On Wikipedia (so reliable, I know), they say that HID lamps have a wall loading at or above 3W per square centimeter. Is this the definition of HID lamps? What category do carbon arc lamps fall under, or other incandescent arc sources? I thought carbon arc was HID, but they don't have walls, so are they? How about medium pressure mercury lamps (MA/V)?

Are there also definitions for low intensity, medium intensity, and ultra high intensity lamps?

Theoretically, if you has a thick basketball-size quartz envelope with electrodes that were only a centimeter apart inside and mimicking the characteristics of something like an MV lamp, would the low watt density per square centimeter of quartz wall exclude it from being considered HID?

I also hear that these lamps may have a minimum temperature requirement, but I can't pinpoint what that would be if that was the case. Is this a thing as well?

Have you ever taken the trouble to read books instead of just Wikipedia?

Some books are even available online as PDF files:

books about lamps on lamptech, James Hookers website

I can highly recommend it.

@Olav
Yes, that is an excellent resource, I have read many of those through in the "literature" tab. I just reread the Electric Lamps: Discharge book, but I once again didn't see any solid definition of HID lighting over there.

That said, I was hoping to get input on the question itself. Are you able to help with that? Do you know of a source that might have the answer?

It's similar to fishing—you have to wait...

Either you get a detailed answer here from people who are really knowledgeable,
or you can look for the answer in other books, but not online as a PDF.

Other book titles are:

- Electric Discharge Lamps, John F. Waymouth
- Discharge Lamps, Chr. Meyer, H. Nienhuis
- Lamps and Lighting, H. Hewitt

These books are available secondhand.