This Idea can only work if notions presented elsewhere, about how conduction-band electrons in a metal can allow "bare" deuterium nuclei to closely approach each other, is true.
The key to this Idea is the realization that "conduction band electrons" don't have to be the ones found in palladium or
Did you ever hear of "metallic hydrogen" before? (see link)
This is an "allotrope" of hydrogen (a unique way in which atoms of just one element can connect to each other, the way ozone is an allotrope of oxygen), and theorists are quite certain that it CAN exist, especially in places like the interior of Jupiter, although it is difficult to say for sure that any has been created here on Earth (an implosion-squeeze is typically used, which is naturally followed very quickly by sample-destroying explosive expansion).
Well, that process, of trying to create metallic hydrogen, reminds me of a research effort known as "Inertial Confinement Fusion". The idea there is to squeeze the sample of hydrogen (a deuterium/tritium mixture) until it exceeds the kind of temperature and pressure found in the cores of stars, at which point a small nuclear fusion explosion occurs. So far they haven't been able to do this well enough to get more energy out of the explosion than they put into the squeeze, but they certainly haven't stopped trying (see link).
Are you thinking about "metallic deuterium" yet?
If Cold Fusion is true, and depends on conduction-band-electrons, then it logically follows that just about any size piece of pure metallic deuterium ought to explode nuclearly.
So let us construct a rocket engine based on that! In this rocket, the fuel tank contains tiny pellets of solid deuterium, each encased in a thin shell of solid hydrogen. These are "ordinary" frozen gases that I'm talking about here.
One pellet at a time is injected into the combustion chamber of the rocket engine. When the pellet reaches the appropriate spot, we will use an electric-discharge system to swat the pellet from multiple directions with blasts of electrons (not laser beams, see link).
When the overall/surrounding blast of electrons strikes the pellet, the outer shell is vaporized and explodes away, while the inner pellet is, per Action and Reaction, imploded significantly.
The key notion here is that we DON'T want an extreme blast. We only want to implode the pellet to the point where it becomes metallic deuterium. When that happens, a conduction-band is formed, full of bare deuterons, all of which are able to approach each other closely, thanks to the SECOND key fact:
Conduction-band electrons in a metal are "slow", while electrons in a hot plasma are "fast". Described in terms of the energy they contain, a slow electron is "very fuzzy", and Quantum Mechanics allows it to to be thought of as existing in a larger volume of space, compared to a high-energy/fast electron. It is precisely that fuzzy nature of slow electrons that the Cold Fusion hypothesis mentioned earlier uses, to explain how many electrons can get involved in-between two fusing deuterons. In a hot plasma the electrons are simply not fuzzy enough!
What I imagine happening in the squeezed pellet of metallic deuterium is that some initial Cold Fusions of the D+D->He4 variety will happen, and most of the electrons in the conduction band will as a result become too "hot" for them to become involved in other Cold Fusions. There may be an intermediate stage, however, before the electrons become too hot/energetic, in which the more-ordinary fusion reactions can occur, in which two deuteriums create Helium-3 or tritium, and a neutron or proton is released, along with gamma radiation. PERHAPS the energy released by these fusions will be enough to encourage the rest of the pellet to be involved; only experimentation can tell us for sure how much fusion will occur. If any, of course!!!
Here I am assuming that if the pellet is too big, we will simply be wasting both deuterium (larger portions of the pellet will fail to experience fusion), and energy (it takes more energy to squeeze a larger pellet), and so that's why I specified "tiny" pellets above.
The main advantage is that it takes a LOT less energy to squeeze a pellet of solid deuterium to the metallic-hydrogen point, than it does to squeeze it past the stellar-core point. "Breakeven", getting more energy out of the reaction than we put in, should be very possible!
Another possible advantage is that by using a blast of electrons to create the metallic hydrogen, when the metallic state forms it should include EXTRA electrons, added to it from the blast. The overall bit of metal, while it exists, will be very significantly negatively charged, and this means more electrons are present, to help catalyze Cold Fusions. This is specifically why I'm choosing electrons over lasers, in this Idea.
Note that since a lot of electromagnetic fields must exist surrounding the combustion chamber, to create the blast of electrons, it follows that those fields can be used to direct the hot plasma created by the fusioning/exploding pellet out the exhaust nozzle.
I tend to doubt that this engine will be powerful enough for direct lift-off from Earth, but it should work fine in outer space. Also, there is the radiation issue, because if an intermediate stage of fusions occurs, we don't want this rocket engine to be operating on Earth! We MIGHT consider containing the explosions and tapping their energy for power plants, but I think that pure Cold Fusion, free of radiation, is inherently superior for that purpose (see link).