800W sound system on an OEM alternator?

Hi all! 

I just bought 2 12-inch subs by Kicker and an 800W amplifier (Harmony Audio HA-A4000.1) from my friend for a great price, wiring kit and bass knob finally arrived too so he’s gonna help me install everything pretty soon. The question that remains is whether or not my recently installed 80A Denso alternator (not recently enough to return sadly) is going to burn itself out trying to power my sound system upgrade. Should I be worried? If so, is there an easy fix or safeguard I can implement without spending a lot of money? A high output alternator would more than 3x my total investment into this, 4x including the cost of the alternator I recently replaced, and I’m simply not prepared to do that. Hoping somebody in here can give me advice! Thanks so much.