1. The phoenix is a mythological bird. 

The bird dies by self-immolation and rises from its own ashes. It is the fire-bird. 
It represents resurrection and immortality, death and rebirth by fire. 
It is also a symbol of royalty, of uniqueness.

2. Phoenix also is the name of a CIA Mind Control Program. 

The program, in the second half of the 60's, was centered around behavior modification experiments to learn how to extract information from prisoners of war in Vietnam. (Quoted by Harry V. Martin and David Caul, from Douglas Valentine's "The Phoenix Program")

Val Valerian conducted several interviews on the matter and came to the conclusion that there actually were THREE Phoenix projects.

  1. Phoenix I was a project that evolved out of the Philadelphia / Rainbow project, and lasted from 1948 until 1968. (It only got the name Phoenix in 1953). Phoenix I was in fact a "double" project. Its purposes were 1° to create devices that could generate time/space tunnels in order to render objects and people invisible, and 2° to influence the weather. In the late 60's, they discovered that the devices they used had an interesting side effect: they could be used for Mind Control purposes.
  2. Hence, Phoenix II came into existence. It was a "pure" Mind Control program, that started somewhere between 1969 and 1971. [This is the Phoenix mentioned above, by H.V. Martin, D. Caul & D. Valentine.]
    It involved the use of pulse modulated waves.
    (Note that another source mentions Phoenix II started in 1969).
  3. Phoenix III, again was more in the line of Philadelphia & Montauk. It started somewhere in the seventies and lasted till the end of the 80's (?).
    Around 1979-1980 the time machine was ready. In 1981 they were able to establish a vortex that connected 1947 and 1981.
    [Al Bielek also talks about this phoenix project as a successor to the Philadelphia and Montauk projects]
    (Note that another source mentions Phoenix III started in 1971).