Tokamak Plasma Tests Carbon Heat Shields Under Entry-Like Heating

Carbon thermal protection systems are hard to validate on the ground because entry heating combines high heat flux, ionized flow, radiation, surface chemistry, and material failure. The Galileo probe’s Jupiter entry remains the reference case: roughly 300 MW/m² peak heating, about 70 s of heat-shield exposure, and large post-flight disagreement between predicted and measured recession. This paper turns the DIII-D tokamak into a controlled ablation testbed for that regime, using the scrape-off layer and divertor plasma to expose carbon samples to heat loads in the same order as giant-planet entry calculations.

The authors do not claim that a tokamak reproduces a full atmospheric entry. It lacks the stagnation pressures of flight, cited as up to 7 atm, and the flow geometry is magnetized plasma rather than a hypersonic shock layer. The claim is narrower and more useful: DIII-D can isolate high heat flux, ionization, carbon emission, ablation-cloud shielding, and impurity transport with diagnostics that are difficult to obtain in arc-jet or flight data.

Core Contribution

The main contribution is an experimental platform, not a new ablation equation. The study combines two exposure modes. Stationary ATJ graphite rods are inserted near the divertor strike point and held in approximately fixed plasma conditions. Slow-launched carbon pellets then traverse the edge and core plasma, so the experiment samples the full ablation history of a moving body.

Figure 3 shows the modified DiMES head used for the rod campaign, including multiple carbon-rod geometries mounted so that cylindrical, wedge-shaped, concave, and SiC-coated samples could be exposed during DIII-D shots.

That geometry comparison is one of the paper’s more concrete engineering findings. Cylindrical and concave rods follow the Park semi-empirical model reasonably well, while the wedge shape loses more material than either Park or Matsuyama predicts. The result points to local heat-flux concentration at sharp edges and curvature as a first-order design issue, not a cosmetic shape effect.

Technical Approach

For stationary rods, the authors reconstruct incident parallel heat flux from X-point reciprocating probes, fixed floor Langmuir probes, strike-point sweeps, and Eich-profile fits. The measured divertor heat flux near the rod positions is about 30–40 MW/m² during the flat-top exposure, with individual shots providing roughly 4.5 s of stationary plasma and about 9 s cumulative exposure for several heads. Spectroscopy tracks carbon emission near 516–520 nm, visible imaging locates the emitting rods, and post-exposure 3D optical profilometry maps recession.

The mass-loss calculation is direct: the authors use pre/post mass changes and profiled exposed area to estimate $\dot{m}=\Delta m/(A\Delta t)$. They compare those rates with two aerospace semi-empirical ablation models, Matsuyama and Park, using wall temperatures near graphite sublimation. The inferred surface temperature from narrow-band visible emission levels off around 3,700–3,800 K, consistent with a steady energy balance at 30–34 MW/m².

For moving pellets, the setup changes from surface recession to trajectory-resolved ablation. Porous graphite pellets with density 0.8 g/cm³ and dense glassy carbon pellets with density 1.4 g/cm³ are launched vertically from DiMES at about 3–10 m/s. Fast visible and infrared cameras reconstruct the 3D path, CO₂ interferometry measures line-integrated electron density from ionized ablation products, and UEDGE-DUSTT models the pellet motion and mass loss under gravity, ion drag, parallel plasma flow, electrostatic forces, and $\mathbf{j}\times\mathbf{B}$ forces.

Figure 9 captures the diagnostic contrast: visible imaging tracks the luminous pellet path, while infrared imaging follows thermal emission as the pellet crosses the separatrix.

Results and Analysis

The rod results support the platform’s basic calibration. The wedge-shaped rod shows the largest mass-loss rate, reported as about (1–3) × 10⁻² g/cm²/s, while cylindrical and concave rods fall near (1.03–1.06) × 10⁻² g/cm²/s. Park predicts (1.28–1.70) × 10⁻² g/cm²/s under the measured conditions; Matsuyama predicts (0.66–0.87) × 10⁻² g/cm²/s. Park is closer for blunt and concave shapes, but it still misses the wedge enhancement, which is the more interesting failure mode for heat-shield modeling.

The pellet experiments add a second validation target: dynamics. UEDGE-DUSTT reproduces the qualitative trajectory only when $\mathbf{j}\times\mathbf{B}$ forces are included. Without that term, the simulated pellet is rapidly lost to the wall; with it, penetration toward the core better matches the reconstructed path. Radiation-cloud shielding also changes the ablation history. For a 3.00 mm pellet, the simulated peak mass-loss rate drops from 0.4 g/s without shielding to 0.22 g/s with shielding, while the onset of active ablation shifts from 0.02 s to 0.06 s.

The strongest caveat is that several measurements are indirect. CO₂ interferometry sees the density perturbation from ionized carbon and later impurity transport, so the paper explicitly avoids interpreting the full ~200 ms density perturbation as instantaneous mass loss. The authors instead use synchronized camera timing and localized density changes to infer rates. The spallation result is also qualitative: glassy carbon pellets fragment even though average heat flux remains below the 146 MW/m² steady spallation threshold from Galileo analysis. That makes the observation valuable, but it also means transient stress and microstructure remain open variables rather than closed model inputs.