Relation between the track of a particle and its energy loss

[Mr rabbit]

Hi,

I'm trying to simulate the process of charged particles attenuation in matter (like this) by a montecarlo-metropolis algorithm in Python. I thought that I could use for the number of particles at thickness $x$ the formula $N (x) = N_0 e^{-\mu x}$, so the probability in this case will be the exponential. What is left is easy.

This is the first approximation, but is not full precise. I want more: I want to consider the energy loss by collisions with the atoms of the medium and the bremsstrahlung, but only the first thing by now. I think I need to use the Bethe-Bloch formula

$\displaystyle S = -\frac{dE}{dx} = \frac{4 \pi}{m_e c^2} \frac{n z^2}{\beta ^2} \left( \frac{e^2}{4 \pi \epsilon _0} \right) ^2 \left[ \ln{\left( \frac{2 m_e c^2 \beta ^2}{I (1-\beta ^2)} \right)} -\beta ^2 \right]$

But I don't know how. I mean: I want to plot the tracks of the incident particles like in the animation I show at the top of the post, but how can I relate the energy loss with the trajectory of the particle? Maybe solving $\displaystyle E = 1/2 m \left( \frac{d \vec{r}}{dt} \right) ^2$? What formula or formulas does Geant4 use?

Thank you.

 

[Vanadium 50]

What formula or formulas does Geant4 use?

You can download it and see exactly what it does for the exact situation you are interested in. It's open source.

 

[mfb]

Which particle types and which energies do you consider? There are cases where an exponential function can be useful (but then secondary particles might be relevant) and there are cases where Bethe-Bloch is relevant, but rarely both together.

but how can I relate the energy loss with the trajectory of the particle?

Calculate its energy loss over some small path, then calculate its new velocity at the new location, update the energy loss estimate, calculate the next step.
Multiple scattering can be important as well.

What's wrong with Geant4 which can do all that?

 

[Mr rabbit]

Which particle types and which energies do you consider?

I was thinking about electrons of 10 keV

Calculate its energy loss over some small path, then calculate its new velocity at the new location, update the energy loss estimate, calculate the next step.
Multiple scattering can be important as well.

What should I do with the variable y? Another Bethe-Bloch? I am a bit lost with that.

What's wrong with Geant4 which can do all that?

I don't know how to use it. And it's interesting for me to do the simulation by myself.

 

[mfb]

What should I do with the variable y? Another Bethe-Bloch? I am a bit lost with that.

What is y? The motion orthogonal to the track? That has nothing to do with Bethe-Bloch, that will mainly come from scattering.

Geant4 has a manual and various examples.

 

[Vanadium 50]

What's wrong with Geant4 which can do all that?

I don't know how to use it. And it's interesting for me to do the simulation by myself.

Whoh!

This is kind of like coming onto an automotive forum and saying "I want to build a car from scratch, including mining the metals and growing the rubber. And you guys are going to give me all the help I need, right?"

Thousands of person-years of effort have gone into Geant to make it what it is. You really want to be learning how to use it rather than trying to rebuild it from scratch.

 

[Lord Crc]

Also, don't underestimate the difficulty of verifying numerical code. At the very least you'll want to compare the results of your code with a reference, and Geant4 seems to be a very solid one as such. So you'll want to know how to generate references for your test cases anyway.