Blog
Articles about computational science and data science, neuroscience, and open source solutions. Personal stories are filed under Weekend Stories. Browse all topics here. All posts are CC BY-NC-SA licensed unless otherwise stated. Feel free to share, remix, and adapt the content as long as you give appropriate credit and distribute your contributions under the same license.
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Magnetic reconnection: Theory and a simple numerical model
Magnetic reconnection is a fundamental plasma process that changes magnetic field topology and converts magnetic energy into kinetic and thermal energy. It lies between idealized frozen-in behavior and complex plasma dynamics, governing explosive phenomena in space and laboratory plasmas. In this post, we explore the physical principles and apply a simple numerical model to illustrate reconnection dynamics.
The solar wind and the Parker model
The solar wind is a continuous, supersonic outflow of ionized plasma from the solar corona into interplanetary space. Its existence and basic properties are now observationally well established, yet its theoretical understanding originates from a remarkably simple hydrodynamic argument developed in the late 1950s by Eugene Parker. Parker’s model not only explains why the corona cannot remain static but also predicts the large scale structure of the interplanetary magnetic field, now known as the Parker spiral. In this post, we present a compact introduction to the Parker solar wind model and the resulting spiral geometry of the heliospheric magnetic field. We complete this brief theoretical overview with a simple numerical experiment that simulates the Parker spiral structure with a simple Python code.
Magnetohydrodynamics (MHD): A theoretical overview with a numerical toy example
Magnetohydrodynamics (MHD) describes the coupled dynamics of a conducting fluid and electromagnetic fields. In this post, we summarize the standard MHD equations, explain ideal and Hall MHD, discuss key qualitative properties, and present a compact numerical experiment in Python illustrating complex structure arising from MHD nonlinearity.
Adiabatic invariants and magnetic mirrors
Adiabatic invariants provide the central simplification behind most practical descriptions of charged particle motion in slowly varying electromagnetic fields. In this post, we derive the three main adiabatic invariants and show how magnetic mirroring arises naturally from the conservation of the first invariant.
Earth’s dipolar magnetic field
In physics and computational mathematics, numerical methods for solving ordinary differential equations (ODEs) are of central importance. Among these, the family of Runge-Kutta methods stands out due to its versatility and robustness. In this post we compare the first four orders of the Runge-Kutta methods, namely RK1 (Euler’s method), RK2, RK3, and RK4.
Single-particle description of plasmas: Equation of motion, gyration, and ExB drift
In plasma physics, the motion of a single charged particle in prescribed electromagnetic fields provides fundamental insights into plasma behavior. In this post, we derive the equation of motion, explore energy conservation, and examine gyration in a uniform magnetic field.
Characteristics of a plasma: Collective behavior, shielding, and intrinsic time scales
Both in space and astrophysics as well as in laboratory settings, plasma is the most common state of matter. In this post, we introduce the characteristic scales that distinguish a plasma from an ordinary ionized gas and explain how quasineutrality, Debye shielding, and plasma oscillations arise.
Restarting my website
In the wake of the COVID-19 pandemic, I have made the decision to relaunch my website. While I have previously utilized my website for smaller personal projects and showcasing my photographs, I now intend to broaden its scope. I will be posting on a range of topics including physics, neuroscience, data science, machine learning, open-source projects, and more. As a result, I will be revamping the website in the upcoming months. Stay tuned for the updates.
Posts from 2013 to 2020 moved to the archive
I just cleaned up my website and put a lot of old stuff from 2013 to 2020 into the archive.