Transfer of kinetic energy

[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.