Assuming that this process is 10% efficent let's take a look at the numbers.
Let's say you can dedicate half of the 1.1GWT (thermal) of the nimitz to aviation fuel production, if you're holding off coast.
And let's assume conservativley that the process is 20% efficent.
Diesel (pretty close to JP1) has an energy density of 35 MJ/L. This means at 20% efficency you'll be needing 175mj to create 1 liter of JP1.
At 1/2 1GWT you're looking at about 3 liters of fuel per second, or about 172,000 liters a day, or about 40,000 gallons. The nimitz has about 3 million gallons of fuel capacity so the refueling time of the entire tank from 0 would be around 2 months. According to this article here
http://large.stanford.edu/cour... (Also about marine jet fuel fabrication, provides some of the hard numbers) 3 million gallons is enough to refuel the onboard fleet about 20 times. So onboard fuel production would provide 1/3 of a full tank of gas for each aircraft onboard per day. Not terribly good, or bad.