Hero999 said:
Rewinding the existing one probably isn't an option. There probably isn't enough room to use the same number of turns of thicker wire and even if there was the leakage inductance is likely to increase to such a point that the voltage drops at higher loads and core saturation could also be a limiting factor.
There was a post earlier on these forums from a guy who had done it, personally it's not something I've ever had the urge to try. I used to have a Yamaha DT400 trail bike, and that had really crap lights - I often thought of ways to try and improve them, but never really came up with a decent idea
I would suspect that the best thing to do is:
1) Convert all the electrics to 12V.
2) Replace the tiny 6V battery with a larger 12V one.
3) Rewind, or replace, the alternator coils with ones to give 12V and a higher current output.
4) Design and fit a charging circuit to avoid over charging.
5) Rewire the headlight so it's powered from the battery, rather than directly from the alternator coil.
Essentially all you're doing is upgrading the electrics to a 'real' system, like larger road bikes have.
The main sticking point though is modifying the alternator coils!.