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\begin{document}

\title{Estimation of the error on the calculation of the pressure-strain term:
application in the terrestrial magnetosphere}



\author[1]{Owen Wyn Roberts}%
\author[1]{Zoltán Voros}%
\author[1]{Klaus Torkar}%
\author[2]{Julia E. Stawarz}%
\author[3]{Riddhi Bandyopadhyay}%
\author[4]{Daniel J Gershman}%
\author[1]{Yasuhito Narita}%
\author[5]{Rungployphan Kieokaew}%
\author[6]{Benoit Lavraud}%
\author[7]{Kristopher Gregory Klein}%
\author[8]{Yan Yang}%
\author[9]{Rumi Nakamura}%
\author[10]{Alexandros Chasapis}%
\author[8]{William H. Matthaeus}%
\affil[1]{Space Research Institute, Austrian Academy of Sciences}%
\affil[2]{Northumbria University}%
\affil[3]{Princeton University}%
\affil[4]{NASA Goddard Space Flight Center}%
\affil[5]{Institut de Recherche en Astrophysique et Planétologie}%
\affil[6]{Laboratoire d'astrophysique de Bordeaux}%
\affil[7]{University of Arizona}%
\affil[8]{University of Delaware}%
\affil[9]{Space Research Institute}%
\affil[10]{University of Colorado}%


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  \date{June 13, 2024}


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\begin{abstract}
Calculating the pressure-strain terms has recently been performed to
quantify energy conversion between the bulk flow energy and the internal
energy of plasmas. It has been applied to numerical simulations and
satellite data from the Magnetospheric MultiScale Mission. The method
requires spatial gradients of the velocity and the use of the full
pressure tensor. Here we present a derivation of the errors associated
with calculating the pressure-strain terms from multi-spacecraft
measurements and apply it to previously studied examples of magnetic
reconnection at the magnetopause and the magnetotail. The errors are
small in a dense magnetosheath event but much larger in the more tenuous
magnetotail. This is likely due to larger counting statistics in the
dense plasma at the magnetopause than in the magnetotail. The propagated
errors analyzed in this work are important to understand uncertainties
of energy conversion measurements in space plasmas and have applications
to current and future multi-spacecraft missions.%
\end{abstract}%



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