Need to upgrade my alternator!

I've just purchased a 12" 4000 watt RMS competition subwoofer for my car. Problem is because of the massive amount of power it's putting out, I'll need to upgrade my alternator to feed it.

Is it poissible to modify my existing alternator to put out more power?

Or does someone know of a replacement that would be suitable?

This is the sub if anyone's curious... the almighty STROKER !