Mission Analysis
2 Oct 2023

Study of the motion of charged particles in planetary magnetospheres using Differential Algebra

Project overview

The study of the motion of plasma and charged particles in planetary magnetospheres can offer important insights to planetary science, as well as on the protection of sensitive infrastructure in space and on Earth from the effects of space radiation.

Dedicated instruments on spacecraft perform measurements on these environments in Earth orbit and throughout the Solar system. To prepare for an instrument’s operation and to help analyze its measurements simulations are typically performed. However simulating the motion of large numbers of particles can be computationally intensive, particularly in cases with strong local magnetic fields, e.g. around Jupiter.

The complex motion of charged particles in the Earth's magnetosphere. Credit: Brian Monroe and Tom Bridgman, NASA GSFC
The complex motion of charged particles in the Earth's magnetosphere. Credit: Brian Monroe and Tom Bridgman, NASA GSFC

Differential algebra (DA), a method invented for beam particle physics and applied among others to spacecraft orbit propagation, has the potential to offer a significant reduction in computational resources for the propagation of large numbers of particles in planetary magnetospheres. DA is a numerical technique to automatically compute high order Taylor expansions of a given function. In the DA framework the Taylor expansion of a system model function is calculated once at relatively high computational expense. This expansion however can then be used to evaluate any input value around the nominal with negligible computational costs. DA thus offers the potential for a significant reduction of computational resources and time used for the propagation of charged particles in planetary magnetospheres.

Following the ACT's continuing interest in the application of DA to space problems, during this project we aim to create a DA-based tool for the propagation of charged particles in planetary magnetospheres. We will then apply the tool to the simulation of measurements of energetic particles as will be encountered, for example, by the JUICE mission in the environment of Jupiter. Such a tool is expected to be valuable to the space physics community as it has the potential to significantly reduce the computational load for the simulation of large numbers of particles in planetary magnetospheres, especially in cases where charged particles are propagated in strong magnetic fields (Jupiter, solar corona, etc.).

References

  1. G. Parks, 2003. "Physics of Space Plasmas: An Introduction", Westview Press, https://ui.adsabs.harvard.edu/abs/1991pspa.book.....P/abstract
  2. P. Di Lizia, 2015. "Relevant Applications of Differential Algebra in Astrodynamics", AstroNet-II International Final Conference, Tossa de Mar
  3. D. Izzo, F. Biscani, 2020. audi and pyaudi differential algebra library (Version v1.8). Zenodo. http://doi.org/10.5281/zenodo.3702783
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