MIST
Magnetosphere, Ionosphere and Solar-Terrestrial
Diffusion Coefficients for Resonant Relativistic Wave-Particle Interactions Using the PIRAN Code
Diffusion Coefficients for Resonant Relativistic Wave-Particle Interactions Using the PIRAN Code
By Oliver Allanson (University of Birmingham; University of Exeter)
Quasilinear diffusion coefficients can be used to model the response of charged particles to resonant wave-particle interactions. The calculation of these coefficients is sufficiently complicated and arduous to render it prohibitive to many potential users, because of the expense in time spent developing the code. The PIRAN software package (”Particles In ResonANce”) is written using Python, and allows the user to calculate local and bounce-averaged relativistic diffusion coefficients in energy and pitch-angle space via the two main current proposed methods in the literature. The code is predominantly based upon the formalisms and methods presented in Glauert and Horne (2005, https://doi.org/10.1029/2004JA010851) and Cunningham (2023, https://doi.org/10.1029/10.1029/2023JA031703). We solve for diffusion coefficients using exact relativistic formulae. We use Gaussian spectra in wave frequency and in tangent of the wave normal angle and solve the full cold-plasma dispersion relation. At present the code supports fully tested calculations for electron diffusion coefficients based on whistler-mode waves in a fully ionized proton-electron cold plasma. However the codebase architecture is built such that future developments to include other wave modes and other plasma compositions should involve incremental additions. The initial release of PIRAN may not have the same number of features as some other numerical codes, but is has the advantages of being a fully open-source diffusion coefficient code that: (a) supports calculation of both local and bounce-averaged diffusion coefficients via both of the two proposed methods; (b) is written fully in Python; (c) has detailed user pages, commit history and changelog on GitHub.
The codebase is made available with the “GNU General Public License version 3” (https://opensource.org/license/gpl-3-0). All users of the code should follow the instructions of that license, and cite this paper in any publications or reports that make use of the PIRAN software package and repository. The work in this paper particularly refers to PIRAN Release 1.1.0 (Kappas et al., 2026).
O.A. and his wife Sophie, and their family, would like to gratefully acknowledge the outstanding support and contributions of the Williams Syndrome Foundation (WSF) in the United Kingdom (https://williams-syndrome.org.uk/). The WSF is a registered charity that promotes research and funding, and provides help and support for families and individuals with the rare congenital disorder known in the UK as Williams Syndrome (sometimes also known as Williams-Beuren syndrome). As such this software package is eponymously named after the son of Oliver and Sophie (who doesn't much care for diffusion coefficients himself). This acknowledgement serves to thank the WSF for their support to the lead author and his family during the preparation of work in this manuscript.
Paper: https://doi.org/10.1029/2025EA004479
Code: https://github.com/RB-ENVIRONMENT/PIRAN
Documentation: https://rb-environment.github.io/PIRAN/
Release 1.1.0: https://zenodo.org/records/18875558
Please email This email address is being protected from spambots. You need JavaScript enabled to view it. with any questions.
The Non-Linear Dependence of Daily Maximum Ionospheric Total Electron Content on F10.7
The Non-Linear Dependence of Daily Maximum Ionospheric Total Electron Content on F10.7
By Martin Cafolla (University of Warwick)
Solar Extreme Ultraviolet (EUV) radiation drives ionisation in the upper atmosphere to create the ionosphere. The variability of the intensity of this radiation results in regions of high electron number density across the ionosphere, characterised by the Total Electron Content (TEC). The daily solar flux at 10.7cm, the F10.7 index, is commonly used as a proxy to EUV in ionospheric models. Typically studies have shown how either the global averages or geographically local values of TEC vary with daily F10.7, F10.7A (the 81-day average) and F10.7p (a combination of daily F10.7 and F10.7A). We study how the daily maximum TEC correlates with daily F10.7 using 15-minute Global Ionospheric Maps (GIMs) from the Jet Propulsion Laboratory (JPL) between 2003-2024.
We find that for F10.7 ≳ 78 − 85 SFU, the daily maximum TEC saturates to a seasonally dependent value between 83−128 TECU. We asses the distribution of the residuals from linear and non-linear least squares fitting as a function of F10.7, as demonstrated in the figure below, and find that a tanh function out-performs a linear function for F10.7 ≥ 150 SFU. Our results are sensitive to different hemispheres, as a result of the construction of JPL-GIMs. Finally, we find that the daily F10.7 clearly resolves the saturation of daily maximum TEC, while F10.7 based on the average does not. Quantifying the value at which the daily maximum TEC saturates with F10.7, and its seasonal dependence, specifies the requirements of systems that are sensitive to extremes in TEC, important in planning of Low Earth Orbit satellite operations.
See publication for more details:
Cafolla, M. A., Chapman, S. C., Watkins, N. W., & Verkhoglyadova, O. P. (2026). The non-linear dependence of daily maximum ionospheric total electron content on F10.7. Space Weather, 24, e2025SW004745. https://doi.org/10.1029/2025SW004745
JWST Discovers the Vertical Structure of Uranus' Ionosphere
JWST Discovers the Vertical Structure of Uranus' Ionosphere
By Paola I. Tiranti (Northumbria University, School of Engineering, Physics and Mathematics, Newcastle, UK.)
Uranus’s upper atmosphere is one of the least understood in our Solar System, despite being critical for understanding how giant planets interact with their space environment. Using the James Webb Space Telescope, we observed Uranus for a full rotation and measured the vertical structure of its ionosphere - the charged layer of the atmosphere where aurorae form. Our results show that temperatures peak around 3,000 - 4,000 km above the planet, while ion densities peak near 1,000 km, and are significantly weaker than predicted by models. We also find two bright bands of auroral emission close to Uranus’ magnetic poles, as well as a surprising region where both emission and density are depleted, likely linked to the unusual geometry of Uranus’ tilted and offset magnetic field. These discoveries not only confirm that Uranus’ upper atmosphere has been cooling for decades, but also reveal new structures shaped by its magnetic environment. Together, they provide critical benchmarks for future missions and improve our understanding of how giant planets (both in our Solar System and beyond) balance energy in their upper atmospheres.
See publication for more details:
Tiranti, P. I., Melin, H., Moore, L., Thomas, E. M., Knowles, K. L., Stallard, T. S., K. Roberts & O’Donoghue, J. (2026). JWST discovers the vertical structure of Uranus' ionosphere. Geophysical Research Letters, 53(4), e2025GL119304. https://agupubs.onlinelibrary.wiley.com/doi/10.1029/2025GL119304
Fig 1: Vertical profiles in different regions as observed by JWST on 2025-01-19. a) and b) H3+ temperature and number density, respectively, for auroral region 1 (A1, 0° - 112°W, dark grey), auroral region 2 (A2, 200° - 251°W, dark green), non auroral region 1 (NA1, 113° - 199°W, orange), non auroral region 2 (NA2, 252° - 360°W, brown), emission dip region (ED, 190° - 240°W, light grey). c) Limb data points projected on disk used for the different regional profiles, as described above, with L-shells contours from the Q3 model (Connerney et al, 1987).