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fusion

Spherical tokamaks take a step forward

Good to see such a promising design gaining ground:

http://www.pppl.gov/news/2016/08/major-next-steps-fusion-energy-based-spherical-tokamak-design

Turbulent Plasma

Plasma turbulence is what makes fusion really hard. If plasma behaved like a fluid we would certainly have tokamaks the size of dishwashers humming away in our basements by now. Here’s a simulation of turbulence in a Tokamak.

 

But plasmas don’t obey the laws of hydrodynamics but the laws of magnetohydrodynamics (henceforth MHD for reasons of sanity). MHD treats a plasma as a fluid but incorporates Maxwell’s laws of electromagnetism. Interesting things happen because when an electron or ion moves in a plasma it constitutes an electric current which in turn produces its own magnetic field modifying the movement of the particles around it. It is the presence of these long-range electrostatic and magnetic forces, which distinguish a plasma from a fluid.

MHD has its limits though. It assumes ions and electrons move more or less together (quasi-neutrality) also in treating the plasma as something like a fluid MHD assumes the number of particles per unit volume is always high. So if we want to study very small scale behaviour or investigate the different behaviour of ions and electrons MHD may not be our ideal model. Enter gyrokinetics.

In plasma gyrokinetics we study a simplified picture of single-particle motion. like this:

 

gyro.png
Figure 1: Gyro motion of an electron with gyro centre in green.

 

By the left hand rule we know that if you put a moving charged particle in a magnetic field (B) we get a force perpendicular to the B field which spools the particle’s motion into a circle. The force is called the Lorentz force and is given by

latex-image-1.png

where q is the charge of the particle. Notice therefore that electrons and ions will experience opposite forces due to their opposite charges and orbit clockwise and anticlockwise respectively.

The centre of a particle’s orbit (shown in green) is called the gyro centre. In gyrokinetics we track the movement of the gyro centre not the particle itself. It is this simplification which makes gyrokinetics valuable.

These was big news out of MIT this past week with two papers on plasma turbulence. It looks like the researchers have found an important relationship between ion and electron turbulence. Naturally this work required gyrokinetic simulation not MHD.  I’ll be posting on these developments once I’ve absorbed the papers.

[The above video is an animation of plasma turbulence in a tokamak. The simulation is run on the Gyro code which is the same as the one used in the two papers I mentioned above]

Safety Factor

I’m gradually absorbing John Wesson’s wonderful book on Tokamaks, and wanted to share a sketch on safety factors.

A major factor in determining plasma stability in a tokamak is the number of complete orbits around the torus a particle completes before returning to its starting point, this number is called the safety factor (q). The bigger the better. We want particles to orbit many times before coming back to where they started, not to spiral around the torus like a phone cord.

The picture below shows q = 2, the title picture above is q=10.

Screen Shot 2015-10-24 at 21.10.46

The safety factor describes the geometry the toroidal and poloidal fields. In fact Poincaré maps made by firing electrons at phosphor screens are typically used to determine that the magnets are behaving correctly before plasma experiments can happen.

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