Machine Learning approach to modeling of neutral particles transport in plasma

A propagator-based approach is investigated for Monte-Carlo (MC) modeling of neutral particles transport in fusion boundary plasmas. The propagator is essentially a Green function for the neutral kinetic equation, which depends on the plasma profiles. A Neural Network (NN) based model for the propagator provides a fast and accurate solution for the neutral distribution function in plasma. Furthermore, continuous and smooth dependence of NN-based reconstruction of the propagator on the plasma parameters opens the possibility for using this approach with Jacobian-based methods for time-integration and root finding. Initial results from a small 1D test problem look promising; however, important research questions are concerned with the scaling of the algorithm to larger systems.

💡 Research Summary

The paper addresses the long‑standing challenge of efficiently modeling neutral particle transport in the edge region of magnetic‑fusion plasmas. Conventional kinetic Monte‑Carlo (MC) neutral codes are flexible and can incorporate detailed atomic physics and complex wall geometry, but they suffer from statistical noise that hampers convergence when coupled to fluid plasma models. To overcome this limitation, the authors reformulate the neutral kinetic equation as a linear operator problem ˆL fₙ = Sₙ and introduce a Green’s‑function‑like object, the “propagator” ˆP, which describes the distribution of neutrals immediately after their first charge‑exchange (CX) collision for a localized source. By repeatedly applying ˆP, successive generations of CX neutrals are generated, and the total CX source can be expressed as a convergent Neumann series (ˆI − ˆP)⁻¹ ˆP Sₙ, provided the norm of ˆP is less than one (i.e., ionization and CX rates are moderate). The neutral density follows directly from the CX source via n_N = S_cx,tot / (n_i K_cx).

In the 1‑D proof‑of‑concept, the authors compute the single‑collision propagator matrix P_ij using a dedicated MC code (MC1D) on a uniform grid of N = 21 points. Each matrix element represents the probability that a neutral originating in cell i suffers its first CX collision in cell j. The propagator‑based solution reproduces direct MC results for a variety of density and temperature profiles and for low, medium, and high collisionality, while being computationally faster and smoother.

Because constructing the propagator matrix is itself expensive, the authors train a dense feed‑forward neural network (NN) to predict the full N²‑dimensional propagator from a compact description of the plasma density profile. The input consists of five density values sampled at equally spaced collocation points; the output is the flattened propagator matrix. The NN has one hidden layer with 11 neurons and uses an exponential activation, linear output, MSE loss, and the NAdam optimizer. Training on 10 000 randomly generated density profiles (values between 0.1 and 1.0) for 10 000 epochs yields a model that predicts propagators with sufficient accuracy to recover neutral density profiles within a few percent of the MC benchmark. The NN‑based approach accelerates the neutral‑response calculation by several orders of magnitude compared with direct MC, though errors increase when the test density profiles deviate strongly from the piecewise‑linear shapes used in training (e.g., tanh‑like profiles).

The discussion compares the present propagator concept with the deterministic KN1D code, noting that the MC‑derived propagator can more easily handle complex geometries and detailed atomic processes. Extending to 2‑D or 3‑D would enlarge the propagator matrix dramatically and change its sparsity pattern, but the underlying linear‑operator framework remains applicable. Incorporating additional plasma parameters (electron/ion temperature, ion drift velocity) would expand the NN input space, requiring larger training datasets and deeper architectures.

A key advantage highlighted is the smooth, differentiable dependence of the NN‑predicted propagator on plasma parameters, opening the door to Jacobian‑based coupling with fluid plasma solvers (e.g., Newton‑type time integration). The authors plan to explore this coupling in future work and to develop more comprehensive training sets that cover realistic temperature and velocity variations.

In summary, the study demonstrates that (i) a single‑collision propagator provides an accurate and computationally efficient alternative to direct MC neutral transport; (ii) a neural network can learn the mapping from plasma profiles to the propagator, delivering rapid neutral‑response evaluations suitable for integrated plasma‑neutral simulations; and (iii) the approach holds promise for scalable, high‑fidelity edge‑plasma modeling in forthcoming fusion devices.