Brock Klippenstein

University of Manitoba

Brock Klippenstein is a Ph.D. student at the University of Manitoba working with Dr. Andreas Shalchi. His research focuses on the study of the transport of energetic particles, such as cosmic rays, moving through turbulent magnetic fields. Brock obtained his Bachelor’s degree in a joint mathematics – physics and astronomy program, with a minor in computer science from the University of Manitoba. He subsequently completed his Master’s degree in mathematics at University of Manitoba, under the supervision of Dr. Raphaël Clouâtre and Dr. Richard Michaël Slevinsky, with a M.Sc. thesis on solving partial differential equations numerically, also done at the University of Manitoba.

One of the big open questions in physics revolves around the origin of cosmic rays. The current favored theory suggests that they acquire their high energy through a process called diffusive shock acceleration. Confirming this theory requires a comprehensive understanding of the complex motion of these particles. Moreover, predicting the trajectory of these particles holds practical significance, given their documented propensity to cause damage on electronics in space. Brock’s doctoral work holds potential in addressing challenges related to controlled fusion, as energetic particles propagating through turbulent plasma share similarities with those found in fusion reactors.

Due the chaotic nature of the magnetic fields that cosmic rays and other high-energy particles interact with in mediums such as the interstellar medium, accurately predicting their exact motion is unfeasible. Hence, the focus lies on determining the probability function of finding a particle at a certain time, position, and velocity, which involves solving the Fokker-Planck equation. In his work, Brock specifically delves into the (approximate) analytical solutions of the Fokker-Planck equation. The fundamental material required to solve this equation encompasses orthogonal polynomials and special functions, such as Airy and Bessel functions.

This figure shows f as a function of z and μ and is a solution of the one-dimensional Fokker-Planck equation in late times. Here, μ=vz/v where vz is the z component of the velocity and v is the total speed. Français: Cette figure montre f comme une fonction de z et μ et est une solution de l’équation de Fokker-Planck en 1D à long terme. Ici, μ= vz/v où vz est la vitesse selon l’axe z et v est la vitesse totale.