Numerical model for pellet rocket acceleration in PELOTON

TL;DR

This work develops and implements a direct numerical model for pellet rocket acceleration in magnetized fusion plasmas within the PELOTON Lagrangian-particle framework, validated by JET shattered pellet injection experiments. The acceleration arises from grad-$\mathbf{B}$-drift–induced asymmetry in the ablation cloud, captured through non-uniform cloud charging, a low-$R_m$ MHD description, and a detailed electron-heat deposition model, all coupled to a PELOTON Cooling Module that provides evolving background plasma states. A scaling law linking the pressure difference driving rocket acceleration to local electron temperature and density is derived from SPI simulations, and the neon component is shown to reduce acceleration, with gradient effects and fragment interactions offering additional modulation of the dynamics. The results offer quantitative predictions for SPI trajectories and highlight the framework’s potential for ITER-scale conditions, while identifying the need for improved diffusion modeling and further scaling analyses to extend applicability to future devices.

Abstract

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.

Figures (11)

• Figure 1: Schematic of non-uniform pellet cloud heating causing the rocket acceleration. $n_{eff}^1$ ($n_{eff}^2$) is the effective electron density on HFS (LFS) due to electrostatic shielding which reduces the intensity of electrons streaming into the ablation cloud along magnetic field lines. $\nabla\cdot q^1$ and $\nabla\cdot q^2$ denote the hot electron energy deposition in the cloud on HFS and LFS, correspondingly. See Section 2.2 for exact expressions.
• Figure 2: SPI plume when fragments enter the plasma. Color mappings provide the speed (a) and radius (b) of each fragment. Additionally, fragment size corresponds to marker size. The plume boundaries are marked by solid lines with angles measured clockwise from the downward vertical direction centered at the injection location in the poloidal plane.
• Figure 3: (a) Evolution of fragment radii over the simulation time. (b) Evolution of the $R_{shift}$ used in ad hoc model for deposition of ablated material. (c) Evolution of rocket acceleration experienced by each fragment as a function of time. Colors are consistent among three plots.
• Figure 4: (a) Trajectories of all SPI fragments during the simulation. (b) Trajectories of selected fragments. In both cases, the green dashed line represents the tracked inboard edge of the SPI plume based on the maximum gradient of the $D\alpha$ emission intensity detected by the KL8 camera in JET #96874 KongNardon2024.
• Figure 5: (a) Electron temperature and (b) electron density predicted by PELOTON's cooling module at selected times.