Regarding Nucleon Penetration into stationary plasma cloud

[RatTrap85]

TL;DR Summary

Is there a set of generalized equations or accepted model for the behavior of a proton beam entering a plasma cloud? In particular with regards to fusion.

Imagine you have a proton beam with sufficient speed say Xc to overcome the Coulomb Barrier for the element in use. The beam collides with a cloud of that element with density (rho) and thickness (l). Obviously you wouldn't achieve 100% fusion and if the cloud is dense enough the beam will not exit the cloud. So a few questions since this in not my area of expertise, but I think that the answers to these question may inform a project in another area that I am working on.

Are there equations or models that could be used to calculate the probability of colliding nuclei?
What equations would be used to calculate the probability of tunneling and fusing?
Are there equations or models that could determine the depth of penetration of the beam into the cloud for the nuclei that don't collide?
What process actually causes the particles in the beam to slow and bleed off energy? Is it a form of quantum drag? Is it more classical like a perfectly inelastic collision?

This is for a thought experiment so feel free to dump thoughts on this. One never knows where an answer might be found.

 

[Mordred]

The answer is yes there are equations for the above.
Start with Bethe Bloch equation

See here
https://pdg.lbl.gov/2004/reviews/passagerpp.pdf
This will give you the needed details to provide the Bragg curve.

Just an aside a common coordinate system involving beams such as cyclotrons etc is Frenet-Serret frame just an awareness as some papers use this frame but forget to mention it

 

[RatTrap85]

The answer is yes there are equations for the above.
Start with Bethe Bloch equation

See here
https://pdg.lbl.gov/2004/reviews/passagerpp.pdf
This will give you the needed details to provide the Bragg curve.

Just an aside a common coordinate system involving beams such as cyclotrons etc is Frenet-Serret frame just an awareness as some papers use this frame but forget to mention it

Thank you very much for the rapid reply. That may be the single most helpful response I have ever seen in a forum. Concise, non-condescending, and actually addressed the questions. What a great experience for my first post to this forum.

Thank you again.

Now hopefully I have the brain power to comprehend what I am reading, but I am not as sharp as I once was.

 

[Mordred]

Your welcome and welcome to PF. Feel free to ask any questions on it. If I can't answer this site has a decent collection of experts that may be able to help as well.

For directing and controlling the proton beam your going to need a good understanding on Maxwell equations in particular Lorentz force law, magnetic force law, Biot Savart, Amperes law and Gauss law.

 

[RatTrap85]

Your welcome and welcome to PF. Feel free to ask any questions on it. If I can't answer this site has a decent collection of experts that may be able to help as well.

For directing and controlling the proton beam your going to need a good understanding on Maxwell equations in particular Lorentz force law, magnetic force law, Biot Savart, Amperes law and Gauss law.

Per one of your suggestions, I was reading up on Bethe and thinking I should probably dust off some of my old books to refresh my memory of a great many things. You are correct. I am going to have to do some refresher reading before I dive into this fully. Afterall if the foundation isn't solid then any insights drawn will be questionable at best.

I am certain that I will have more questions but I do not yet know what I don't know, so I will hold off until I can formulate the needed questions.

The material you sent and information you suggested has certainly been useful and the over eager over achiever engineer in me wants to just take that little bit and run with it. Fortunately time has taught me humility and more reading and learning is needed before I start trying to incorporate what I have read into my design.

again thank you for the guidance.