Blog

A blog of Python-related topics and code.

Types of plasma

Two important parameters in plasma physics are the electron Debye length, $\lambda_{\mathrm{D}e}$, a measure of the distance over which charge-screening effects occur and deviations from quasi-neutrality are observed, and the number of paricles in a "Debye cube" (of side length $\lambda_{\mathrm{D}e}$), $N_\mathrm{D}$.

The Debye length

An important concept in plasma physics is the Debye length, which describes the screening of a charge's electrostatic potential due to the net effect of the interactions it undergoes with the other mobile charges (electrons and ions) in the system. It can be shown that, given a set of reasonable assumptions about the behaviour of charges in the plasma, the electric potential due to a "test charge", $q_\mathrm{T}$ is given by $$ \phi = \frac{q_\mathrm{T}}{4\pi\epsilon_0 r}\exp\left(-\frac{r}{\lambda_\mathrm{D}}\right), $$ where the electron Debye length, $$ \lambda_\mathrm{D} = \sqrt{\frac{\epsilon_0 T_e}{e^2n_0}}, $$ for an electron temperature $T_e$ expressed as an energy (i.e. $T_e = k_\mathrm{B}T_e'$ where $T_e'$ is in K) and number density $n_0$. Rigorous derivations, starting from Gauss' Law and solving the resulting Poisson equation with a Green's function are given elsewhere (e.g. Section 7.2.2. in J. P. Freidberg, Plasma Physics and Fusion Energy, CUP (2008)).

A simple colouring grid

Just a simple Python app to try out the TkInter interface to the Tk GUI toolkit and to keep my children occupied. It shows a window with a square grid of cells which can be coloured by selecting from a palette. Run with

Plotting nuclear fusion cross sections

In a nuclear fusion reaction two atomic nuclei combine to form a single nucleus of lower total mass, the difference in mass, $\Delta m$ being released as energy in accordance with $E = \Delta m c^2$. It is this process which powers stars (in our own sun, hydrogen nuclei are fused into helium), and nuclear fusion has been actively pursued as a potential clean and cheap energy source in reactors on Earth for over 50 years.

Constructing Reuleaux polygons

A Reuleaux polygon is a curvilinear polygon built up of circular arcs. For an odd number of vertices, it has a constant width, and for this reason many polygonal coins, such as the UK's 50p piece and this Bermudian dollar coin are Reuleaux polygons.