# Posts about particle-in-cell

# Post mortem for my engineering thesis code, PythonPIC

I'm giving a presentation on this less-than-glorious subject on Friday, so I figured, hey, it might be a nice time to write a summary of what that old repository on my GitHub page is. In a single video:

Admittedly, this post is going to be rather personal - this messy little code was basically my life for a few hundreds of hours.

# On the recent "On the Boris solver in Particle-in-cell simulations" paper

I recently came across a pretty cool paper by Zenitani and Umeda named "On the Boris solver in particle-in-cell simulation". There are many splendid descriptions of the Boris solver on the Internet, so while I would rather not duplicate them, here's a brief overview. In PIC simulations, the Boris solver (or pusher) is the usual algorithm of choice for moving and accelerating particles in given electric and magnetic fields.

You may wonder, since the equations of motion are ordinary differential equations, what's wrong with using the usual Runge-Kutta 4 solver? As it turns out, that one has a pretty major flaw. It has great accuracy for short term calculations, but over time your particle's motion will lose energy. This is a deal breaker for periodic motion, and simulations of, for example, plasma waves need to conserve that energy to provide accurate results.

Boris came up with his solver in the 1950's, and in a single sentence: the algorithm splits the acceleration via electric field into two parts and sticks a rotation about the magnetic field between them. This turns out to conserve energy and will probably come up again on this blog as I read more about symplexicity.

# Particle in Cell methods

I think it might finally be about time to do some plasma physics discussion on this blog, stay true to the name and so on…

Basically the only actual “scientific” work I have actually done with plasmas up until now is writing a PIC simulation, PIC standing for Particle-in-Cell. I thought I would take this opportunity to explain in my own words what the concept is - I think it’s a clever one.