There is a proposed solution which would kinda work the way you want.

The "Nuclear salt-water rocket" (NSWR) https://en.wikipedia.org/wiki/Nuclear_salt-water_rocket

TL:DR;

The NSWR has a fuel tank of enriched radioactive salts dissolved in water. The tank is filled with neutron absorbing materials, so it does not go critical!

The fuel is pumped into the reaction chamber/ nozzle where it can go (prompt!) critical. This heats the water, which acts a propellent.

Versions of the design have an IPS of 6,730 seconds (the best chemical rockets top out at about 450 seconds).

The rocket is more efficient/powerful, with more highly enriched fuel. So for the sake of your story, you could have an after-market 'boost tank` of, lets say, 90% enriched Uranium. Which could be bled into the main supply when you really need to be going places.

I strongly encourage you to watch Scott Manley's video on this:

https://www.youtube.com/watch?v=cvZjhWE-3zM

See also: https://en.wikipedia.org/wiki/Aqueous_homogeneous_reactor

So there is a real one of these. (no magic needed) https://en.wikipedia.org/wiki/Godiva_device

There is a proposed solution which works as a rocket.

The "Nuclear salt-water rocket" (NSWR) https://en.wikipedia.org/wiki/Nuclear_salt-water_rocket

TL:DR;

The NSWR has a fuel tank of enriched radioactive salts dissolved in water. The tank is filled with neutron absorbing materials, so it does not go critical!

The fuel is pumped into the reaction chamber/ nozzle where it can go (prompt!) critical. This heats the water, which acts a propellent.

Versions of the design have an IPS of 6,730 seconds (the best chemical rockets top out at about 450 seconds).

The rocket is more efficient/powerful, with more highly enriched fuel. So for the sake of your story, you could have an after-market 'boost tank` of, lets say, 90% enriched Uranium. Which could be bled into the main supply when you really need to be going places.

I strongly encourage you to watch Scott Manley's video on this:

https://www.youtube.com/watch?v=cvZjhWE-3zM

See also: https://en.wikipedia.org/wiki/Aqueous_homogeneous_reactor

There is a proposed solution which would kinda work the way you want.

The "Nuclear salt-water rocket" (NSWR) https://en.wikipedia.org/wiki/Nuclear_salt-water_rocket

TL:DR;

The NSWR has a fuel tank of enriched radioactive salts dissolved in water. The tank is filled with neutron absorbing materials, so it does not go critical!

The fuel is pumped into the reaction chamber/ nozzle where it can go critical. This heats the water, which acts a propellent.

Versions of the design have an IPS of 6,730 seconds (the best chemical rockets top out at about 450 seconds).

The rocket is more efficient/powerful, with more highly enriched fuel. So for the sake of your story, you could have an after-market 'boost tank` of, lets say, 90% enriched Uranium. Which could be bled into the main supply when you really need to be going places.

I strongly encourage you to watch Scott Manley's video on this:

https://www.youtube.com/watch?v=cvZjhWE-3zM

See also: https://en.wikipedia.org/wiki/Aqueous_homogeneous_reactor

There is a proposed solution which would kinda work the way you want.

The "Nuclear salt-water rocket" (NSWR) https://en.wikipedia.org/wiki/Nuclear_salt-water_rocket

TL:DR;

The NSWR has a fuel tank of enriched radioactive salts dissolved in water. The tank is filled with neutron absorbing materials, so it does not go critical!

The fuel is pumped into the reaction chamber/ nozzle where it can go (prompt!) critical. This heats the water, which acts a propellent.

Versions of the design have an IPS of 6,730 seconds (the best chemical rockets top out at about 450 seconds).

The rocket is more efficient/powerful, with more highly enriched fuel. So for the sake of your story, you could have an after-market 'boost tank` of, lets say, 90% enriched Uranium. Which could be bled into the main supply when you really need to be going places.

I strongly encourage you to watch Scott Manley's video on this:

https://www.youtube.com/watch?v=cvZjhWE-3zM

See also: https://en.wikipedia.org/wiki/Aqueous_homogeneous_reactor