# Particle conservation in numerical models of the tokamak plasma edge

## TL;DR

This paper discusses numerical diagnostics and algorithms to ensure particle conservation in Monte-Carlo models of tokamak edge plasma, addressing errors caused by statistical methods and residuals, and proposing solutions for efficient, accurate simulations.

## Contribution

It introduces diagnostics and algorithms to identify and reduce particle balance errors in Monte-Carlo tokamak edge models, enabling larger time-steps without sacrificing accuracy.

## Key findings

- Diagnostics can unambiguously identify residual-induced errors.
- Algorithms allow large time-steps while maintaining particle conservation.
- Techniques improve the accuracy and efficiency of plasma edge modeling.

## Abstract

The test particle Monte-Carlo models for neutral particles are often used in the tokamak edge modelling codes. The drawback of this approach is that the self-consistent solution suffers from random error introduced by the statistical method. A particular case where the onset of nonphysical solutions can be clearly identified is violation of the global particle balance due to non-converged residuals. There are techniques which can reduce the residuals - such as internal iterations in the code B2-EIRENE - but they may pose severe restrictions on the time-step and slow down the computations. Numerical diagnostics described in the paper can be used to unambiguously identify when the too large error in the global particle balance is due to finite-volume residuals, and their reduction is absolutely necessary. Algorithms which reduce the error while allowing large time-step are also discussed.