I see nothing in the rules about you must start field day with a discharged battery so i would plan starting with a fully charged battery having a fully charged battery in reserve and having a solar panel charging station off site to recharge the first depleted battery if you think your power usage would require more than one.
Field day solar panel.
So a fresh deep cycle marine battery with 100w solar panel about 5a charge if the sun is good will run a kx2 at 10w all day with ease.
As a heads up i hear solar power chargers can be very rf noisy.
This is called the nameplate rating and solar panel wattage varies based on the size and efficiency of your panel.
5 hours x 290 watts an example wattage of a premium solar panel 1 450 watts hours or roughly 1 5 kilowatt hours kwh.
How much energy does a solar panel produce.
Watch out for the current drawn by the laptop as some laptops can be rather thirsty for power.
Solar field day 2017.
So a rather small solar panel operated over a period of days could put enough charge on a battery to allow it to be used for the field day bonus.
This is exactly what my club did.
Perhaps a more economical mobile phone could be used.
There are plenty of solar calculators and the brand of solar system you choose probably offers one.
That said there is a simple equation to calculate the amount of kilowatt hours kwh your solar panel system will produce.