Scratch that. What I meant was, is it safer / more efficient to have a nuclear atomic booster in space? I read a paper saying that nuclear powered boosters would be too dangerous, and that chemical propulsion would be better, for reasons I am unaware of. Of course, it is 'nuclear', which gives room for problems. If the picture didn't show up, I posted it again. It has a link to the gallery I am using.
View image in gallery
Still no picture, and the link to the gallery comes up with an invalid album error. I dutifully did as the error asked and sent a message to the admin. You should see if if the gallery is set to public, if not, then that would easily explain why I can't see the gallery or the picture inside.
About your question- one reason, leaving accidents aside for a moment, is radiation exposure. Every time the engine lights, the nuclear rocket is spewing radioactive exhaust, and the engine itself gets "hot" as well, leading to some amount of radiation winging it's way to where the crew is. The shielding on the reactor part of the engine, the distance from the crew to the reactor, and anything in between(structure, propellent, whatever) does decrease the amount of radiation they are exposed to, but it's still exposure.
Crews on a journey to Mars will face getting irradiated from sources like the Sun and galactic cosmic rays(GCRs), so the long they spend traveling between Earth and Mars, the more exposure they will get from natural sources. One way to minimize that exposure is use a nuclear rocket, benefiting from it's high ISP(relative to chemical engines) to enable faster trajectories that should lead to less exposure overall, even with the portable radioactive flame-dragon pushing them around. The same high ISPs also mean fewer kgs of propellent for the same oomph, meaning less mass has to be delivered to LEO to feed the beasts of burden: allowing smaller, cheaper launch vehicles, or fewer flights, That's the hope, though the trade-off between radiation from the nuclear powered rocket and the exposure time the rocket prevents isn't a sure thing. One sure thing about a nuclear stage is that it will cost more than a chemical stage.
That brings us to reason two, nuclear rocketry is capital intensive, both of the money-kind and human: nuclear propulsion on the scale needed for Mars is still a while from flight-ready, and getting to get it there means dealing with a reactor that lives in a rocket engine(and vice-versa), demanding special people to work the problems and the money to pay for everything. And of course, development would take time. It is, leaving aside potential catastrophes, the biggest hurdle to putting a nuclear rocket in space. I think you can imagine why coming up with both the money and patience to see a nuclear rocket stage sized for Mars flights through to a productive use would be difficult to imagine.
The last reason is of course, is potential accidents and general safety(leaving radiation exposure as it's own separate thing). There is of course people who are dead-set against nuclear anything, but nuclear rockets present challenges that are real and to deserve some questioning. Making sure the reactor's container could survive likely launch failures is one thing that should be addressed, along with disposal, to name two that I'm aware of.
Now, the above might scare you off of investigating nuclear options for your Mars mission, but nuclear engines do have the advantages of higher ISPs than chemical engines, and what that means for both the rocket and other parts of the architecture(the LVs that launch it, the payloads it moves around) isn't something I think should be dropped lightly.
TL;DR version: nuclear rockets are more efficient than chemical rockets and could enable faster trajectories, but pose a bunch of problems linked to their radioactivity and are more capital intensive than chemical engines.
Couldn't you use SkylabII?
Certainly seems reasonable enough as a habitat, though Skylab 2 might not have a feature like a shielded place to sleep and hide from big solar events in, which would be really handy on the way to and from Mars. I say "might not" because it should be easy enough(engineering-wise) to add in, though it will kick up the mass of Skylab 2 by quite a lot, depending on the materials that are doing the shielding. Atomic Rockets should have the info you'll need, but I'm at a loss for a specific section and I can't go searching right now.
, and I have been coming up with some ideas for how to add aero-braking onto the Lynx (more on that later)...
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