The God Thing wrote:
(2) The rocket could have been a nuclear heated rocket - maybe siphoning some antimatter from the warp core for a boost.
But from where could have Cochrane sourced the astronomical (by today's standards) quantities of anti-matter he required for the project if such is the case? That shantytown where he was building the Phoenix didn't exactly strike me as a place which would be equipped with its own dedicated Fermilab-like particle collider.
Trying to cram all the goodies of a "modern" warp drive into an ICBM will just make your head hurt. We are limited in what we can carry, and we are limited by the tech level of the era. I can accept that we will have inertia and gravity control in our lifetimes, and fusion as well. Antimatter production on a "massive" scale, not so much.
I highly doubt it carried that huge quantities of matter and antimatter or anything resembling a modern warp core at all. This thing was being built on a budget as a proof of concept, not a heavy-cruiser on a rocket.
The drive could have been powered by a small fusion reaction... after all they only hit warp 1 (or was it a wee bit higher?) and sustained it for a few moments. Heck a couple of friends and I postulated that maybe the drive ran off the scavenged nuclear warheads from the missiles. A combination fission ignited fusion bomb, detonated in a vac chamber and the resulting power (gamma rays/neutron stream) directed to the nacelles where it energized the crude coils.
The prototype for a design often looks nothing like its descendants... and I doubt the prototype warp-drive had all the features and abilities of a "modern" era warp-drive.
After that all important proof-of-concept flight when research hits high gear in the "big labs" things like focusing crystals, antimatter fuel for higher energy output and stuff like that will come into play. Exotic materials for coils comes later, with the "first" coils being made out of "mundane" exotic materials found in the earth's crust and around the solar system.
Zephram wasn't trying to build a full-fledged starship-on-a-rocket he was trying to prove his design to get more funding. All he needed was proof that he could reach lightspeed/go past it by a small fraction and the money would pour in... and he would retire to an island full of naked girls.
One more note. Nuclear fission "steam kettle" rockets actually worked in trials but there were issues with the material science of the cores, no material known can stand that level of thermal and neutron flux for long. Say the problem is solved by the time of the Pheonix. You have a small high-temp fission reactor "steam kettle" drive for the upper stage, a powerful "modern" chemical drive for the first stage.
So you got your small fission reactor (size of a 50 gallon drum) providing thrust, you have your small "exotic" reactor (size of two 50 gallon drums) providing juice to the nacelles, that leaves room for the inertial and gravity control stuff, computers, life support and fuel along with the servos to move the nacelles into position.
There you have it. One crude single-shot warp rocket according to my understanding of science, engineering and Treknology.