A Sampling Electrons from a 2D Projection: Is There a Functional Form?

[Malamala]

Hello! I have some electrons produced from a 3D gaussian source isotropically inside a uniform electric field. The electric field guides them towards a position sensitive detector and I end up with an image like the one below (with more electrons on the edge and fewer as you move towards the center). I want to run some simulations and for that I need to sample electrons from this 2D projection. Is there a functional form for this 2D distribution? Can someone point me towards some reading/Wikipedia page? Thank you!

 

[jedishrfu]

I don't know the distribution but the picture reminds me of the recent universe map that used logarithmic distances.

Also it looks like a sphere so that maybe you could assume equally spaced dots on a sphere projected onto a plane that slices the sphere in half.

Lastly, you might be able to construct the distribution using the value of a sin() function as the percentage of dots in a given ring around the center.

R = radius of your circle
r = radius of a ring

r/R = ranges from 0 to 1

$\frac{\pi}{2} \times \frac{r}{R}$ = ranges from 0 to $\pi/2$

percentage of dots in a ring = $sin(\frac{\pi r}{2 R})$

or something like that -- your call.