A closer examination of this concept reveals some weaknesses. As if it's gargantuan size wasn't enough.
The show stopper here isn't necessarily its size, although there are not rockets in existence yet that can lift such a mass. It cannot lift itself as its thrust will be insufficient.
This may be a surprise since it is based upon nuclear explosions, but the explosions are small---hence the name "mini". The amount of energy release is some small multiple of the energy released from the Saturn V's F1 engines. That it has a nozzle that isn't vaporized is a clue that these are small bombs. In fact, the fissile material is only 21 grams, or less than an ounce.
The problem in the configuration is that it is so big, after all. It requires a lot of other stuff to make the thing work. By the way, the use of nuclear bombs is not an issue. They are useless as bombs because the rocket itself provides the hardware needed to make the thing explode. Without that, the bombs can't explode. It shouldn't scare anti-nukes too much, but you never know with those people. Anyway, even with the small amount of fissile material, it is very rare stuff and you need a lot of it, relatively speaking. Over a ton in this configuration. That's enough in itself to be a show stopper unless you find a way to make the stuff more abundant.
The second show stopper, with respect to the configuration shown, was that it was one way. What good does all that performance do if you can't get home? You'll need a bunch more of the rare stuff waiting for refueling purposes, or you are stuck at Mars. You might get there fast, but you will be stuck there unless you can get a shitload of "bombs" delivered to Mars orbit. That ain't in the cards, I suspect.
It wouldn't be too difficult to send a bit over a ton of the rare stuff by itself, but the other stuff that is necessary would have to be manufactured on Mars somehow. Good luck with that, although it may not be impossible. The bomb looks like a cone with the fissile material at the tip of it. If there was a way to make the stuff needed for the bomb "casing" as it were, this may not have to be a show-stopper.
Besides all this, the idea may not work anyway. The article says that feasibility wasn't even proven. There wasn't enough funding. So, the thing may not even work.
In spite of all this, I still like the idea, but it is a bit far-fetched without a huge commitment from the government and that is the biggest show stopper of them all.
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