Comparing Diffusion Coefficients from Particle and Guiding Centre Approaches

Project Description:

Understanding the diffusion of charged particles perpendicular to a background magnetic field due to turbulence is crucial to model the modulation of cosmic rays in the heliosphere realistically. While most theories calculate the perpendicular diffusion coefficient from the guiding centre (GC) position of the particle (the imaginary point about which the particle gyrates), most simulation codes calculate it from the particle position. Qin & Shalchi (2016, ApJ, 823, 23) found excellent agreement between the two approaches from simulations for a limited set of parameters. However, analytical considerations suggest that this might be only valid under certain conditions. This work will revisit their findings using a simulation code developed recently in our group (see Els & Engelbrecht, 2024, ApJ, 969, 51) and extend the verification over a more extensive range of particle energies and turbulence levels. It will also explore how the definition of the GC position relative to the total (background + turbulent) magnetic field, rather than the background field alone, affects the computed diffusion coefficients. The student will use an existing C code that can generate synthetic magnetic turbulence from a given turbulence spectrum and integrate the equations of motion for charged particles moving in such turbulent fields. The first task is to modify the code to calculate the GC position with respect to both the background and total magnetic field, enabling the calculation of perpendicular diffusion coefficients from both the particle and GC position. The second task is to run simulations for several different particle energies, turbulence strengths, and (time permitting) turbulence geometries (such as pure slab turbulence, pure 2D turbulence, and composite turbulence with some ratio of slab to 2D turbulence). The third task is to plot and compare the resulting diffusion coefficients to determine whether the different approaches agree across the parameter range.

Research Area:

Space Physics

Project Level:

Honours

This Project Is Offered At The Following Node(s):

(NWU)

Special Requirements:

This project offers a hands-on introduction to computational plasma physics and cosmic ray transport theory, making it an excellent choice for students interested in pursuing postgraduate studies in computational heliospheric physics or astrophysics. The student will deepen their theoretical understanding of charged particle propagation in turbulent magnetic fields, GC theory, and spatial diffusion processes in plasmas. They will also learn how to calculate diffusion coefficients from simulations to interpret the statistical properties of particle transport, while gaining practical experience in modifying scientific code and visualising results. While prior exposure to turbulence theory is not required, this project is best suited to a student with an aptitude for theoretical and computational work. Proficiency in Python is essential for data analysis and visualisation, and a working knowledge of (or willingness to learn) C is vital for code modification. The simulation code will be provided, and computations can be run on a standard office PC.