Why Do Ions Lose More Kinetic Energy Than Electrons in Collisions with Neutrals?

[TOD]

Hey all,

Just a bit of background info:
I'm doing an investigation on low temperature plasmas and one of the things I've come across is that electron temperature is always much higher than ion temperature.

Now I believe one of the reasons that causes this is that ions lose a lot more kinetic energy than electrons do when colliding with neutrals (the uncharged particles which make up the most part of a low temperature plasma). I think this is because when an ion collides with a stationary neutral particle, the transfer of kinetic energy is much more than when say an electron - with the same kinetic energy but a much smaller mass - collides with a stationary neutral particle of the same size as before. This thus causes the temperature gradient between electrons and ions.

QUESTION:
My question is how do I show or what do I use to derive that fact where energy transfer between the collision of similar masses is more efficient than say between a much smaller mass and a large mass (but of course, both cases must have the same initial energies). If it simplifies the derivation, please assume that one of the masses is stationary before the collision (the large one in the latter case).

I think I might have come across this some time during high school but I don't remember now =D

Thanks in advance,
TOD

 

[Dale]

If you have an elastic collision of a moving mass, m, with a stationary mass, M, the final velocity of m is given by

vf = vi (m-M)/(m+M)

So if M>>m then m rebounds with the same KE, just different direction, but if M=m then m is stopped and transfers all KE to M. It gets more complicated if M is not initially at rest, but the basica idea remains that the transfer of KE is most efficient for matched masses.

 

[astrokreng]

Hello TOD,

Thank you for sharing your background information and question. I can provide some insight into the transfer of kinetic energy and how it relates to your investigation on low temperature plasmas.

First, let's define what kinetic energy is. Kinetic energy is the energy an object possesses due to its motion. It is directly proportional to the mass of the object and the square of its velocity. In other words, the larger the mass and the faster the velocity, the more kinetic energy an object has.

In your case, you are looking at the transfer of kinetic energy between ions and electrons in a low temperature plasma. As you mentioned, the electron temperature is always higher than the ion temperature. This is because, as you correctly pointed out, ions lose a lot more kinetic energy than electrons when colliding with neutrals. This is due to the difference in mass between ions and electrons.

When an ion collides with a neutral particle, the transfer of kinetic energy is much more efficient compared to when an electron collides with a neutral particle. This is because ions have a larger mass compared to electrons and therefore, have more kinetic energy to transfer. In other words, the larger the mass, the more kinetic energy can be transferred in a collision.

To derive this fact mathematically, we can use the equation for kinetic energy: KE = 1/2 * mv^2, where m is the mass and v is the velocity. If we assume that both the ion and electron have the same initial kinetic energy (KEi), we can set up the following equations:

For the ion: KEi = 1/2 * mi * vi^2
For the electron: KEi = 1/2 * me * ve^2

Where mi and me are the masses of the ion and electron, and vi and ve are their velocities.

Now, let's consider a collision between the ion and a neutral particle. After the collision, the ion's velocity will decrease to vf, and the neutral particle will gain some velocity, vn. Using the conservation of momentum, we can set up the following equation:

mi * vi = (mi + mn) * vf + mn * vn

Where mn is the mass of the neutral particle.

Now, we can solve for vf in terms of vi and vn:

vf = (mi * vi - mn * vn) / (mi + mn)

Substituting this into our equation for kinetic energy for the