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The first brand that comes to mind when I think of external batteries is Electrovaya, which makes the PowerPad range. One nice thing about Electrovaya is that you can use your laptop's charger to recharge the PowerPad, since it allows charging at different voltages. That's one less thing to carry around. It would probably be my first choice.
An option that you might want to consider is one of those portable power units/vehicle jump starters that you see at auto parts stores and some big box stores. They are basically a 12 volt car battery in a case with a converter to power a couple of 120V AC outlets. Much cleaner power source than most generators, although a friend of mine has a Yamaha gas generator that has clean GFIC...that he paid $1000 for. I think I paid $75 for a Schumacher portable unit that you plug in and recharge. I've used mine with my laptop many times and it has worked great. One thing I did find was that my laptop uses more power than I though, so even with this large but still portable unit, the laptop drained it in a few hours.
One of those solar battery/charger combos might also be worth a try. You could use it, then once discharged, switch over to your internal batter while letting it recharge. I've only used those will smartphones, though, so I'm not sure if the capacity is enough to power a laptop for a significant amount of time.