Elevated Electron Temperatures in Plasmas

The relationship of the applied electric field to the resulting elevated electron temperature can be seen by a simple analysis. Consider a high velocity electron colliding with an initially stationary heavy particle, as shown below. 

Conservation of energy and axial momentum for this system gives 

The energy gain of an electron in an electric field equals the force on it times the distance it moves. In a time t, a particle acted on by a force F will move x distance given by 

Therefore, the energy the electron gains between collisions is 

In looking at plasmas in the most general way, we can categorize phenomena in terms of characteristic parameters. For example, a simple gas can be dealt with in terms of a mean-free path, mean collision frequency, or mean thermal energy. If the mean-free path is less than the dimensions of the vessel holding the gas, it can be treated as a continuum. Otherwise, we would have to look at free molecular flow. In contrast, a plasma has many more characteristic parameters than a simple gas. 

---