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Machine Learning approach to modeling of neutral particles transport in plasma

M. V. Umansky, G. J. Parker, R. D. Smirnov

TL;DR

The paper tackles neutral transport in fusion boundary plasmas, where accurate modeling of neutrals is essential for self-consistent edge dynamics; neutrals obey the kinetic equation $\hat{L} f_n = S_n$ and can be represented by a Green function (propagator). It introduces a propagator-based Monte Carlo framework using a single-collision propagator $\hat{P}$ to construct the total CX source via $\vec{S}_{cx,tot} = \sum_{m\ge1} \hat{P}^m \vec{S}_n$ and solves $(I-\hat{P}) \vec{S}_{cx,tot} = \hat{P} \vec{S}_n$. A densely connected neural network learns to map plasma density profiles to the propagator matrix (size $N^2$) with architecture: input 5, hidden 11, output $N^2$, trained by MSE with NAdam, yielding smooth, differentiable propagator outputs. 1D tests show agreement with direct MC and demonstrate speed-ups, with results suggesting feasibility of extending to higher dimensions and coupling to plasma solvers via Newton-Krylov time integration, while scaling remains for future work.

Abstract

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.

Machine Learning approach to modeling of neutral particles transport in plasma

TL;DR

The paper tackles neutral transport in fusion boundary plasmas, where accurate modeling of neutrals is essential for self-consistent edge dynamics; neutrals obey the kinetic equation and can be represented by a Green function (propagator). It introduces a propagator-based Monte Carlo framework using a single-collision propagator to construct the total CX source via and solves . A densely connected neural network learns to map plasma density profiles to the propagator matrix (size ) with architecture: input 5, hidden 11, output , trained by MSE with NAdam, yielding smooth, differentiable propagator outputs. 1D tests show agreement with direct MC and demonstrate speed-ups, with results suggesting feasibility of extending to higher dimensions and coupling to plasma solvers via Newton-Krylov time integration, while scaling remains for future work.

Abstract

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.
Paper Structure (8 sections, 10 equations, 3 figures)

This paper contains 8 sections, 10 equations, 3 figures.

Table of Contents

  1. Introduction
  2. Model
  3. MC neutral transport
  4. Propagator
  5. Neural network model
  6. Results
  7. Summary and conclusions
  8. Appendix

Figures (3)

  • Figure 1: Test problem with a single delta-peak for the neutral source. The left plots show the profiles of plasma temperature $T_{e,i}(x)$ and neutral source $S_n(x)$. The middle column shows the plasma density profile $n_{e,i}(x)$ (top) and the corresponding calculated neutral density profile $n_N(x)$ (bottom) for test case with short neutral MFP. The right column the profiles for a similar test case but with long neutral MFP. Results for neutral density are shown for direct MC calculation (cross marks) and from the propagator (blue line).
  • Figure 2: Test problem for $S_n(x)$ represented by three delta-functions. Results for neutral density $n_N(x)$ are shown for direct MC calculation (cross marks), directly calculated propagator (blue line), and NN-predicted propagator (green line). The left plots show the profiles of plasma temperature $T_{e,i}(x)$ and neutral source $S_n(x)$. The second left column shows the plasma density profile $n_{e,i}(x)$ (top) and the corresponding calculated neutral density profile $n_N(x)$ (bottom) for flat $n_{e,i}(x)$. The second right column shows results for a similar test but with piece-wise-linear $n_{e,i}(x)$. The right column shows results for a similar test but with tanh-shaped $n_{e,i}(x)$.
  • Figure 3: Test problem for $S_n(x)$ of a general shape. Results for neutral density $n_N(x)$ are shown for direct MC calculation (cross marks), directly calculated propagator (blue line), and NN-predicted propagator (green line). The left plots show the profiles of plasma temperature $T_{e,i}(x)$ and neutral source $S_n(x)$. The second left column shows the plasma density profile $n_{e,i}(x)$ (top) and the corresponding calculated neutral density profile $n_N(x)$ (bottom) for flat $n_{e,i}(x)$. The second right column shows results for a similar test but with piece-wise-linear $n_{e,i}(x)$. The right column shows results for a similar test but with tanh-shaped $n_{e,i}(x)$.