DC alternator - ramp up the voltage?

[THATguy]

I have an alternator with a charge regulator - came off a pedal-a-watt.
Then I made a frame from bicycle bits, so I could have a portable generator.
However the 125mm diameter cog only generates max 3v
A bicycle wheel generates somewhere in the vicinity of 12 to 15v, the regulator limits this to 12v.

As you can see from the picture I've been experimenting with making larger cogs - real pain to build.
I've no information about the alternator, the pedal-a-watt company removed all the labels - I suspect it is from a scooter (moped).


I saw this video
https://youtu.be/wh8FbnZdhJg?t=469

As you can see there are feedback wires to generate higher voltage.
Could I do something similar, so I'm able to use the smaller cog and get my 12v output?