Charge battery with AC
Two to four diodes and a capacitor will get you a long ways, without the complications of battery charging (which is picky to do well, depending on the type/chemistry, some being more difficult than others.) The concept you are after at that level is not too complicated - a rectifier (converts AC to DC) and a filter (smooths out the pulsing DC.) You'll want those anyway for a system with a battery, but with a small LED current and a fairly large capacitor, you may find that your application can be adequately covered with just the capacitor.

You'll also typically get more output if you shift your generator position towards the rim of the wheel, so the magnets go past the coil faster. More magnets will also help, and there's more room for them out there.

Mind you, it's far more convenient with current technology to simply use a rechargeable battery powered light, in practical terms for most riders - you really need an odd set of circumstances to make the "on bike generator" actually make sense in the era of rechargeable lithium-ion batteries and LED lights. But it can be fun to tinker with.







simulate this circuit &ndash; Schematic created using CircuitLab