While watching the finale of the Chernobyl miniseries yesterday a question came to my mind. An NTR is type of a nuclear reactor which means it cannot be just turned on/off like (some) chemical rockets. I looked up articles about NTR propulsion, but found little specific about startup/operation/throttling/shutdown. Presumably because how quickly can the engine adjust its thrust generally wouldn't be relevant for long-term missions. Mostly I found out the engine can explode if shut down abruptly.
My question comes from wondering if it is realistic to expect a combat spacecraft to be able to rapidly change thrust of its NTR from minimal to full in order to evade (dodge) enemy attacks. If the engines cannot do that, it would be probably necessary to run them constantly at (nearly) full thrust and use other means that can be operated quickly to facilitate rapid maneuvers. Most likely taking advantage of thrust vectoring and changing facing of the craft. This would be however rather wasteful on fuel, especially for smaller ships.
If anyone has any information I would be really grateful.
Reactors can be turned on as fast as the structure can handle the thermal expansion stress. When you turn the reactor 'off', it indeed won't shut off fully instantly, rather after shutdown it will still produce about 5-6% of nominal power output right after shutdown. So this should be dealt with using radiative cooling, though using the cooling loop through the nozzle (the one normally used for regenerative cooling) in a closed loop fashion could potentially provide enough cooling to not need an additional radiator.
For example, considering an NTR that during full throttle produces 1 GW of thermal power, it will produce around 50 MW of thermal power right after shutdown.
The Stefan-Boltzmann law for thermal radiation goes like this: radiated power = area*emissivity*5.67*10^-8*temperature^4
Since emissivity can be close to one, we'll drop this factor and rearrange the formula like this:
Area = P/(T^4*5.67*10^-8) to find the radiating area needed to cool our reactor post shutdown. Assuming we're willing to let our surface heat up to 3000 K we get the following:
Area = 50*10^6 W/(3000^4*5.67*10^-8) = 10.89 m² of radiative surface, which is quite a lot, but this cooling requirement drops further as more time after the burn passes.
Alternatively, since we tend to run our NTR's a lot hotter we might be willing to accept a hotter radiating surface, for example at 3500 K.
In that case we need only 5.88 m² of radiative surface.
Alternatively, open cycle cooling could be used to supplement radiative cooling until the reactor core has 'cooled down' a bit.