# Why does an oscillating electric field couple more strongly to electrons than to ions?

As stated in Principles of Plasma Discharges and Materials Processing, by M. A. Lieberman and A. J. Lichtenberg, about capacitively coupled plasmas:

(...) the light and heavy charged particles in low-pressure processing discharges are almost never in thermal equilibrium, either between themselves or with their surroundings. Because these discharges are electrically driven and are weakly ionized, the applied power preferentially heats the mobile electrons, while the heavy ions efficiently exchange energy by collisions with the background gas.

See also this answer to a related question. This difference in coupling strength is given as a reason for the difference between electron temperature and ion temperature:

$$T_e>T_i$$

However, I don't quite see the reason for this difference in coupling strength. Why is it that an oscillating electric field transfers energy less efficiently to ions than to electrons?

• These plasmas are not in equilibrium because they were not given enough time to get into equilibrium. It's not a matter of coupling but of not letting the system go trough the relaxation process. – CuriousOne May 22 '16 at 22:03
• @CuriousOne But if it's not about the coupling, then what is the reason that the electron temperature is higher than the ion temperature in a CCP? – Jeff May 22 '16 at 22:11
• Just what I said: the electrons didn't have enough time to interact with the ions. If you excite such a plasma and it's in a large enough volume and you let the electrons interact long enough with the ions, then both temperatures will, eventually, be the same. The coupling is the same, by the way. The force of an electric field on a unit charge is exactly the same, whether it's positive or negative. The electrons just have a much smaller mass, so they will accelerate to a higher velocity than the ions, and it's the velocity distribution that sets the temperature. – CuriousOne May 22 '16 at 23:12
• @CuriousOne Aah, that was exactly my point of confusion. I overlooked the fact that it's the velocity, not the kinetic energy, that matters for the temperature. Thanks. – Jeff May 23 '16 at 6:10
• No problem... it took me a while before it clicked what makes the actual difference. My plasma physics class was a very long time ago... :-) – CuriousOne May 23 '16 at 7:10

The mass of the electron is thousands of times less than that of the ions - about 1,800 times lighter than a proton. The motions move the entire ion core, so inertia tends to resist the change of motion much more than is possible for an electron.

For example, see Improved Two-Temperature Model and Its Application in Ultrashort Laser Heating of Metal Films. The model was originally developed in the 1950's to explain observed plasma physics of fusion weapons.

It is very far-from-equilibrium physics. The rapidity of equilibrium between the electrons and the ion cores depends upon the electron-ion coupling coefficient for that material. One need not create a plasma for this to occur: ultrashort laser pulses are able to generate these conditions in a non-destructive, repeatable fashion.

Why is it that an oscillating electric field transfers energy less efficiently to ions than to electrons?

This is not generally true. There are multiple cases where an oscillating electromagnetic field transfers energy/momentum much more efficiently to ions than electrons (e.g., Alfvén waves do not care about electrons in many situations).

In lab plasmas, there is an additional issue of having a very high number density of both charged and neutral particles compared to plasmas in space. The high densities raise the charge-charge ad charge-neutral collision rates, which can alter the dynamics significantly. For instance, high particle-particle collision rates can act to inhibit plasma instabilities and prevent either species from gaining too much energy.

If the plasma is weakly or completely collisionless, then the energy/momentum transfer to/from electromagnetic fields from/to particles is not a simple mass-ratio argument and can be highly dependent upon the local plasma parameters, oscillation frequency, etc.