Hall thruster

One of my latest projects that I'm doing in parallel with others is designing and making a Hall thruster! This is probably one of the least theoretical projects that I've ever done! I have no idea really what inspired me to do this, I was just thinking of accelerating plasmas in discharge tubes when I thought it would be fun to build a small scale one.

A Hall thruster is a device which accelerates a plasma through a discharge chamber via an electric field. The accelerated ions meet with electrons that are rotated around the devices axis by means of a radial magnetic field and so the now neutral atoms pass out of the discharge chamber.

It may not be possible to miniaturise a Hall thruster due some physical restrictions, if this is the case I can try to construct a similar type of device, generic ion thruster etc. So far I've made a basic model using COMSOL Multiphysics and I'm just in the process of testing different materials.

Simulating magnetic fields

Very early design of thruster

I don't really want to use the thruster for anything, I may even just make a general plasma accelerator. I'd like to look into attaching a simple plasma discharge chamber to some capacitor bank and see what amounts of thrust can be produced.

Modelling two populations competing for a resource

I'm currently working on modelling two populations competing for a resource using a continuous approach rather than discrete. The system consists of three coupled non linear differential equations. One representing a resource and the other two, populations.

At the start I was unsure what approach I should use to model this system, I considered using a discrete method such as with cellular automata but it just didn't feel right. I had already worked on modelling reaction-diffusion systems with coupled differential equations and so I thought I would stick with my strength.

I found a number of books rather useful:

• Complex population dynamics - Blasius, Kurths and Stone :  ISBN-13: 978-9812771575

• Mathematical methods of population biology - Hoppensteadt :  ISBN-13: 978-0521282567

• Pattern formation and dynamics in non-equilibrium systems - Cross and Greenside : ISBN-13: 978-0521770507

I coded the simulation of the system in FreeBaisc. The model itself is in 0 + 2 dimensions. I haven't analysed the 2D output screen capture yet although I have been analysing the phase portraits of specific spatial locations and also the stability analysis of the equations themselves. But in the interest of prettiness here is a picture of a 2D output (explanation to follow).

 

Pattern formation in hot chocolate

Found these patterns in my mug whilst working late one night :). Hope to model the pattern formation with fluid dynamics at some point.

Useful papers:

• Nonlinear dynamic and pattern bifurcations in a model for spatial patterns in young mussel beds - Rong-Hua, Quan-Xing, Gui-Quan, Zhen Jin and van de Koppel  
   http://rsif.royalsocietypublishing.org/content/early/2009/02/09/rsif.2008.0439.full.html#
  
  
• Pattern Formation in Draining Thin Film Suspensions - Buchanan, Molenaar, de Villiers and Evans
  http://pubs.acs.org/doi/abs/10.1021/la063282a