Application of State Quantization-Based Methods in HEP Particle Transport Simulation

Lucio Santi,Soon Yung Jun,Krzysztof Genser,Daniel Elvira,Rodrigo Castro,Nicolás Ponieman

doi:10.1088/1742-6596/898/4/042049

Abstract

Simulation of particle-matter interactions in complex geometries is one of the main tasks in high energy physics (HEP) research. An essential aspect of it is an accurate and efficient particle transportation in a non-uniform magnetic field, which includes the handling of volume crossings within a predefined 3D geometry. Quantized State Systems (QSS) is a family of numerical methods that provides attractive features for particle transportation processes, such as dense output (sequences of polynomial segments changing only according to accuracy-driven discrete events) and lightweight detection and handling of volume crossings (based on simple root-finding of polynomial functions). In this work we present a proof-of-concept performance comparison between a QSS-based standalone numerical solver and an application based on the Geant4 simulation toolkit, with its default Runge-Kutta based adaptive step method. In a case study with a charged particle circulating in a vacuum (with interactions with matter turned off), in a uniform magnetic field, and crossing up to 200 volume boundaries twice per turn, simulation results showed speedups of up to 6 times in favor of QSS while it being 10 times slower in the case with zero volume boundaries.

Highlights

A significant challenge in high energy physics (HEP) particle simulations is an accurate and efficient tracking of particles affected by physics processes in complex detector geometries consisting of a variety of materials and many adjacent 3D volumes of different shapes
The aforementioned intersection point detection algorithm can be rather expensive, as it needs to iterate back and forth until a candidate point satisfying the intersection accuracy constraints is found. This suggests that methods such as Quantized State Systems (QSS), which naturally provide a lightweight handling of discontinuities, are good candidates for simulating HEP setups with frequent volume crossings
This idea was rooted in the fact that classical discrete–time solvers need to apply iterative algorithms to detect discontinuities, while for QSS methods the handling of discrete events calls only for a lightweight root finding of piecewise polynomial segments

Summary

Introduction

A significant challenge in high energy physics (HEP) particle simulations is an accurate and efficient tracking of particles affected by physics processes in complex detector geometries consisting of a variety of materials and many adjacent 3D volumes of different shapes. (vi) if segment 1 - 4 happened to cross a volume boundary, Geant computes the intersection point on the boundary using a custom iterative algorithm based on RK4 As it can be seen, simulation performance strongly depends on the computing efforts needed by the numerical integration methods. The aforementioned intersection point detection algorithm can be rather expensive, as it needs to iterate back and forth until a candidate point satisfying the intersection accuracy constraints is found This suggests that methods such as QSS, which naturally provide a lightweight handling of discontinuities, are good candidates for simulating HEP setups with frequent volume crossings. Equations are expressed in μ-Modelica [8], a subset of the more general Modelica language [9]

Case study

Findings

Conclusions and outlook