Particle beams: energy of released electrons

[ORF]

Hello

When a beam* pass through a thin layer of material (some microns), at the exit some electrons are released; so a electron cloud is formed around the exit point of the beam.

My question is: what is the energy distribution of these released electrons? (Maxwell, random,... )

I think they follow a Maxwell distribution (because of statistical mechanics), but I'm not sure.

Thank for your time :)

Greetings!
*of ions at low energy (eg, ISOLDE)

 

[Dr. Courtney]

Have you tried searches on Google Scholar?

 

[ORF]

Hello

Yes, I tried searching in google, with some keywords as "beam" "particle" "layer" "electron" , but after two hours I got tired, and I decided to ask for.

I accept any suggestion (as some righter keywords for searching on my own).

Thank you for your time :)

Greetings!

 

[mfb]

A Maxwell-Boltzmann-distribution would surprise me. Ionization from charged beam particles is not a thermal process. You might get a good approximation if you take the energy loss of the ion in extremely thin layers (thin enough to neglect multiple scattering).

 

[ORF]

Hello

You might get a good approximation if you take the energy loss of the ion in extremely thin layers (thin enough to neglect multiple scattering).

I can understand that the energy loss, E, can be computed by the Bethe-Bloch formula.

But I don't know how compute the distribution of this energy E among the electrons (I tried a tracking of these electrons by GEANT4, but the step was too rought and I don't trust on the results).

I thought the cloud of electrons was an ideal gas in thermal equilibrium, and because of that, I thought they will follow a Maxwell distribution. This idea is (probably) wrong and because of that I asked.

Thanks for your time :)

Greetings!

 

[mfb]

I can understand that the energy loss, E, can be computed by the Bethe-Bloch formula.

That formula just gives you the average, not the distribution itself. It might be possible to use its derivation to make it differentially in the electron energy.

I thought the cloud of electrons was an ideal gas in thermal equilibrium, and because of that, I thought they will follow a Maxwell distribution.

You would need hot plasma to get that, otherwise you get Fermi distributions in metals and various valence shells in all materials. Anyway, this is the initial electron energy, the energy transfer is a different point. Many electrons get so much energy that their previous energy is not relevant.

 

[ORF]

Hello

I made further searching, which took me to the Auger electrons (delta rays don't stay near the layer) as cause of the electron cloud.

I found a energy distribution for Auger electrons (an empirical formula), but I didn't find a theoretical derivation of the experimental spectrum (there are some models, but don't fit the experimental data very well).

Anyway, I don't need it (the theoretical derivation was just by curiosity).

On the other hand, I discovered that I had to activate the Auger process in GEANT4, it's disactivated by default; because of that, the electron's tracking show me 1 keV electrons (delta rays). For Auger electrons in GEANT4,
https://twiki.cern.ch/twiki/bin/view/Geant4/LoweAtomicDeexcitation

It might be possible to use its derivation to make it differentially in the electron

In the derivation, you suppose the ionization energy is 10Z eV (Bloch approx)... with this hypothesis, how can you differenciate in electron's energy?
By the way, here is the derivation of the Bethe-Bloch formula: http://lowette.web.cern.ch/lowette/UA6_particle.pdf

You would need hot plasma to get that, otherwise you get Fermi distributions in metals and various valence shells in all materials.

The gas of electrons is outside the material... why did you talk about valence shells? :)

Thanks for your time :D

Greetings!

 

[mfb]

The gas of electrons is outside the material... why did you talk about valence shells? :)

The gas of electrons is in the material your beam passes through. I would expect negligible interactions between those electrons and no time to thermalize.

In the derivation, you suppose the ionization energy is 10Z eV (Bloch approx)... with this hypothesis, how can you differenciate in electron's energy?

That's the lower energy cutoff, but there is also the energy an electron at a distance x gets if ionization energy is negligible.

 

[ORF]

Hello

The gas of electrons is in the material your beam passes through.

Experimentally I found a gas of electrons outside. If there is a gas of electrons inside, I don't mind (it's just a model of bound electrons in matter, isn't it?).

I found an article where it's explained: The Relationship Between Electron and Ion Induced Secondary Electron Imaging: A Review With New Experimental Observations. S. Y. Lai, D. Briggst, A. Brown and J. C. Vickerman. Surface and interface analysis, VOL. 8, 93-111 (1986).

Still I don't know how to differenciate Bethe-Bloch formula in order to get the energy spectrum. Delta rays are secondary radiation, whose energy spectrum might be obtained by this method, but the Auger electrons follow other process.

I still don't know clearly if the electrons are Auger or something else. I only know they have few eV and they are produced by ion bombardment (and the Auger electrons are the most probable option).

Thank for your time :)

Greetings!

 

[mfb]

Experimentally I found a gas of electrons outside.

I would expect some individual electrons moving away from the impact point. I wouldn't call that a gas. And the electrons are not in thermal equilibrium.

but the Auger electrons follow other process.

Right, you wouldn't get those.

 

[ORF]

Hello

Right, you wouldn't get those.

So... any ideas? :D

Greetings!