k in electric terms is kilowatt. 1000 watts.
M is megawatts. 1000 kilowatts.
A typical US house uses around 10,000 watts or 10 kilowatts (kW).
For what you want nuclear is just not needed.
Just use a CODAG system. Combined diesel and gas turbine propulsion. Add in a gas turbine or two for extra electrical generation.
You can get 40 foot containers with 2 625 kW generators in them for 1250 kW or 1.25 MW per container. You can fly those off the ship.
I'm focused on the ship to shore power capabilities for this post. The paper I linked to in
post #5 was written back in spring of 2006, and as such is over 14, years old now, in the late fall of 2020, and more of a home research product than a professionally researched study. That being the case, I'm going to barrow from your post and extrapolate from there, so the following numbers are not arrived at by good, methodical, scientific research, but just a (poorly) educated guess.
In Mr Scott's paper, he used his own home's then current electric bill as the basis for a 'standard' american home using 1.7 kW, but for sake of argument, I'm going with your 10 kW for a typical home, and will further simplify the conversion as simply taking his electrical loads as being 1/5 current (even though 1.7 X 5 is not equal to 10, but rather 8.5, and 8.5 + 1.7 would give us 10.2, and a 6:1 ratio, but I like the 5:1 ratio instead, so hey) in respect to houses and hospitals. So a hospital would come in not at 2 MW, but as 10 MW each.
In Mr. Scott's paper he gives some numbers that I am going to take at face value, and these are the limits of the current electrical load's currently (or at least, current as of spring of '06) in use, and those were ~21 MW for shore to ship connections for a carrier, and 2.5 MW for the group used by smaller vessels, keeping in mind that no vessels at that time had been designed to provide their full power to shore installations, and that this is not what I am envisioning here in this thread, for my notional CVLN's.
Using the 40' containers mentioned above, each with 2 X 0.625 MW Generators, flying one such container ashore and emplacing them near where they can do the most good, a set of 8 such containers would be able to power up a single hospital (using the 10 MW guestimate from above), so we would need 8 containers worth of generators, all flown right to the local hospital. Next, we need fuel for each of these 16 generators, and the capacity of the fuel containers, the airlift capabilities of the choppers (how much weight, over the required distances), and the fuel usage of each of the 16 generators when operating for maximum power output. I don't have any of those numbers on hand at the moment, but just wanting to cover that there will need to be consideration given to these things, but my main concern right now is, just how much space is all this generator/fuel stuff going to take?
Let's take a 1 week period as a test case, so our airlifted generators, which require 8 40' containers for their own shipping, are then going to be working around the clock at maximum power output, and thus burning through their fuel supplies at the maximum rate per hour, what does a 168 hour fuel supply look like for each of these generators? How many additional 40 containers equivalent would this fuel supply take up? I leave that question up for anyone that would care to take the time and look it up and post back here, but I'm thinking that just the requirements for keeping a single hospital in electric power, for a single week, is going to account for far more of the space afloat than folks realise, and then it's already going to be a tradeoff between supplying electricity, or water/food/medicines...
CVLN's, on the other hand, don't need the capability to perform landing operations taking up space better used for DR supplies and equipment. Admittedly, Nuclear power would require the ability for the ship to "plug in" to the local power grid, and this would pose some problems of it's own. Namely, if the local power grid has a "plug" for ship to shore power input, it means prebuilding such things into your grid as a forethoughtful bit of prevention, and this would also require knowing that there was going to be at least the possibility of getting some DR ship to shore power. Without that, this would require the CVLN and/or her escorting/supporting vessels to be carrying not just the required components afloat, but also to be able to build them under less than ideal conditions.
I have yet to get a good number for the electrical backup generators at Fukushima, the ones that were supposed to power the reactor coolant systems, and whose failure led to the meltdowns in 2011. Varying numbers for the total output of the Fukushima power plant go from 4,700 MW to over 5,000 MW, but this isn't anything to do with the amount of power required to run the coolant system. My question for your consideration, gentle readers, is if the local power grid can send GW forth, then surely a shore "plug" could be built to tie into said grid, and allowing a ship to shore connection of at least 20 MW (the same as existing shore to ship carrier "plugs" in use back in 2006, five years BEFORE the 2011 disaster), might this not have been enough to prevent the meltdowns?