Solid Core Nuclear Thermal rocketry has existed for a while and I was thinking about using it as the primary propulsion in my setting. Now most Solid Core rockets still have fairly long transit times (Something like 3-4 months just to get to Mars, longer to get elsewhere). Would it be safe to assume technology has advanced enough to reduce travel times a bit, or is this the maximum performance? The reason I am looking into Nuclear Thermal is that I don't want full on torch-ships like the Orion running around, along with all their implications.
The maximum theoretical performance of NTR's was calculated back in the 60's as being ISP @ 1000. While considerably better than a LOX/H2 engine (theoretical ISP @ 450) the primary sticking point is the temperature where metals lose their strength. Having your thrust structure bending like taffy while under full thrust would tend to ruin your day.
The Atomic Rockets Engine Table takes this as the starting point:
Solid core nuclear thermal rockets have a nominal core temperature of 2,750 K (4,490° F).
This is pretty close to the melting point of many common engineering materials, so you can see you are already operating with some pretty thin margins.
The high heat needed for good performance also has another negative side effect:
One problem with solid-core NTRs is that if the propellant is corrosive, that is, if it is oxidizing or reducing, heating it up to three thousand degrees is just going to make it more reactive. Without a protective coating, the propellant will start corroding away the interior of the reactor, which will make for some real excitement when it starts dissolving the radioactive fuel rods. What's worse, a protective coating against an oxidizing chemical is worthless against a reducing chemical, which will put a crimp in your wilderness refueling. And trying to protect against both is an engineering nightmare. Oxidizing propellants include oxygen, water, and carbon dioxide, while reducing propellants include hydrogen, ammonia, and methane. Carbon Monoxide is neither, as the carbon atom has a death-grip on the oxygen atom.
Keep in mind that the oxidizing/reducing effect is only a problem with solid-core NTRs, not the other kinds. This is because only the solid-core NTRs have solid reactor elements exposed to the propellant (for heating).
Over the years, various iterations of NTR's have been proposed. Perhaps the closest to a flight article was "TIMBERWIND", a pebble bed nuclear core with a thrust to weight ratio greater than one (i.e. a TIMBERWIND powered rocket could have lifted off from Earth). This uses high temperature carbon/carbon materials to both deal with the intense heat and nuclear radiation, as well as dramatically reducing the mass of the engine.
A final trick which might be used on an NTR is a "Pulsed Solid-core NTR". This uses a strange nuclear trick where the reactor is run at a much higher output in pulses, allowing the fuel to capture some of the neutron energy which is otherwise not captured:
Specific Impulse Amplification: This is really clever. For this trick you keep the propellant mass flow the same as it was.
In a fission nuclear reactor 95% of the reactor energy comes from fission-fragments, and only 5% come from prompt neutrons. In a conventional solid-core NTR the propellant is not exposed to enough neutrons to get any measurable energy from them. All the energy comes from fission fragments.
But in pulse mode, that 5% energy from neutrons could be higher than the 95% fission-fragment energy in stationary mode. The difference is that fission fragment energy heats the reactor and reactor heat gives energy to the propellant. And if the reactor heats too much it melts. But neutron energy does not heat the reactor, it passes through and directly heats the propellant.
The end result is that in pulse mode, you can actually make the propellant hotter than the reactor. Which means a much higher specific impulse than a conventional solid-core NTR which running hot enough to be right on the edge of melting.
Thermodynamics will not allow heat energy to pass from something colder to something hotter, so it cannot make the propellant hotter than the reactor. But in this case we are heating the propellant with neutron kinetic energy, which has zippity-do-dah to do with thermodynamics.
The drawback of course is that the 95% fission-fragment energy is increased as well as the neutron energy. The important point is by using pulsing you can use an auxiliary cooling system to cool the reactor off before the blasted thing melts, unlike a conventional NTR.
One gets the sense that this is not for the faint hearted, and any miscalculations will have pretty severe effects on your rocket.
So it is possible to improve the performance of NTR's through the use of high temperature resistant and lightweight carbon/carbon materials, nuclear "pebble bed" reactors and tricky modulation of neutron outputs. The performance will mostly be in the form of much higher ISP (i.e. you get a lot more performance for the same amount of reaction mass) rather than higher thrust, but careful reading of the articles should allow you to calculate roughly where the "sweet spot" is for whatever story purposes you desire. A high thrust engine will likely be larger and use more reaction mass, while a high ISP engine will be far more economical of reaction mass for similar performance compared to low ISP engines.
Edit to add:
A commenter noted I had not mentioned liquid or gas core NTR's. This is an oversight on my part, but I generally don't consider them since the engineering is far more speculative than with solid core NTR's and the higher performance engines which would overtake NTR technology in the future. In essence I believe liquid and gas core NTR's are technological blind alleys, and will be overtaken by other technologies long before they can be perfected.
Solid Core Nuclear Thermal rocketry has existed for a while
No, not really.
Would it be safe to assume technology has advanced enough to reduce travel times a bit, or is this the maximum performance?
Far from it.
Plans and test rigs have been around for a while, but that's far from actual rockets lifting off the ground.
The reason I am looking into Nuclear Thermal is that I don't want full on torch-ships like the Orion running around, along with all their implications.
But you're writing fiction, and that means SCNTR can have advanced to the point of usefulness, and people not be terrified of hard, ionizing radiation.