TorbeamNN: Machine learning based steering of ECH mirrors on KSTAR

The paper introduces TorbeamNN, a machine learning surrogate model that achieves over a 100-fold speed-up compared to the real-time TORBEAM code while maintaining full-fidelity accuracy, enabling precise, real-time steering of KSTAR's electron cyclotron heating mirrors with a minimal tracking error of 0.5 cm.

The Gist

Imagine you are trying to heat a giant, swirling pot of soup (the plasma) inside a futuristic fusion reactor (the tokamak). To keep the soup hot and stable, you need to shoot a laser beam (microwaves) into it. But here's the catch: the soup isn't empty; it's filled with invisible magnetic fields and swirling currents that bend the laser beam like a straw in a glass of water.

If you aim the laser wrong, it might miss the soup entirely or hit the wrong spot, potentially damaging the pot or failing to heat it. To fix this, scientists use a "GPS" system called TORBEAM to calculate exactly where the beam will land.

The Problem: The old GPS (TORBEAM) is accurate, but it's slow. It takes about 10 milliseconds to calculate a path. In the world of fusion, where things change in the blink of an eye (like a sudden splash in the soup), 10 milliseconds is an eternity. By the time the GPS gives you the answer, the soup has already moved, and your aim is off.

The Solution: TorbeamNN
The authors of this paper created TorbeamNN, a new "GPS" powered by Artificial Intelligence (Machine Learning). Think of it like this:

• The Old Way (TORBEAM): Like a master chef who manually measures every single ingredient, does the complex math for the recipe, and then tells you where to pour the sauce. It's perfect, but it takes time.
• The New Way (TorbeamNN): Like a sous-chef who has watched the master chef cook 650,000 times. The sous-chef has memorized the patterns. When the chef says, "I'm pouring sauce now," the sous-chef instantly knows exactly where it will land without doing the math from scratch.

How It Works (The Analogy)

1. Training the Brain: The team fed the AI a massive library of "practice shots." They took data from the KSTAR fusion reactor (a real-world fusion experiment in South Korea) and ran the slow, perfect calculations 650,000 times. They taught the AI: "When the magnetic field is X and the mirror is tilted Y, the beam lands at Z."
2. The Speed Boost: Once trained, TorbeamNN doesn't do the heavy math. It just looks at the current situation and instantly recalls the answer. It is 100 times faster than the old system. Instead of taking 10 milliseconds, it takes less than a blink of an eye (about 0.05 milliseconds).
3. The Steering: Because it's so fast, the system can now adjust the mirrors in real-time. If the plasma shifts (like the soup splashing), the AI instantly recalculates and tells the mirrors to tilt slightly to keep the laser beam hitting the perfect spot.

Why This Matters

• Precision: In their tests, the AI predicted where the beam would land with an error of only 0.5 centimeters (about the width of a pencil). That is incredibly precise for a beam traveling through a chaotic, super-hot environment.
• Safety and Stability: Fusion reactors need to be incredibly stable. If the heating beam drifts, it can cause the plasma to become unstable (like a wobbly tower of Jenga blocks). With TorbeamNN, the system can react fast enough to stop these instabilities before they grow.
• Future of Fusion: This technology is a stepping stone for future reactors like ITER. As we try to run fusion reactors that do multiple tasks at once (heating, stabilizing, and cleaning the plasma), we need systems that can think and react instantly. TorbeamNN proves that AI can be the "fast brain" needed to control these complex machines.

The Bottom Line

The paper introduces a smart, lightning-fast AI assistant that helps fusion reactors aim their heating beams perfectly. It replaces a slow, calculating computer with a fast, intuitive one, allowing scientists to control the "star in a jar" with the precision needed to eventually power our world with clean, limitless energy.

Technical Summary

1. Problem Statement

Electron Cyclotron Heating (ECH) and Electron Cyclotron Current Drive (ECCD) are critical for controlling tokamak plasmas (e.g., suppressing Neoclassical Tearing Modes (NTMs), controlling sawteeth, and managing impurities). These applications require precise aiming of microwave beams to specific absorption locations within the plasma.

• The Bottleneck: Current real-time control relies on the TORBEAM ray-tracing code. While a simplified real-time version of TORBEAM runs in approximately 10 ms, this latency is problematic for:
  • Fast Transients: Phenomena like Edge Localized Modes (ELMs) or sawteeth occur on timescales of 20–50 ms. A 10 ms delay consumes a significant portion of the control cycle, potentially causing the system to react to outdated plasma conditions.
  • Multi-Tasking: Future reactors (like ITER) require ECH systems to switch rapidly between multiple control objectives within a single discharge.
  • Data Requirements: Full-fidelity TORBEAM requires complete real-time profiles of electron temperature ($T_e$) and density ($n_e$), which are often unavailable or computationally expensive to reconstruct in real-time on devices like KSTAR.
• The Goal: Develop a surrogate model that predicts ECH absorption locations with full-fidelity accuracy but with sub-millisecond latency to enable faster, more robust plasma control.

