Simple Linear and Nonlinear Examples of Truncated Power Series Algebra

TL;DR

This paper demonstrates the application of Truncated Power Series Algebra (TPSA) to linear and nonlinear systems, comparing analytical calculations with TPSA results using CERN's MAD-X and Cornell's BMAD libraries.

Contribution

It provides practical examples of TPSA calculations for linear and nonlinear systems, illustrating its effectiveness and accuracy in beam physics simulations.

Findings

TPSA accurately models linear systems.

TPSA effectively handles nonlinear calculations.

Comparison shows good agreement with analytical results.

Abstract

The paper displays calculations of linear systems as explained by Dr. Guido Sterbini. We also show a simple nonlinear calculation involving a rotation followed by an octupole kick. Some analytical calculations are compared to the Truncated Power Series Algebra (TPSA) results. The examples use the library PTC which is in MAD-X of CERN and BMAD of Cornell (see Ref. [1]).