# Why does resistance decrease as the temperature increase in plasma?

I am writing about Ohmic heating as a heating method for fusion for a class in school. But I wonder why the resistance decreases as the temperature increases in the plasma? This seems odd because doesn't supercooled conducters have lower resistance while heated conducters have more resistance?

• The higher the temperature the greater the number density of mobile charge carriers (ions and electrons). Jan 19, 2018 at 11:48
• Since plasma has a lot of free electrons moving around due to the heat. So do you mean that the hotter it gets the "free'er" the electrons which makes the resistance lower and the electricity flows easier? Jan 19, 2018 at 11:53
• I suggest that more of the atoms are ionised. Jan 19, 2018 at 11:59
• I think that your answer has a typo as more positive ions also results in more free electrons. Jan 19, 2018 at 12:09
• maybe you should read up on plasma ? hyperphysics.phy-astr.gsu.edu/hbase/Chemical/plasma.html Jan 19, 2018 at 15:43

You are mixing two things in your question which are well separated:

1. Superconductivity
2. Resistivity in a plasma

Note that superconductivity only sets in, when you are below a certain threshold, it is not a continuous decrease of the resistivity (or increase of the conductivity) as you said it indirectly in your question.

After we have clarified this, I will now try to answer your question:

First of all, you have to be aware of what a plasma is: a plasma consists of charged particles (ions and electrons) and some neutrals. The charged particles interact with each other via the Coulomb force and that is a major difference as compared to a gas: in a gas the particles only interact via direct collisions, they have to hit each other. In a plasma, however, they interact on much longer ranges via their electric fields. These type of "collisions" are called Coulomb collisions and the particles in a plasma almost never "touch" each other (only their electric fields interact).

While collisions in a classical gas can lead to large changes of the original direction of the particles (just think of two billiard balls hitting each other), the situation is different in a plasma. Imagine a positively charge ion sitting somewhere and an electron passing by in some distance. Due to the Coulomb interaction the trajectory of the electron will be somewhat distorted (and this is what we call a Coulomb collision in a plasma).

The change of the initial trajectory depends on the distance between the particles, the closer they are, the stronger the force between them and the larger the change. But it depends also on the velocity of the electron: to get the new trajectory of the electron - the new direction - you add the vector components of the velocity, i.e. that of the original direction and that due to the Coulomb force. It that of the original direction is now very large, the resulting change of the trajectory is small. Having a high velocity can be translated to having a high temperature, thus the higher the temperature, the less the change of the original direction of the electron.

To have some analogy to a classical gas, we usually define a collision in a plasma as the sum of those Coulomb collision that lead to a change of the original direction of 90°. Combining with what I have written in the last paragraph, it means that a higher temperature requires more of those Coulomb-interactions to get a change of the original direction by 90°.

Therefore, a higher temperature means a decrease of the effective collision frequency. And a decrease in the collision frequency results in an increased conductivity since the particles are less disturbed on their way through the plasma, they collide less often. And that should answer your question.

• This is the correct answer. You should accept it. Jul 4, 2018 at 14:51