Returning to the Equatorial Plasma Fountain: Updating My Early Plasma Models for the GPU Era

Revisiting My Early Ionospheric Modelling Work Through a Modern Lens

Over the past several weeks, I have been restoring and digitizing some of my early research work from the mid‑1990s — work that originally existed only as printed pages filled with equations, derivations, and numerical modelling notes. Using a custom image‑processing pipeline that I developed recently (shadow removal, LAB‑space gradient correction, safe margin detection, and high‑accuracy OCR), these pages are now preserved in a clean, high‑quality, fully searchable digital archive.

This digitization effort has been more than a technical exercise. It has been a return to a period when I was deeply immersed in ionospheric physics, geomagnetic coordinate transformations, and numerical modelling of the Equatorial Plasma Fountain — the mechanism responsible for the well‑known Equatorial Ionization Anomaly (EIA).

My PhD thesis, “A Theoretical Study of the F2‑Region Equatorial Anomaly in Solar Maximum and Minimum” (Andhra University, 1995/1996) [1], formed the foundation of this work. The thesis explored the physics of the F2‑region, the equatorial plasma fountain, and the quiet‑time behavior of the anomaly across solstices and solar activity levels.

The ChiWriter Era — How the Thesis Was Created

The thesis was created using ChiWriter, a pre‑Windows scientific typesetting system. ChiWriter required equations to be assembled manually — symbol by symbol — using bitmap fonts and non‑Unicode encoding. It was not “typed” in the modern sense; it was constructed.

This context matters. The tools and computational resources of the early 1990s shaped the modelling choices I made, the structure of the thesis, and the limitations of the numerical simulations.

Early Modelling Work and Its Limitations

The thesis itself clearly acknowledged several limitations — many of which were unavoidable at the time:

• Centred dipole magnetic field approximation

• Single molecular species (O⁺)

• Simplified electrodynamics

• Coarse spatial resolution

• Dependence on early MSIS, TGCM and HWM models

Despite these constraints, the work produced meaningful insights into the quiet‑time behavior of the equatorial plasma fountain at solar maximum and minimum.

The Original Fortran‑77 Model Still Exists

A working version of the original Fortran‑77 model that I developed during my PhD is still with me. It includes dependencies on:

• MSIS atmospheric model

• HWM (Horizontal Wind Model)

The code is compact, efficient, and characteristic of the computational era in which it was written — optimized for RISC‑based workstations and limited memory environments.

1995 IRI Workshop Presentation

In January 1995, I presented aspects of this work at the IRI Workshop on Low and Equatorial Latitudes, held in New Delhi (January 9–13, 1995), organized by Dieter Bilitza. The workshop brought together researchers working on ionospheric modelling and the International Reference Ionosphere (IRI). The report is archived here: https://irimodel.org/docs/iri_95_report.html

This presentation was an important milestone in my early research career

A Renewed Scientific Impulse

Recently, I came across the paper “Equatorial Ionization Anomaly (EIA): Unraveling the Phenomenon of Ionospheric Disturbance” (Abbas et al., 2024). The paper provides a clear and contemporary overview of the EIA, describing how:

• The equatorial plasma fountain lifts plasma upward via E×B drift

• Plasma diffuses along magnetic field lines to form crests around ±15° magnetic latitude

• Neutral winds, composition changes, and storm‑time electrodynamics modulate the structure

Reading this brought back memories of the modelling challenges I faced decades ago — and how much more could be explored today with modern computational tools.

Extending the Work with GPU‑Accelerated Fortran

The landscape of scientific computing has changed dramatically since the 1990s. With GPU‑accelerated Fortran, it is now possible to revisit ionospheric models with far greater spatial and temporal resolution.

Modern Fortran: A Different World from Fortran‑77

Modern Fortran (2003/2008/2018) is fundamentally different from the Fortran‑77 environment in which my original model was written:

• COMMON blocks are obsolete — replaced by modules and explicit interfaces

• Implicit typing is discouraged — implicit none is standard

• Dynamic memory allocation replaces fixed‑size arrays

• Modules, derived types, and interfaces enable clean, maintainable code

• Parallelism is native through OpenMP, Coarrays, and CUDA Fortran

• Error handling and I/O are far more robust

Updating my original model is not a simple port — it requires re‑architecting the solver into a modern, modular, GPU‑friendly structure.

The New Modelling Framework

I am now planning to build a GPU‑accelerated Fortran simulation framework to explore:

• The equatorial plasma fountain

• Daytime and storm‑time E×B drift dynamics

• Hemispheric asymmetry driven by neutral winds

• Crest‑to‑trough variability

• Fountain behavior during geomagnetic storms

• Comparisons with latest EIA models

This effort is both a continuation and a modernization of the computational physics work I began three decades ago.

A Personal Reflection and a New Chapter

Looking back, my career took a different path than I had originally imagined. The ionospheric modelling work of the 1990s gave way to new domains — Radar's and Sonars to diagnostic imaging, signal processing, embedded systems, and applied research. But revisiting these early models has reminded me that scientific curiosity does not expire; it simply waits for the right moment to re‑emerge.

This renewed effort also aligns with a new chapter in my professional journey. I have founded Intuitus Research and Innovation Services LLP, a deep‑tech research and innovation practice focused on scientific modelling, AI‑driven analytics, and computational problem‑solving.

Beyond ionospheric and plasma‑dynamics modelling, my current work spans several deep‑tech domains. Through Intuitus Research and Innovation Services LLP, I am actively engaged in biomedical signal modelling and annotations, AI‑assisted diagnostic workflows, and computational tools for medical research. These areas share a common thread with my early scientific work — the need for rigorous modelling, high‑quality data, and computational precision. Whether it is plasma transport in the equatorial fountain or ECG annotation pipelines for clinical AI, the underlying philosophy remains the same: combine physics‑based understanding with modern computational power to solve meaningful problems. I am always open to collaborations in these domains and in other emerging areas of deep‑tech innovation.

With today’s computational capabilities, I can finally explore the questions that were out of reach decades ago. This renewed effort is not just about completing unfinished work — it is about reconnecting with the intellectual threads that shaped my scientific journey and extending them into new directions with clarity and purpose.

References

[1] PhD_Thesis_KSRN_Murthy.pdf