2. Methodology

The authors developed TorbeamNN, a machine learning (ML) surrogate model trained to replicate the output of the full-fidelity TORBEAM ray-tracing code.

A. Dataset Generation

• Source Data: 2712 unique time slices from 336 different KSTAR shots (2024 campaign, tungsten divertor).
• Simulation: The full offline TORBEAM code was run 647,267 times across random gyrotron angles (within safe operating limits) and plasma conditions.
• Separation: Six distinct models were trained (3 gyrotrons $\times$ 2 modes: X-mode and O-mode) because the physics of absorption differ significantly between modes.
• Input Features:
  • Mirror Geometry: Poloidal ($\theta$) and toroidal ($\phi$) angles.
  • Plasma Equilibrium: Derived from real-time EFIT (EFITRT1): Magnetic field ($B_T$), plasma current ($I_P$), magnetic axis ($R_0, Z_0$), minor radius ($a$), elongation ($\kappa$), plasma inductance ($l_i$), volume ($V$), and normalized pressure ($\beta_N$).
  • Density: A simplified 3-point electron density profile ($n_e$) derived from a separate ML surrogate using CO2 interferometer data (Core, off-axis $\psi_N=0.5$, edge $\psi_N=1.0$).
  • Note: The model successfully eliminated the need for full 3D magnetic field grids or complex $T_e$ profiles by using global parameters like $\beta_N$.
• Output Targets: Poloidal radius ($\rho_{pol}$), Absorption location ($R, Z$), and Current Drive efficiency ($\eta_{CD}$).

B. Model Architecture

• Framework: Keras library with the Adam optimizer.
• Structure: A feedforward neural network with 3 dense layers (60 neurons each) using ReLU activation, followed by a linear output layer.
• Deployment: Models were converted to C functions using the keras2c library for integration into the KSTAR Plasma Control System (PCS).

3. Key Contributions

1. Speed-Up: Achieved a >100x speed-up compared to the existing real-time TORBEAM implementation.
   • TorbeamNN Inference Time: ~50–60 $\mu$s per model.
   • Total Cycle Time: <180 $\mu$s for all three gyrotrons (vs. ~10–20 ms for TORBEAM).
2. Accuracy Preservation: The surrogate model maintains accuracy comparable to the full-fidelity offline TORBEAM code, not just the simplified real-time version.
3. Real-Time Integration: Successfully deployed on the KSTAR PCS, demonstrating that ML surrogates can replace physics-based ray-tracing in live control loops without requiring full $T_e$ profile reconstruction.
4. Dynamic Tracking: Demonstrated the ability to track moving absorption targets in dynamic plasmas with minimal error.

4. Results

Offline Validation

• Performance: All models achieved an $R^2$ value > 0.992.
• Error Metrics: The Mean Absolute Error (MAE) for the Z-absorption location prediction was 0.2 cm.
• Mode Comparison: O-mode predictions were slightly more accurate than X-mode, consistent with physical expectations (less refraction in O-mode).
• Limitations: Predictions degraded during the rapid ramp-up phase (before the L-H transition) due to inaccuracies in the real-time magnetic equilibrium reconstruction (EFIT) during that specific campaign.

Experimental Deployment (KSTAR)

• Feedforward Control: In a poloidal angle scan, TorbeamNN predictions matched offline TORBEAM results with an $R^2$ of 0.995 and MAE of 0.44 cm (improving to 0.28 cm during the stable flat-top phase).
• Feedback Control: A PID controller using TorbeamNN successfully tracked a target Z-location while simultaneously changing the toroidal mirror angle.
  • Tracking Error: Average absolute error of 0.535 cm over a 10-second interval.
  • Responsiveness: The system reacted to plasma transients significantly faster than a TORBEAM-based system could, as the calculation delay was reduced from ~10 ms to <0.1 ms.

5. Significance and Future Outlook

• Enabling Advanced Control: The massive reduction in computation time allows for:
  • Faster Steering: The ability to react to fast transients (ELMs, sawteeth) that were previously too fast for ray-tracing codes.
  • Multi-Tasking: Facilitates switching between multiple control objectives (e.g., NTM suppression + scenario optimization) within a single shot.
  • Optimization: Future controllers could leverage the differentiability of neural networks to perform gradient-based optimization (finding optimal angles directly) rather than relying on slower PID or brute-force search methods.
• Scalability: The approach is applicable to future reactors (e.g., ITER, SPARC) where real-time $T_e$ profiles may be unavailable or where control speeds must be extremely high.
• Broader Impact: This work validates the use of ML surrogates as a standard component in fusion plasma control systems, moving beyond simple diagnostics to active, real-time actuation.

Conclusion: TorbeamNN successfully bridges the gap between high-fidelity physics modeling and real-time control constraints, providing a robust, fast, and accurate method for steering ECH mirrors in complex, dynamic tokamak plasmas.