Phase-Aligned Fuel Injection in a Reduced Burn Propagation Model

Abstract

Fuelling studies in magnetically confined plasmas typically focus on fuelling rate, deposition location, and penetration depth. The temporal phase of fuelling relative to evolving burn structures has received far less attention. In systems where burn propagates as a moving structure, timing may also influence the outcome. This work examines that possibility using a reduced one-dimensional toroidal model in which crest propagation is represented through prescribed advection together with simplified source, transport, thermalisation, and exhaust closures. The model is intended as a conceptual mechanism study rather than a predictive plasma calculation.

The model supports a travelling burn crest sustained by fusion heating and localised fuel input. Injecting fuel at different angular offsets relative to the tracked crest reveals strong phase sensitivity in the lag scan. Injection close to the crest produces the strongest local burn response, but this regime is short-lived. By contrast, delayed injection into the wake sector sustains propagation for much longer, whereas asynchronous injection collapses on nearly the same timescale as the no injection baseline despite receiving the same scheduled fuel input per orbit as the phase-aligned cases.

Sensitivity tests confirm that the behaviour remains robust across a range of parameters, with grid refinement demonstrating convergence of the crest structure and thermalisation sweeps preserving the same qualitative lag dependence. To probe the model more broadly, two Monte Carlo ensembles were generated: one varying thermalisation and pumping parameters, and another varying crest geometry and transport parameters around baseline. Across these runs, the phase-dependent propagation window persists. The response shows a clear transition between a strong-burn, short-lived near-crest regime and a longer-lived delayed-fuelling regime, with the longest runtimes occurring in the sector closer to the anti- crest side of the domain. Across the tested parameter sets, this longer-lived phase window persists with only modest shifts in location, while termination-criterion variation mainly affects the detected collapse boundary rather than the existence of the regime.

The results indicate that structured fuelling can influence propagation dynamics in this reduced system even when total fuel input is unchanged. The model is intentionally simplified and excludes magnetic geometry and stability physics. It is presented as an advection-diffusion-reaction dynamics study of phase-coupled forcing, not a plasma prediction, and motivates further investigation of phase-structured fuelling in higher-fidelity simulations.