Hydrogen bomb without fission stage The majority of existing nuclear warheads are Thermonuclear devices implementing the Teller--Ulam design. It includes a first stage of "traditional" nuclear fission explosive (Uranium and/or Plutonium) that floods the fuel for the second stage (typically Deuterium) with neutrons and gamma triggering the fusion. They may or may not have a third stage, either fission or fusion, which I'm not interested in.
The question is:
Has anyone ever considered and/or investigated a purely fusion type of explosive device? I imagine the "trigger" would have to be much larger to generate conditions necessary to initialize the fusion reaction without a primary stage, if at all possible.
I'm not asking for schematics ;) but whether it's possible at all. From both theoretical and engineering perspective.
 A: 
The question is: Has anyone ever considered and/or investigated a
  purely fusion type of explosive device?

Oh yes, the so-far mythical pure-fusion bomb.
For a pure-fusion reaction, let's consider the easiest case, D-T. This is basically what an h-bomb uses, with intermediate steps.
The problem is the required (pressure * dwell time) to get enough reactions in the fuel in order that their output energy will heat the surrounding fuel so it also undergoes fusion. This is known as ignition.
In existing bomb designs, if the public literature is to be believed, the tamper pressure is estimated to be on the order of 1000 TPa and the fuel is pressed inward at perhaps 500 km/sec. That is going to be difficult to achieve without some serious energy input.
The closest we've come so far is the inertial confinement fusion concept, with its showcase system, NIF. NIF uses around 4 MJ of laser light to heat up a light plastic capsule which collapses inward to compress the thin layer of fuel on the inside of the capsule. This is the same overall mechanism as a bomb (which, today anyway, is the stated reason for building it). This produces an ultimate pressure of 3 EPa, but that's measured in the center of the fuel, not the outer surface, so it's actually a much smaller value than an h-bomb in a head-to-head measure. IIRC, the resulting implosion speed is around 350 km/sec, but the overall fuel density is much less than the bomb case (where's its solid LiD) so the overall compression is much less than a bomb - but by 1 order of magnitude or 4? Can't say.
In spite of much effort, NIF has failed to reach ignition. That means it can't be used to spark-plug a bomb, even though it's several football fields long.
The only person (of consequence) who has claimed such a device actually exists is Sam T. Cohen, who made the rather unlikely claim that "red mercury" is a magical explosive with the right qualities to make a pure-fusion device, and that Saddam had dozens or hundreds of them that he was going to use on the US when the invaded.
