# Relation between the track of a particle and its energy loss

• A
• Mr rabbit
In summary, the conversation discusses the process of charged particles attenuation in matter and the use of a montecarlo-metropolis algorithm to simulate it in Python. The first approximation is using the formula ## N(x) = N_0 e^{-\mu x} ##, but it is not fully precise. The individual wants to consider energy loss by collisions with atoms and bremsstrahlung, but is unsure how to do so. They mention using the Bethe-Bloch formula and relate the energy loss to the trajectory of the particle. The conversation also mentions the use of Geant4 and the difficulties of building a simulation from scratch.
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.

Mr rabbit said:
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.

Mr rabbit
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.
Mr rabbit said:
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
mfb said:
Which particle types and which energies do you consider?
I was thinking about electrons of 10 keV

mfb said:
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.
mfb said:
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.

Mr rabbit said:
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.

Mr rabbit
mfb said:
What's wrong with Geant4 which can do all that?
Mr rabbit said:
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.

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.

Mr rabbit

## 1. How does the track of a particle relate to its energy loss?

The track of a particle is a visual representation of its path through a medium. It is affected by various factors such as the particle's charge, mass, and the properties of the medium. As the particle travels through the medium, it may experience interactions that result in energy loss.

## 2. What factors can cause a particle to lose energy along its track?

Particles can lose energy through various mechanisms such as ionization, excitation, and scattering. These interactions can occur with the particles in the medium or with other particles that the particle encounters along its path.

## 3. Is there a relationship between the energy loss and the length of the particle's track?

In general, the longer the track of a particle, the more energy it has lost. This is because the particle has had more interactions and collisions with the particles in the medium, resulting in a greater overall energy loss.

## 4. How does the energy loss of a particle affect its track shape?

The energy loss of a particle can cause changes in its track shape. For example, as a particle loses energy, it may become more deflected or scattered, resulting in a curved or more chaotic track. Additionally, the energy loss may also affect the length and width of the track.

## 5. Can the energy loss of a particle be predicted based on its track?

While the track of a particle can provide some information about its energy loss, it is not possible to accurately predict the exact amount of energy lost based solely on the track. This is because there are many factors that can affect the energy loss, and the track only provides a visual representation of the particle's path and interactions.

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