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I've always seen plasma as (in a dumbed down state) a combination of electricity and fire. I know the electricity part is correct (I hope) but I don't know about the fire part. Could someone confirm or deny my suspensions.

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To paraphrase Socrates, all men are mortal, but not all mortals are men.

A "plasma" is a state of matter where there are "lots" of free charges. Quantitatively, a free charge in a gas produces and electric field which is damped out over some distance, because the gas molecules can be polarized and cancel out the field from the free charge. If there are more than a few free charges in each of these "Debye volumes," then the electric-electric interactions have more influence over the motion of the ions than do scattering interactions with the neutral atoms.

A candle flame does produce a plasma region, because the combustion process releases enough energy to produce some number of ions. A classroom demonstration is to put a candle between the plates of an electrostatic generator and admire how the flame separates into two pieces as the positive and negative ions are attracted in opposite directions. Any system with a temperature above a few "electron-volts" will have many free charge carriers and function as a plasma.

However, not every plasma is a flame. In a vacuum system, once the pressure is low enough, the "mean free path" for ions may become larger than the size of the vacuum chamber. In this case, ions can follow electric fields without interference from the residual gas molecules, and the vacuum becomes conducting.

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