Russell's Blog

New. Improved. Stays crunchy in milk.


Posted by Russell on December 10, 2008 at 4:01 p.m.
I just got the email from AIP a few hours ago; my first paper as first author is published!

It was a surprisingly long process. I think most of the delays were due to my own lack of experience. Hopefully, they are lessons learned, and my next trip through the publishing gauntlet will be easier, faster, and hopefully even more fun.

My uncle asked me if I would try to explain what I did in simple terms, so here it goes.

There is a thingy called a tokamak that is basically a very fancy Thermos. It keeps hot things hot. If you can make the stuff inside hot enough, it will work like a nuclear reactor. This is interesting because it is possible to build much better, much safer nuclear reactors this way. The trouble is, these Thermos things cost billions of dollars. The one they are building in France is going to cost something like nine billion bucks, and it will get barely hot enough enough to work as an experiment. Real ones would cost even more.

The good news is that the current designs for these fancy bottles only use a few percent of their heat-trapping capacity. That's what 'beta' means in the title; you can think of it as the heat-trapping efficiency of the machine. This is different from the energy efficiency, though. The heat trapping efficiency is more like how full you can fill the Thermos. Right now, we are building a nine billion dollar Thermos, and only filling it to 2% of its theoretical capacity. If we could use more of the heat-trapping capacity, then you could maybe reduce the cost by a factor of ten or a hundred (or increase the performance by that much).

So, this line of research is all about computer simulations of these doughnut-shaped nuclear Thermoses, and how they behave when they are nearly full.

In some other papers, I helped show that it is likely possible to build a nuclear Thermos that you can fill almost all the way up. In another paper, I also helped my friend Pierre show that it is possible to start with a nearly empty Thermos, and fill it to nearly full without anything bad happening (it all comes down to how you pour, to stretch the metaphor).

Typically, you have a theory that you trust, and you want to know if your computer simulation matches the theory. In this case, however, we built a computer simulation that contained very few assumptions. It solves Maxwell's equations (for magnetic fields and currents) and Newton's equations (for moving masses). This is nice, because those equations have been tested really, really well over the last 130 years. It also means that you can take the output of the computer program, and very easily check to see if it is correct.

As a result, we had the opposite problem one normally faces in science; a computer program that we trusted, and a theory that maybe we didn't. In this paper, I used the computer program to validate that the theory was correct. I did this in an unusual way. The theory is approximate, and so we expected it to go funny in some places. I treated the computer-generated output as the "exact" solution, and showed that when you subtract the theoretical result from the result we got from the computer, the difference is precisely the amount by which we expected the theoretical result to go funny. (In more rigorous language, I proved that the deviation from the numerical result has the same scaling as the error term in the expansion.)

Here is a link to the paper, in case you don't have access to AIP.

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