### Magnetic Bottles.

Okay, firstly, sorry for not having posted in the last month or so. I'm just sending this apology into the vast expenses of the world wide web as i don't really know who follows my blog and who doesn't. Y'all need to comment more and give me feedback! And I promised myself last summer that the only articles on this blog will be ones on science or at the very least related to the pursuit science and technology. And lately, I have been a bit involved with my course work and the like. So, I was looking for the right topic to blog on. And whatdoyaknow, I stopped looking for the right topic and started making a topic the right one! So, here is something interesting I learnt a couple of weeks back.

As part of a course on Radiative Processes in Astrophysics here at IIT Madras, I was studying the behavior of particles in uniform Electric and Magnetic fields. Something most of us studied during our 12th and maybe in a bit more detail in college, if you pursued science i.e. Anyway, we've all studied how particles move in straight lines or conic sections in the presence of Electric fields and how particles move in helixes in the presence of constant Magnetic fields. Here is where the catch comes.

There is such a thing defined as the Adiabatic Invariant for particle motion and using the adiabatic invariant, we can study how the motion of a particle is in the presence of a slowly varying magnetic field! Look at the picture for a better idea of what i'm referring to -

So, as you can see, the strength of the magnetic field is slowly varying along the horizontal axis! Now, if we look at the motion of a particle in such a field - the motion will be a helix but one whose radius keeps getting smaller and smaller, as is obvious from the picture!

We can derive the change in longitudinal momentum of the particle, which as it turns out is dependent on the square root of the strength of the magnetic field. And we already know that the magnetic field does not do any work on the particles i.e it does not impart energy to the particles i.e the sum of the squares of the longitudinal and transverse momenta should be constant!

$$P_0^2 = P_t^2 + P_l^2 = constant$$
$$P_t^2 \alpha \sqrt{H}$$

Using these two results, we can infer that, for the energy of the particle to remain constant while the particle is moving to regions of stronger and stronger magnetic fields, the longitudinal momentum of the particle will increase and the transverse momentum will decrease.

$$P_l^2 \geq 0$$

And since the square of the transverse momentum has to be greater than or equal zero, we can infer that there exists an invisible wall where the magnetic field is so strong that all of the transverse momentum of the particle is lost before it reaches this wall and the particle will then start moving backwards into regions of lower magnetic field. Which is why it is an invisible wall, a barrier the magnetic field is creating which particles cannot cross! This is what is referred to as a magnetic bottle, which can and is used to confine plasma! This can also be used to filter particles based on their energy as only particles with energy above a threshold will be able to cross the barrier! This threshold can be varied by varying the strength of the magnetic field.

Further, the concept of magnetic confinement is the first step towards building nuclear fusion reactors. Specifically, the Tokamak Fusion Test Reactor, uses the theory behind magnetic confinement to be able to hold plasma - plasma so hot that no material container will be able to withstand the temperature!

References :
(1) Motion in constant and uniform B fields, Sect. 21, Ch. 3, Landau & Lifschitz Book 2 - Classical Theory of Fields
(2) Adiabatic Invariance of flux through the orbit of a particle, Sect 5, Ch. 12, J.D. Jackson - Classical Electrodynamics.
(3) Motion in a slowly varying magnetic field, Sect. 8.4, Ch. 3, T. Padmanabhan - Theoretical Astrophysics - Vol 1.

### Animation using GNUPlot

Animation using GNUPlotI've been trying to create an animation depicting a quasar spectrum moving across the 5 SDSS pass bands with respect to redshift. It is important to visualise what emission lines are moving in and out of bands to be able to understand the color-redshift plots and the changes in it.
I've tried doing this using the animate function in matplotlib, python but i wasn't able to make it work - meaning i worked on it for a couple of days and then i gave up, not having found solutions for my problems on the internet.
And then i came across this site, where the gunn-peterson trough and the lyman alpha forest have been depicted - in a beautiful manner. And this got me interested in using js and d3 to do the animations and make it dynamic - using sliders etc.
In the meanwhile, i thought i'd look up and see if there was a way to create animations in gnuplot and whoopdedoo, what do i find but nirvana!

In the image, you see 5 static curves and one dynam…

### on MOOCs.

For those of you who don't know, MOOC stands for Massively Open Online Course.

The internet is an awesome thing. It's making education free for all. Well, mostly free. But it's surprising at the width and depth of courses being offered online. And it looks like they are also having an impact on students, especially those from universities that are not top ranked. Students in all parts of the world can now get a first class education experience, thanks to courses offered by Stanford, MIT, Caltech, etc.

I'm talking about MOOCs because one of my new year resolutions is to take online courses, atleast 2 per semester (6 months). And I've chosen the following two courses on edX - Analyzing Big Data with Microsoft R Server and Data Science Essentials for now. I looked at courses on Coursera but I couldn't find any which was worthy and free. There are a lot more MOOC providers out there but let's start here. And I feel like the two courses are relevant to where I …

### On programmers.

I just watched this brilliant keynote today. It's a commentary on Programmers and the software development industry/ecosystem as a whole.

I am not going to give you a tl;dr version of the talk because it is a talk that I believe everyone should watch, that everyone should learn from. Instead, I am going to give my own parallel-ish views on programmers and programming.
As pointed out in the talk, there are mythical creatures in the software development industry who are revered as gods. Guido Van Rossum, the creator of Python, was given the title Benevolent Dictator For Life (BDFL). People flock around the creators of popular languages or libraries. They are god-like to most programmers and are treated like gods. By which, I mean to say, we assume they don't have flaws. That they are infallible. That they are perfect.
And alongside this belief in the infallibility of these Gods, we believe that they were born programmers. That programming is something that people are born wit…