Sorry to butt in here but there would be no need to increase the thickness of the shielding around the reactor, if something stops 1 gamma wave it stops another,power doesn't come into it.
Whew. Um.
That's absolutely false. Radiation shielding is and always has been expressed, at least in engineering-fidelity calculations, in an exponential-decay sense. The decay rate is a function of both the material and the energy of the incident particle.
This is a matter of basic science and really is not up for debate.
Generally with reactors it's possible to increase the standard output by simply increasing the radius of it
This too is absolutely false, at least in the context of naval reactors. No less a luminary than Norman Friedman has noted (in
US Aircraft Carriers: An Illustrated Design History):
Nuclear-carrier design entailed some unique problems. First the development of any given reactor was difficult and expensive enough to require ships to be designed around specific power plants... non-nuclear reactors were infinitely more elastic in their design than nuclear ones were. That is, it was far easier to design a new non-nuclear plant say, 30 percent more powerful than an existing one, than to develop a wholly new reactor...
Indeed, multiple US nuclear carrier programs (CVAN 7/57 being a notable example) failed
specifically because they could not quite meet their design speed requirements based on the exact shaft horsepower produced by the nuclear plant then available.
Apologies, the first point is a bit of a screwup, shows why I shouldn't post at 2am...
You misunderstand me, the method I stated was for working out what would be the size of a new higher powered core design of a Rolls Royce PWR 1.
Obviously just increasing the core size of the existing reactor would not work as all systems in a reactor are tailored to the size of the reactor so increasing the core size would require a total redesign of the reactor systems.
Most of the work in reactor design is developing a cooling system and steam plant for the new core that has enough efficiency to produce the desired output.
EDIT
Indeed, multiple US nuclear carrier programs (CVAN 7/57 being a notable example) failed specifically because they could not quite meet their design speed requirements based on the exact shaft horsepower produced by the nuclear plant then available.
That is a common problem when you Develop the ship then try to use an off the shelf reactor, I believe however that a British carrier would have a purpose designed reactor by virtue or the fact that Britain never attempted a nuclear cruiser program therefore no off the shelf solution is available save buying an American reactor (Which wouldn't happen in Britain in the 80s).