Spectral methods for space plasma physics using Dedalus: Applications to ionospheric phenomena

Spectral methods are well known for outstanding accuracy and scale very efficiently when simple boundary conditions are applicable and no shocks or discontinuities are expected. Numerous problems in space physics have these characteristics. In this work, I will briefly describe the "Dedalus" library for solving PDEs using spectral methods and outline some applications to ionospheric physics. We will use this library to simulate simplified, but representative phenomena such as incoherent scatter radar spectra, Farley-Buneman instabilities, equatorial plasma bubbles, and Langmuir turbulence. These problems will allow us to explore different aspects of Dedalus' versatility. Furthermore, we will outline some research questions that may be investigated using this tool.