat Sheet looks at the ingredients you want (e.g., "thinner wall," "hotter temperature") and instantly tells you, "Based on my previous baking, this will take 12 minutes and use 5 cups of flour."
• The Magic: This Cheat Sheet is millions of times faster than the real simulation but still accurate enough to make good decisions.

3. The Two-Step Dance: Micro and Macro

The researchers used a "Multiscale" approach, which is like looking at a city through two different lenses:

• Lens 1 (The Micro View): They looked closely at the individual "bricks" of the power plant (the walls facing the plasma). They used a sophisticated tool called TMAP8 to simulate how Tritium moves, gets stuck, and escapes from these bricks. They tested different materials (like Tungsten armor) and thicknesses.
• Lens 2 (The Macro View): They zoomed out to look at the whole power plant (the "Fuel Cycle"). This includes the pipes, the pumps, the storage tanks, and the breeding blanket (where new Tritium is made).

The Innovation: Usually, you can't put the Micro View inside the Macro View because the Micro View is too slow. But because they built the Cheat Sheet (Surrogate Model) for the Micro View, they could plug it right into the Macro View. Now, they could simulate the entire power plant's behavior in seconds, while still knowing exactly what was happening inside the tiny cracks of the walls.

4. The "Two-Step" Discovery

One of their coolest findings was about time.

• Old Thinking: They used to think Tritium moves through the walls at a steady, predictable speed, like a car driving down a highway.
• New Discovery: They found that Tritium actually has a "delay." It hits the wall, gets stuck for a while (like a car stuck in traffic), and then suddenly starts moving again.
• The Fix: They updated their Cheat Sheet to include this "traffic jam" delay. This made their predictions much more accurate, showing that the power plant might actually hold less dangerous Tritium than previously feared because it gets stuck and released in a specific pattern.

5. Why This Matters

This research is like giving power plant designers a GPS and a time machine.

• Speed: They can now test thousands of design ideas in a day instead of a year.
• Safety: They can predict exactly where the "sticky" Tritium will hide and ensure the plant doesn't accidentally run out of fuel or leak radiation.
• Efficiency: By understanding the "traffic jams" of Tritium, they can design walls that let the fuel flow better, making the plant more efficient and cheaper to build.

In a nutshell: This paper shows how scientists are using "smart shortcuts" (Surrogate Models) to solve a very sticky problem. They are teaching computers to predict how a super-hot, super-rare fuel behaves inside a future power plant, ensuring that when we finally turn on the fusion lights, we have enough fuel to keep them burning forever.

Technical Summary

1. Problem Statement

Tritium accountancy is a critical challenge for the viability of deuterium-tritium (D-T) fusion energy systems due to tritium's radioactivity, short half-life (12.33 years), and scarcity. Fusion plants must achieve tritium self-sufficiency by breeding tritium onsite. However, a significant portion of injected tritium is not burned but is instead retained in plasma-facing components (PFCs) or lost through permeation.

Current fuel cycle modeling often relies on constant residence time assumptions for subsystems. This approach is insufficient because:

• It fails to capture the complex physics of tritium diffusion, trapping, and desorption at the component level.
• It is highly sensitive to uncertain residence time values.
• Running high-fidelity component-level simulations (e.g., using TMAP8) for every design iteration in a system-level fuel cycle model is computationally prohibitive, slowing down the optimization of fusion pilot plant designs (such as Tokamak Energy's ST-E1).

2. Methodology

The authors developed a multiscale modeling framework that integrates high-fidelity component-level physics with system-level fuel cycle analysis using Surrogate Models. The workflow consists of three main stages:

A. Component-Level Modeling (High-Fidelity)

• Tool: Tritium Migration Analysis Program, Version 8 (TMAP8), based on the MOOSE framework.
• Components Modeled: Divertor (DIV), Center Column First Wall (CCFW), Blanket First Wall (BKFW), and Vacuum Vessel (VV).
• Physics: The models solve coupled equations for:
  • Tritium Transport: Diffusion and trapping kinetics (governed by Arrhenius equations for trapping/release rates).
  • Heat Transfer: Transient heat conduction coupled with tritium transport.
• Conditions: Simulations covered pulsed operation (50 pulses, 80,000 s total) and bake-out scenarios. Inputs included varying tritium/heat fluxes, armor thickness (Tungsten), pipe thickness (V44 or Tungsten), and coolant temperatures.

