"Once in the history of each scheme, an avatar from the constellation Capricorn appears on mental levels. This level is the lowest one on which these inter-planetary deities appear. No more can be communicated on this matter. The mystery of the goat lies hidden here. This avatar makes His appearance in the third round of the third chain and disappears in the fifth round of the fourth chain."

this is pergaps one of the clearest references i know to what you refer as Archons/Authorities of CHaos

Archons reside in the mental plane (5th) of our universe

you can imagine them as living mental entities that can influence us down here directly only via thougths, and indirectly to astral entities (4th plane). They are strengthened by giving mental energy to the ideas which are part of their nexus.

Mental entities do obey the law of free will though, so you need to acknowledge those ideas pertaining to them out of free will, or do actions that will put you in their scope.

The above mentioned avatar from capricorn is not hard to figure out just follow the line of research about the nature of the Saturn deity which is the proxy in our solar system for the Capricorn constellation.

Another very important thing to remember is that we have just ended the 5th round of the 4th chain, so the job of the capricorn avatar is done and he has no rulership on humanity anymore.

The reason why the mental archons/ideas under his allegiance still hold a strong pull on many is pretty straight forward too...it's up to human individuals to do their own work, move thorough the mental constructs of the past, find home in the hearts of hearts which is the 6th plane and dispel the obsolete mental constructs still roaming the collective mind of humanity