Last edited 14dec15 by lhansel2@illinois.edu
Find this document at http://new.math.uiuc.edu/math198/lhansel2

# Stellarator: New Interest in an Old Theory

After researching what to pursue for my project I decided to expand on Nick Connolly's tokomak model from 2012. Click here to see Nick's website

## Abstract

There are several different methods currently used to create nuclear fusion. This project will be to create a model of the more common types, specifically a stellarator, using VPython. The ability to watch particles move around the machine will help to give students a better understanding on the basic workings and structure of these devices. This knowledge can then be used to work on and improve exixting theories.

### Nuclear Fusion at a Glance

Nuclear fusion is the combination of two or more smaller atoms to create a larger atom. This process realeases orders more magnitude energy compared to nuclear fission and is what powers all of the stars in the universe. When trying to replicate stellar fusion on Earth, scientists widely use the same process. Due to abundant fuel, deuterium-tritium fusion is the most pursued method of fusion. It uses two isotopes of hydrogen, deuterium (hydrogen with 2 neutrons) and tritium (hydrogen with 3 neutrons) to produce energy. Along with the abundant energy, this process produces a helium atom and an alpha particle.

### Math Behind the Project

Particles inside of both stellarators and tokomaks move with what is called the Larmor Radius, or gyroradius. This is the path that particles take when under the effect of a magnetic field, which both fusion systems use extensively. Below is a simple picture describing this path.

Particles in both tokomaks and stellarators experience gyroradiation but stellarators use the shape of the machine to keep the particle in a similar position relative to the walls. The maintenance of relative positions greatly increases the stability of stellarators.

### Current Status

Nuclear fusion has yet to reach ignition, meaning it has yet to reach a point where it produces more energy than it takes in. Stellarators are recieving a lot of interest because they are more stable than tokomaks. The Max Planck Institute in Germany recently finished building the largest and most complex stellarator to date, the Wendelstein 7-X. Containing over 70 magnets in its construction it is able to contain plasma at a density of 3 x 10^20 particles/cubic metre, and a plasma temperature of 60 - 130 million K. A picture of the Wendelstein 7-X can be found here.

### My Project

My project was a very basic model and wireframe of a stellarator in vPython. It models the motion of particles inside of a basic stellarator. Below is a picture of my wireframe and my closed model. In the wireframe you can see the Larmor radius simulated.