# Eliminating poor statistics in Monte-Carlo simulations of fast-ion losses to plasma-facing components and detectors

## TL;DR

This paper introduces a Backward Monte Carlo method for simulating fast-ion losses in plasma devices, which overcomes the poor statistical issues of traditional Forward Monte Carlo approaches, leading to more accurate and efficient predictions.

## Contribution

The paper presents the BMC algorithm tailored for fast-ion loss simulations, detailing its implementation and advantages over the conventional FMC method.

## Key findings

- BMC eliminates poor statistics in small detector domains.
- The method provides more accurate loss signal simulations.
- Numerical examples demonstrate improved efficiency.

## Abstract

With Wendelstein 7-X now up and running, and the construction of ITER proceeding, predicting fast-ion losses to sensitive plasma-facing components and detectors is gaining significant interest. A common recipe to perform such studies is to push a large population of marker particles along their equations of motion, the trajectories randomized with Monte Carlo operators accounting for Coulomb collisions, and to record possible intersections of the marker trajectories with synthetic detectors or areas of interest in the first wall. While straightforward to implement and easy to parallelize, this Forward Monte Carlo (FMC) approach tends to suffer from poor statistics and error estimation as the detector domain is often small: it is difficult to guess how to set up the initial weights and locations of the markers for them to remain representative of the source distribution, yet record enough hits to the detector for good statistics. As an alternative, the FMC method can be replaced with a so-called Backward Monte Carlo (BMC) algorithm. Instead of starting with a given initial marker population, one starts from the end condition at the detector and records how the hit probability evolves backwards in time. The scheme eliminates the statistics issue present in the FMC scheme and may provide more accurate and efficient simulations of fast-ion loss signals. The purpose of this paper is to explain the BMC recipe in the fast-ion setting and to discuss the associated nuances, especially how to negate artificial diffusion. For illustration purposes, our numerical example considers a 1-D stochastic harmonic oscillator as a mock-up of a charged particle.