A 200A alternator will provide a ton of audio power. Unless you plan to try to run that 4kw amp at near full volume a LOT of the time it should cover you.
You'll also need to upgrade your 3 main charging system wires -- alt output to batt (+), batt (-) to chassis and engine block to chassis.
The capacitor suggestion was ignorant. For one, they're Farad's, and for another - capacitors are simply very small batteries that charge and discharge faster than a standard starting battery, but the amount of energy they provide would have no effect at all on an amp that size.