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

In summary, the conversation discusses a 2D projection of electrons produced by a 3D gaussian source in a uniform electric field. The speaker is looking for a functional form for this distribution and suggestions are made, including assuming equally spaced dots on a projected sphere and using a sin() function to determine the percentage of dots in a given ring.
  • #1
Malamala
299
27
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!

electrons.png
 
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  • #2
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.
 
Last edited:

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

1. What is the purpose of sampling electrons from a 2D projection?

The purpose of sampling electrons from a 2D projection is to understand the underlying functional form of the data. This can help in identifying patterns, relationships, and trends within the data set.

2. How is the sampling process carried out?

The sampling process involves taking small, representative samples from the 2D projection and analyzing them using statistical methods. These samples are then used to make inferences about the entire data set.

3. What is the significance of finding a functional form in the data?

Finding a functional form in the data can provide valuable insights into the underlying processes that generated the data. It can also help in making predictions and understanding the behavior of the system.

4. Are there any limitations to sampling electrons from a 2D projection?

Yes, there are limitations to this method. Sampling may not accurately represent the entire data set, and the results may be affected by factors such as sample size and selection bias. Additionally, the functional form may not be able to fully explain all variations in the data.

5. How can the results of sampling electrons from a 2D projection be used?

The results of sampling electrons from a 2D projection can be used for various purposes, such as developing mathematical models, testing hypotheses, and making predictions. They can also be used to inform further research and experiments.

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