Kinetic Equilibrium Prediction at TCV using RAPTOR and FBT

This paper presents a new Kinetic-Equilibrium Prediction workflow that couples RAPTOR transport simulations with FBT inverse equilibrium calculations to enable rapid, accurate pre-shot predictions of plasma parameters and coil currents for TCV discharges, thereby improving shot preparation and operator decision-making.

The Gist

Imagine you are trying to bake the perfect, complex cake in a high-tech kitchen. You have a recipe (the "pulse schedule") that tells you when to turn on the oven, when to add ingredients, and how long to bake. But here's the catch: the cake batter behaves unpredictably. It expands, it changes texture, and it might even collapse if you don't adjust the heat just right.

In the world of nuclear fusion, that "cake" is a super-hot ball of plasma (a soup of charged particles) inside a machine called a tokamak (specifically, the TCV machine in Switzerland). The goal is to keep this plasma stable and hot enough to generate energy, but it's incredibly difficult to control.

This paper introduces a new "smart baking assistant" that helps scientists predict exactly how the cake will behave before they even turn on the oven.

The Problem: Guessing the Game

Traditionally, when scientists wanted to run an experiment, they had to guess what the plasma would look like inside. They would set the magnetic "molds" (coils) based on simple assumptions.

• The Risk: If their guess was wrong, the plasma might wobble, hit the walls, or collapse (a "disruption"), ruining the experiment and potentially damaging the machine.
• The Old Way: It was like baking a cake by guessing how much the batter will rise, hoping for the best, and then adjusting the oven temperature after you see smoke.

The Solution: The "Smart Baking Assistant" (KEP)

The authors developed a new workflow called Kinetic-Equilibrium Prediction (KEP). Think of it as a two-part team of super-smart computers working together to simulate the entire baking process before the real thing happens.

1. The "Batter Predictor" (RAPTOR)

First, they use a code called RAPTOR. Imagine this as a simulator that predicts how the "batter" (the plasma) will react to the heat and ingredients.

• It calculates how the temperature, density, and pressure will change from the moment the oven turns on until it cools down.
• It's incredibly fast. It can run a simulation of a whole experiment in just a few minutes, giving scientists a "movie" of what the plasma should look like.

2. The "Mold Designer" (FBT)

Next, they take that "movie" of the plasma and feed it into a second code called FBT.

• Think of FBT as the engineer designing the magnetic mold (the shape of the cake pan).
• In the old days, FBT had to guess what the batter looked like inside the mold. Now, it gets the actual prediction from RAPTOR.
• Because FBT knows exactly how the batter will expand and push against the walls, it can calculate the perfect amount of electricity needed in the magnetic coils to hold the shape perfectly.

How They Work Together: The "Tango"

The magic happens when these two codes talk to each other.

1. RAPTOR says: "If you use these coil settings, the plasma will get hot and push out here."
2. FBT says: "Okay, I see that. I need to tweak the coils slightly to keep it centered."
3. They do this back-and-forth a few times (like a quick dance) until they agree on the perfect settings.

This process is called coupling. It ensures that the magnetic shape and the internal physics of the plasma are perfectly matched before the experiment starts.

Why Does This Matter? (The Real-World Impact)

The paper tested this new assistant on over 200 real experiments. Here is what they found:

• Better Accuracy: The new method predicted the plasma's behavior much more accurately than the old guessing game. It could tell them exactly how much "pressure" (beta) and "internal stiffness" (inductance) the plasma would have.
• Saving the Cake: In one specific test, they used the new method to bake a very tricky "Snowflake" shaped plasma (a complex, delicate shape).
  • Old Way: The plasma wobbled and struggled to stay in shape.
  • New Way: Because the coils were programmed with the correct predictions, the plasma stayed perfectly stable and held its shape for the entire experiment.
• Safety: By knowing exactly how the plasma will behave, operators can avoid dangerous situations where the plasma might crash into the machine walls.

The "Secret Ingredient": Density

One of the hardest things to predict is how much "gas" (fuel) is in the oven. The paper admits that predicting the exact amount of gas is still a bit of a guesswork game (like guessing how much water evaporates from a pot). However, even with this small uncertainty, the new system worked remarkably well.

The Bottom Line

This paper describes a major step forward in fusion research. Instead of flying blind and hoping the plasma behaves, scientists now have a predictive simulator that acts like a flight simulator for pilots.

Just as a pilot practices in a simulator to learn how the plane reacts to storms before ever leaving the ground, fusion scientists can now "fly" their plasma experiments in a computer first. This allows them to adjust their plan, set the perfect magnetic controls, and run safer, more successful experiments to help us one day harness the power of the stars.

Technical Summary

1. Problem Statement

Optimizing tokamak performance requires operating close to physical limits, where disruptions or machine protection systems can prematurely terminate a pulse. Traditional shot preparation relies on "predict-first" tools that simulate plasma evolution, but these often face a critical disconnect:

• Transport vs. Equilibrium: Transport codes (predicting temperature, density, and current profiles) and equilibrium codes (calculating magnetic fields and coil currents) are often run separately.
• Inaccurate Initial Conditions: Equilibrium solvers like FBT (used at TCV) typically rely on simplified, polynomial assumptions for internal plasma profiles (pressure gradient $p'$ and current function $TT'$) based on operator experience. These assumptions often fail to capture the complex physics of H-mode transitions, negative triangularity, or specific confinement regimes.
• Consequences: Inaccurate internal profiles lead to errors in calculating the Shafranov shift, poloidal beta ($\beta_{pol}$), and internal inductance ($l_i$). This results in suboptimal feedforward Poloidal Field (PF) coil currents, causing plasma shape misalignment, vertical instabilities, or failure to achieve target configurations (e.g., Snowflake divertors).

