The temperature is always related to the energy distribution function of the system = the probabilty that a certain particle A has the energy En. Think of the simple model of the hydrogen atom then the probabiltiy that the electron is sitting on energy level En is proportional to exp(-En/(kT)).This is the generell definition of a temperature.

When going to the temperature of a plasma consisting of neutrals, ions and electrons one usually assumes a Boltzman distribution which is equivalent to a Maxwellian velocity distribution for the particles. When electrons, neutrals and ions have the same temperature they move with different mean velocities determined by the formula you are mentioning. As already said and visible from the formula the temperature is related to the mean ENERGY -> the velocity of ions/neutrals and electrons is different at the same temperature.

A Maxwellian distribution requires a thermodynamic equilibrium. This is an equilibrium between all collisions and radiative processes in the plasma. Often the plasma is not optically thick and the energy distribution is determined by collisions - then there is the local thermal equilibrium or even only a partial local equilibrium  (e.g. only the lower energy levels are in a thermal equilibrium).

Can electron and ion temperature differ? Yes, the electron-electron and electron-ion slowing down time is much faster than the ion-electron slowing down time) its all about the mass ratio. If electrons are cooled, e.g. in the edge of a hot confined fusion oriented plasma the ions cannot follow and stay hotter in the edge than the electrons. In small plasmas with electron heating the confinement times are often to small to allow for sufficient energy transfer from the electrons to the ions leading to rather cold ions and hot electrons. the ions-ion energy transfer and electron-electron energy transfer are rather quick allowing for an equilibrium for the electrons, another for the ions but different temperatures for ions and electrons.

Hope this gives you a little bit additional insight,

Werner

I'm no plasma expert, but the mean speed has to be calculated for each species separately (due to their different mass). Whether ions and electrons have the same temeprature or not depends on your plasma type (hot or cold plasma)

As far as I know, you speak about "plasma temperature" in the case of a thermal equilibrium - in this particular case, all constituents of the plasma follow the a Maxwellian behaviour of the same temperature. Of course, the individual distributions of the speed will be different because of the different masses. In practice, you will generally not observe a thermal equilibrium - you may have local thermal equilibrium or even no equilibrium at all. In those cases, the temperatures for the individual particles may differ substantially and have to be accounted for separately. Hope this helps, Dirk

The temperature is always related to the energy distribution function of the system = the probabilty that a certain particle A has the energy En. Think of the simple model of the hydrogen atom then the probabiltiy that the electron is sitting on energy level En is proportional to exp(-En/(kT)).This is the generell definition of a temperature.

When going to the temperature of a plasma consisting of neutrals, ions and electrons one usually assumes a Boltzman distribution which is equivalent to a Maxwellian velocity distribution for the particles. When electrons, neutrals and ions have the same temperature they move with different mean velocities determined by the formula you are mentioning. As already said and visible from the formula the temperature is related to the mean ENERGY -> the velocity of ions/neutrals and electrons is different at the same temperature.

A Maxwellian distribution requires a thermodynamic equilibrium. This is an equilibrium between all collisions and radiative processes in the plasma. Often the plasma is not optically thick and the energy distribution is determined by collisions - then there is the local thermal equilibrium or even only a partial local equilibrium  (e.g. only the lower energy levels are in a thermal equilibrium).

Can electron and ion temperature differ? Yes, the electron-electron and electron-ion slowing down time is much faster than the ion-electron slowing down time) its all about the mass ratio. If electrons are cooled, e.g. in the edge of a hot confined fusion oriented plasma the ions cannot follow and stay hotter in the edge than the electrons. In small plasmas with electron heating the confinement times are often to small to allow for sufficient energy transfer from the electrons to the ions leading to rather cold ions and hot electrons. the ions-ion energy transfer and electron-electron energy transfer are rather quick allowing for an equilibrium for the electrons, another for the ions but different temperatures for ions and electrons.

Hope this gives you a little bit additional insight,

Werner

yes is it an electron temperature...

Depends on the context. There are different 'temperatures', for instance Electron and ion temperatures. These refer to the distribution of the velocities of the plasma particles. In addition, there is a level temperature, which means that the relative population of a species in level i to the population of the species in level j is exp(-Eij/kT).

If you are very lucky, all these temperatures are the same. Very often highly excited states for example follow this law, while lower lying ones do not. You can look up the LTE (Local Thermal Equilibrium) and coronal limits and they have to do with the collisionality of the plasma: higher levels are more polarizable and hence collisions are stronger and bring them into equilibrium faster . So it really depends on what you want to do. What do you want the temperature for?