B. Surrogate Model Development

• Technique: Gaussian Process (GP) regression models were trained using the Stochastic Tools Module (STM) in MOOSE.
• Inputs: Seven key parameters (tritium flux, heat flux, W armor thickness, pipe thickness, coolant temperature, trapping fraction, and release energy).
• Outputs:
  1. Steady-state tritium flux at the coolant surface ($J_\infty$).
  2. Two-Parameter Residence Time: A novel approach replacing the traditional single-parameter model. It defines:
     • $\tau_0$: Delay time before tritium reaches the coolant.
     • $\tau_1$: Time constant for reaching steady state.
• Training Data: Generated from 200 to 6,400 component-level simulations per dataset.

C. System-Level Integration

• Model: A zero-dimensional (0D) fuel cycle model comprising 17 subsystems (e.g., breeding blanket, isotope separation, pumping).
• Integration: The surrogate models replaced the standard constant residence time assumptions for the DIV, CCFW, and BKFW. This allowed the system-level model to rapidly evaluate tritium inventory and recycling dynamics under various design configurations.

3. Key Contributions

1. Two-Parameter Residence Time Model: The study introduced a more physically accurate residence time model ($\tau_0$ and $\tau_1$) that accounts for the delay in tritium release from PFCs, which single-parameter models miss.
2. Surrogate Model Acceleration: Successfully demonstrated that Gaussian Process surrogate models can approximate high-fidelity TMAP8 results with high accuracy while reducing computational costs by a factor of approximately $2.7 \times 10^6$.
3. Multiscale Framework: Created a seamless workflow linking detailed 1D component physics to system-level fuel cycle optimization, enabling rapid design iteration for fusion pilot plants.
4. Bake-out Analysis: Modeled the thermal desorption (bake-out) process, quantifying tritium release rates and vacuum pressure evolution during maintenance.

4. Key Results

• Surrogate Accuracy:
  • For steady-state flux ($J_\infty$), the surrogate model achieved a Root Mean Squared Percentage Error (RMSPE) as low as 9.92% (for V44 pipes) and 1.60% (for W pipes).
  • For residence times ($\tau_0, \tau_1$), RMSPEs were higher (up to ~31%) due to the complexity of transient fitting, but still sufficient for system-level screening.
• Component Behavior:
  • Armor Thickness: Reducing Tungsten armor thickness significantly decreased total tritium retention (due to lower volume/traps) but increased flux to the coolant.
  • Pipe Material: The choice between V44 and Tungsten pipes had a minimal impact on total inventory but influenced the flux profile at the coolant interface.
  • Bake-out: Over 95% of retained tritium was released after ~33 hours of baking, with vacuum pressure peaking early in the process.
• Fuel Cycle Impact:
  • The two-parameter model predicted lower tritium inventories in PFCs compared to the traditional one-parameter model. This is because the delay time ($\tau_0$) prevents immediate release, altering the transient inventory profile.
  • Sensitivity analysis revealed that heat flux has the strongest influence on tritium inventory evolution, while tritium flux has the weakest influence within the studied ranges.
  • Thinner armor and pipe walls generally led to higher inventory rates initially but faster release.

5. Significance

This work provides a critical pathway for the rapid design and optimization of fusion pilot plants. By decoupling the computational cost of high-fidelity physics from system-level analysis, the methodology allows engineers to:

• Perform extensive parametric studies to optimize component geometries (e.g., armor thickness) for minimal tritium retention.
• Accurately assess tritium self-sufficiency and safety margins without waiting days for simulations.
• Move beyond empirical residence time estimates toward physics-based, data-driven design.

The study validates the use of TMAP8 and surrogate modeling as a standard workflow for future fusion reactor development, specifically addressing the urgent need for accurate tritium accountancy in the ST-E1 and similar pilot plant designs. Future work aims to extend this to 2D/3D geometries and incorporate irradiation damage evolution.