Exploring the Structure of the Solar Wind as an Initial Value Problem

Advisor: Roger Scott

The solar wind is an ever-present flow of ionized particles from the surface of the sun into the heliosphere and beyond. It is responsible for structuring the Sun’s interplanetary magnetic field and Earth’s magnetopause—the boundary between the Earth’s magnetic field and the magnetic field of the larger heliosphere. Understanding the properties of the solar wind and how these vary with respect to changes in the magnetic field of the solar corona is a topic of great importance in Solar and Heliospheric Science.

Thanks to a newly developed method we are able to calculate the plasma parameters for individual solar wind streams as an initial value problem (IVP), subject to the choice of initial conditions at the solar surface; however, the determination of appropriate initial conditions is challenging as it requires inspection of the solution to the IVP for each choice of initial condition to determine whether it is physically meaningful. Hence, this method falls under a larger class of problems known as “shooting problems.”

In this project, the selected student will first 1) gain familiarity with “shooting problems” by developing an algorithm for determining appropriate initial conditions for a simple, well understood IVP. The student will then 2) expand this method for cases where the solution structure is less well known, using the ideal case for validation. The student will then 3) apply their algorithm to the Solar Wind IVP to determine appropriate initial conditions for a given magnetic arrangement in order to determine the speed, density, and temperature of the solar wind in the near-Earth environment. Finally, if time allows, the student will 4) explore the variation in solar wind properties across different arrangements of the magnetic field and different model parameters.

This project will involve code development and computation, and candidates with coding experience will be given first consideration. Python experience is preferred, but not required.