arXiv subjects

Maxim V. Umansky

Publications and source records attributed to Maxim V. Umansky.

3 recordsLinked to original sources

arXiv2025

A Propagator-based Multi-level Monte Carlo Method for Kinetic Neutral Species in Edge Plasmas

We propose and investigate a new multi-level Monte Carlo scheme for numerical solutions of the kinetic Boltzmann equation for neutral species in edge plasmas. In particular, this method explicitly exploits a key structural property of neutral particle dynamics: the prevalence of frequent collisions for which the outgoing velocity is determined by local plasma parameters. Using this property, we derive a multi-level algorithm based on collision event propagator and show, both analytically and through numerical experiments, that it reproduces the results of standard Monte Carlo methods. We further demonstrate that, in the context of coupled plasma-neutral edge simulations employing correlated Monte Carlo, the proposed scheme retains trajectory correlation to machine precision as the system evolves, whereas conventional methods exhibit rapid decorrelation. These results indicate that the propagator-based multi-level Monte Carlo scheme is a promising candidate for use in fully implicit Jacobian-free Newton-Krylov (JFNK) solvers for coupled plasma-neutral systems.

physics.plasm-ph↗

arXiv2025

Coupling Fluid Plasma and Kinetic Neutral Models using Correlated Monte Carlo Methods

While boundary plasmas in present-day tokamaks generally fall in a fluid regime, neutral species near the boundary often require kinetic models due to long mean-free-paths compared to characteristic spatial scales in the region. Monte-Carlo (MC) methods provide a complete, high-fidelity approach to solving kinetic models, and must be coupled to fluid plasma models to simulate the full plasma-neutrals system. The statistical nature of MC methods, however, prevents the convergence of coupled fluid-kinetic simulations to an exact self-consistent steady-state. Moreover, this forces the use of explicit methods that can suffer from numerical errors and require huge computational resources. Correlated Monte-Carlo (CMC) methods are expected to alleviate these issues but have historically enjoyed only mixed success. Here, a fully implicit method for coupled plasma-neutral systems is demonstrated in 1D using the UEDGE plasma code and a homemade CMC code. In particular, it is shown that ensuring the CMC method is a differentiable function of the background plasma is sufficient to employ a Jacobian-Free Newton-Krylov solver for implicit time steps. The convergence of the implicit coupling method is explored and compared with explicit coupling and uncorrelated methods. It is shown that ensuring differentiability by controlling random seeds in the MC is sufficient to achieve convergence, and that the use of implicit time-stepping methods has the potential for improved stability and runtimes over explicit coupling methods.

physics.plasm-ph↗

arXiv2024

Analysis of high-field side plasma instabilities in tokamak edge

Balanced double-null configurations are of general interest for boundary plasma physics, and they have been proposed for some future designs. Experimental observations demonstrate absence of plasma fluctuations in tokamak high-field side scrape-off layer in a balanced double-null configuration [Smick et al 2013 Nucl. Fusion 53 023001], and it is commonly assumed that plasma instabilities are suppressed on high-field side in the edge plasma due to the stabilizing effect of magnetic curvature. At the same time, the experimental evidence points to extremely steep plasma density profiles on high-field side, which should provide a strong instability drive. In the present study, the drift-resistive-ballooning mode instability model is investigated analytically and numerically to determine the characteristics of plasma instabilities, turbulence, and transport in tokamak scrape-off layer on high-field side.

physics.plasm-ph↗