Numerical model for pellet rocket acceleration in PELOTON

A direct numerical simulation model for the rocket acceleration of pellets in thermonuclear fusion devices has been developed for PELOTON, a 3D Lagrangian particle pellet code [R. Samulyak et al, Nuclear Fusion 61 (4), 046007 (2021)], and validated using shattered pellet injection (SPI) experiments in JET. The pellet rocket acceleration is driven by grad-B drift of the ablation cloud that creates asymmetry and non-uniform heating of the cloud. The model accounts for non-uniform charging of the ablation cloud by hot plasma electrons as well as local plasma gradients. The increased pressure on the high-field-side compared to the low-field-side leads to pellet (fragment) rocket acceleration. Pure deuterium and deuterium-neon mixture models have been implemented. The background plasma states have been obtained by using a new plasma cooling model for PELOTON. The cooling model distributes the ablated material within the corresponding flux volumes and accounts for ionization and other energy losses, Ohmic heating by toroidal currents, and the energy exchange between ions and electrons. Plasma profiles predicted by PELOTON cooling model have been compared with JOREK and INDEX simulations. PELOTON simulations of rocket acceleration and the corresponding trajectories of deuterium fragments are consistent with experimentally measured trajectories in JET. We show that composite deuterium-neon pellets containing 0.5% of neon experienced smaller deviation of their trajectories compared to the pure deuterium case. We simulate various spatial configurations of pellet fragments and demonstrate the cloud overlap impact on rocket acceleration. Additionally, we demonstrate the effect of plasma state gradients on the rocket acceleration. Future work will focus on the rocket acceleration of SPI in projected ITER plasmas and the development of the corresponding scaling law for the rocket acceleration.

💡 Research Summary

The paper presents a comprehensive direct‑numerical‑simulation (DNS) framework for modeling the “rocket acceleration” of cryogenic pellets and shattered‑pellet‑injection (SPI) fragments in magnetically confined fusion plasmas, implemented within the three‑dimensional Lagrangian particle code PELOTON. The authors first describe the physical origin of the acceleration: hot plasma electrons stream along magnetic field lines into the ablation cloud surrounding an injected pellet, but because the cloud is displaced by the grad‑B drift, the high‑field side (HFS) experiences weaker electrostatic shielding than the low‑field side (LFS). Consequently, a larger electron heat flux reaches the HFS, raising the local gas pressure. The pressure imbalance ΔP = P_HFS − P_LFS generates a net force that pushes the pellet (or its fragments) toward the LFS, a phenomenon traditionally called “rocket acceleration.”

To capture this mechanism quantitatively, the authors formulate a low‑magnetic‑Reynolds‑number MHD model for the partially ionized ablation cloud. In Lagrangian form, the continuity, momentum, and energy equations (4)–(6) are solved together with an equation of state that accounts for multi‑species ionization. The electron heat deposition is modeled using a kinetic‑theory‑based expression (9)–(18) that includes a sophisticated electrostatic‑shielding (albedo) correction derived from a nonlinear Poisson‑type equation (16). This yields spatially varying effective electron density n_eff and heat fluxes q± on the HFS and LFS. The grad‑B drift is represented by a simplified transverse force f_D, leading to an acceleration equation (8) that integrates the pressure difference along the magnetic field line.

A novel plasma‑cooling module supplies the background plasma state for the pellet simulations. It distributes the ablated material over magnetic flux volumes, incorporates ionization losses, Ohmic heating, and ion‑electron energy exchange, and produces temperature and density profiles that have been benchmarked against the JOREK and INDEX codes. For deuterium‑neon mixtures, a fully coupled set of Saha equations (19)–(23) is solved iteratively to obtain species fractions, radiation losses, and transport coefficients; the results are tabulated for rapid lookup during the time‑dependent simulations.

The model is validated against shattered‑pellet injection experiments on JET. Simulations of pure deuterium pellets reproduce the measured fragment trajectories, confirming that the pressure‑difference term dominates the acceleration while the momentum‑flux term from asymmetric ablation rates is negligible. The authors explore a range of fragment configurations (linear, circular, random) and demonstrate that cloud overlap can either mitigate or amplify the pressure imbalance, thereby altering the net acceleration. Adding a small amount of neon (0.5 % by atom) reduces the electrostatic shielding length, lowers the electron heat flux on the HFS, and consequently diminishes ΔP, leading to smaller trajectory deviations compared with pure deuterium pellets.

Finally, the paper outlines future work aimed at extending the model to ITER‑scale plasmas and deriving a scaling law for rocket acceleration as a function of pellet size, composition, and background plasma parameters. Such a scaling law would be valuable for optimizing pellet fueling strategies, minimizing impurity penetration, and controlling plasma instabilities in next‑generation fusion reactors.