Plasma isn’t always purple but nitrogen plasma is and air is mostly nitrogen. (Oxygen to a degree adds to the color).
You get the same color when you ionize air in other ways, such as lightning discharge (don’t look directly at the lightning strike).
Each element has its own specific emission spectrum of color, based on the energy in the orbit of the electrons.
You can look at glowing stuff and tell what it is made up out of by looking at the color.
For air it is purple.
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