I have some alien laser cannons that I pulled out of a perpetual hurricane. They're cylinders that are two feet long and one foot across. They can only be charged by magnetodynamic coupling - that is, one armature spins outside them and one spins inside them, transferring power from the outside to the inside.
The problem is that these little two-foot-by-one-foot numbers can store 6.1 megajoules of energy, and someone is trying to use it to shoot down ICBMs. There are a lot of ICBMs. There are significantly fewer of these things. They need to be recharged fast.
How quickly can modern armature technology recharge these things? Assume that they absorb 100% of the energy directed at them, provided that it's in the form of magnetic energy directed at them by an armature.