The paper addresses the need for a unified workflow that couples kinetic transport predictions with inverse equilibrium calculations to provide realistic, self-consistent initial conditions for shot preparation.

2. Methodology: The KEP Workflow

The authors developed a Kinetic Equilibrium Prediction (KEP) workflow that couples two codes:

1. RAPTOR: A fast 1.5D transport code (MATLAB/C) solving radial transport equations for current density ($j_\parallel$), electron/ion temperatures ($T_e, T_i$), and density ($n_e$).
2. FBT: A static free-boundary equilibrium solver used at TCV to determine the PF coil currents required to sustain a target shape.

The Coupling Process:

• Input: The pulse schedule (plasma current $I_p$, auxiliary power $P_{aux}$, shape parameters $\delta, \kappa$, etc.) is fed into RAPTOR.
• Transport Simulation: RAPTOR predicts the evolution of kinetic profiles ($T_e, T_i, n_e, j_\parallel$) based on a gradient-based transport model and scaling laws.
• Profile Extraction: RAPTOR outputs the pressure gradient ($p'$) and current function ($TT'$) profiles.
• Equilibrium Calculation: These profiles are fed into FBT as constraints to solve the Grad-Shafranov equation. FBT calculates the required PF coil currents ($I_a$) to match the target shape.
• Iteration: The process iterates (typically 2–3 times) until the $p'$ and $TT'$ profiles and the resulting $\beta_{pol}$ and $l_i$ converge between the two codes.
• Output: A refined set of feedforward PF coil currents is generated for the TCV control system.

Key Physics Models & Extensions:

• Transport Model: Uses a gradient-based model with a "stiff" core and a pedestal.
• H-Mode Transition: Extended the Martin scaling law to account for magnetic configuration (favorable vs. unfavorable ion grad-B drift) and double-null configurations.
• Negative Triangularity (NT): Added specific parameters to model NT plasmas, which exhibit high L-mode performance but resist H-mode transitions.
• Ion Temperature: Implemented a full ion heat equation solver (solving for $T_i$ dynamically) alongside a simpler electron-to-ion scaling law.
• Density Prediction: Introduced ad-hoc rules to predict line-averaged density ($n_{e,l}$) from gas programming, a critical but difficult step for pre-shot modeling.

3. Key Contributions

• First Full Discharge KEP at TCV: Demonstrated a fully predictive workflow coupling RAPTOR and FBT for entire discharge trajectories (ramp-up to ramp-down).
• Extended Physics Models:
  • Adapted H-mode transition criteria for various divertor geometries (Single Null, Double Null, Snowflake) and triangularity (Positive vs. Negative).
  • Validated the gradient-based model for Negative Triangularity plasmas, capturing their unique confinement properties.
• Robust Coupling Algorithm: Developed a loose-coupling strategy that converges rapidly (within minutes) by treating transport and equilibrium as quasi-independent, allowing for integration into existing TCV preparation systems without major overhauls.
• Experimental Validation: Successfully tested the workflow on real TCV discharges, comparing pre-shot predictions with post-shot reconstructions and experimental outcomes.

4. Results

The methodology was benchmarked against 211 TCV discharges (including L-mode, H-mode, Ohmic, NBI-heated, Positive and Negative Triangularity).

• Convergence: The RAPTOR-FBT coupling converges within a few iterations (typically 2 steps), reducing the discrepancy in $\beta_{pol}$ and $l_i$ to less than 1–5%.
• Energy Prediction: RAPTOR predicts total electron and ion energy content ($W_e, W_i$) within 20% of experimental values across the database.
• H-Mode Transition: The extended Martin scaling law successfully predicted L-H transitions for 48 out of 51 Single Null (SN) shots within a 100ms window. Failures were primarily attributed to high X-point heights or unfavorable double-null configurations.
• Coil Current Corrections: The KEP significantly altered the feedforward PF coil currents compared to standard FBT preparations. Corrections often ranged from tens to hundreds of Amperes, particularly in the H-mode phase where internal profiles change rapidly.
• Experimental Impact:
  • Shot #81882 (Standard H-mode): The KEP improved the alignment of the X-point with the target throughout the discharge compared to standard preparations.
  • Shot #83575 (Negative Triangularity Snowflake): This difficult-to-control configuration showed marked improvement. The KEP-prepared shots maintained the Snowflake divertor shape (primary and secondary X-points) much closer to the target for longer durations compared to shots prepared with standard low-$\beta$ assumptions.

5. Significance and Future Outlook

• Operational Reliability: By providing more accurate estimates of $\beta_{pol}$ and $l_i$, the KEP reduces the risk of vertical displacement events (VDEs) and shape misalignment, crucial for high-performance scenarios.
• Scalability: The workflow is fast enough (approx. 2.3–2.7 minutes per second of discharge) to be used for rapid scenario testing and optimization before experiments, a prerequisite for future devices like ITER.
• Future Work:
  • Density Modeling: Improving the predictive model for line-averaged density ($n_{e,l}$) is identified as the next critical step for fully autonomous prediction.
  • Tight Coupling: Future iterations may integrate heating and current drive models (e.g., TORBEAM, RABBIT) directly into the loop for higher fidelity.
  • Advanced Scenarios: Extending the model to include magnetic shear effects and turbulence surrogate models (e.g., QLKNN) for advanced scenarios.

In conclusion, this work establishes a robust, physics-based framework for pre-shot equilibrium preparation, bridging the gap between transport prediction and magnetic control, and demonstrating tangible improvements in plasma stability and shape control at TCV.