First of all, this would require a massively higher energy density than the order of magnitude improvement over existing cells stated in the o.p. Second, it isn’t just energy density that is the driving factor; you also have to have high throughput in order to generate enough power to pump up the laser in the short amount of time necessary to achieve high levels. The necessary minimum throughput is about 50 dB[sub]p[/sub] (100000X) improvement over existing thermal battery systems in order to power this kind of directed energy weapon. Existing systems use highly reactive chemical isomers to provide this kind of throughput which is one of the major stumbling block with systems like Airborne Laser insofar as it is really hazardous to have giant tanks of caustic, flammable liquids in a jumbo aircraft just so you can kick off two or three shots. And the heating and venting requirements for such a device may be prohibitive even if you can supply the necessary power into the weapon without issue.
Realistically, lithium sulfur batteries are the only rechargeable electrolyte which offers the promise of significantly higher energy density above lithium-ion batteries (estimated to be about a 3X theoretical improvement, although the latest work I’ve seen indicates that technical limitations make make it closer to 2X), and may also offer reduced production costs. There are potential electrolyte mediums for fuel cells which may provide higher energy density and also rapid refuelability, but the stumbling block there are the catalysts that are typically required to release the energy medium from the matrix, which use rare earth metals, are very sensitive to small amounts of contamination, and are often physically delicate and therefore poorly suited to mobile applications without sophisticated isolation from noise, shock, and vibration.
The kind of energy density and power throughput necessary to allow for man-portable directed energy weapons is likely beyond chemical energy storage (save for the previously mentioned chemical isomers, which would be not unlike walking around with a vial of nitroglycerine in your pocket). Nuclear isomer ‘batteries’ and other speculative technologies could potentially offer the required energy and power throughput capabilities but are at this point highly speculative.
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