Radial profiles of deposition in a cylinder

An infinite cylinder of radius $1$ is surrounded by a uniform, isotropic, collisionless gas of particles. When particles enter the cylinder region, they are absorbed with some mean free path $\lambda$. I provide an expression for the radial profile of absorption (deposition) intensity $i(\rho, \lambda)$ Read more 02 Nov 2024

Interpolating in log-log space is often nice

In nuclear and atomic physics it’s common to have data spanning many order of magnitude, like cross sections or reaction rates. If we want to plot, integrate, or generally do calculations on the data, we usually need an interpolation scheme to generate values between the existing data points. The interpolation scheme one chooses affects the accu... Read more 28 Sep 2024

Radial profiles of deposition in a disk: a tricky Taylor series

The previous post calculated the fraction of particles encountering a 2D disk which pass though the disk before being absorbed (deposited) with some mean free path $\lambda$. This post calculates the radial profile of the intensity of deposition in the disk: the number of particles are deposited per unit area at radius $0 \lt \rho \lt 1.$ Read more 20 Jul 2024

Fraction of particles passing through a disk

This is a problem in 2D. Read more 18 Jul 2024

Particles from a Maxwellian distribution in a slab with a time-based decay probability

This problem is explored in rough analogy to the problem of ionization of neutrals coming from the wall in the edge plasma of a magnetic fusion device. This problem is almost the same as the one in the previous post, but explores a time-based interaction rather than a distance-based interaction. This allows us to consider the effect of a full ve... Read more 21 Apr 2024