ion drift velocity and statistical velocities

[aussie_laser_dude]

Imagine a low density of positive ion's accelerated in a uniform electric field in air. An ion would accelerate to a high speed, hit an air molecule, slow down from the recoil and then repeat the process of accelerating and hitting another molecule.
The statistical average speed is the drift velocity, for air this is about 1.95E-4 m2/V∙s;.

I want to know the following:
* the statistical distribution of path length between collisions
* the statistical distribution of time between collisions
* this is more advanced, inelastic billiard ball collisions that happen at an angle cause recoils at angles, air ions should do the same when hitting air. Information on the statistical math of this would be nice, but this question might be too  tricky.

Any help, maybe with equations, links, terminology, concepts would be appreciated.

[sandalcandal]

This will likely have many equations you're interested in: https://www.nrl.navy.mil/ppd/content/nrl-plasma-formulary

I think your linear drift velocity value might be an incomplete picture. Warburg’s law describes ion drift in a point-to-plane corona discharge and might be a good starting point that looks at the physics of ion drifts in a simple system more amicable to theoretical analysis.

Path length between collisions in a kinetic gas is mostly studied under the term "mean free path" The complete probably density function is a bit more complex though and seems to be fairly recent research. I found two papers which model it to be a logarithmic decay.

Source: Steve T. Paik Is the mean free path the mean of a distribution? American Journal of Physics 82, 602 (2014) https://aapt.scitation.org/doi/10.1119/1.4869185


Source: Paolo Visco, Frédéric van Wijland, and Emmanuel Trizac Collisional statistics of the hard-sphere gas Phys. Rev. E 77, 041117 (2008) https://journals.aps.org/pre/abstract/10.1103/PhysRevE.77.041117

Probably density for time between collision is similar and also used to derive path length in the above two papers.

Source: Paolo Visco, Frédéric van Wijland, and Emmanuel Trizac Collisional statistics of the hard-sphere gas Phys. Rev. E 77, 041117 (2008) https://journals.aps.org/pre/abstract/10.1103/PhysRevE.77.041117

Neither of these studies are for an ionised gas so are probably not 100% accurate for what you're trying to study.

I suggest also posting your questions to a more physics based forum e.g. https://www.reddit.com/r/Physics/ You'll likely get better answers for this problem and type of investigation you're undertaking than here which is more an EE forum. Edit: Not to say I dislike your endeavours or you sharing them here but you'll probably get better responses in physics communities than here. If nothing else it seems like a nice vehicle for exploration of ion kinematics.

If you can't get access to the papers PM me.

[aussie_laser_dude]

Cheers, hard sphere model papers looks pretty close. Papers sound interesting. I tried a really simple back of the envelope calculation, pretended air molecules were still and projected a molecule wide cylinder through the air, anything well within that cylinder is approximately a straight on collision and anything further out is just a scrape that can be ignored. My previous calculations without collisions were magnitudes off, now they're nearly matching experimental values! Keen to see how a more advanced model does.