Ok now I think we are starting to see the same light. A larger capacity alternator should help tremendously, but you are correct that a cap does serve a purpose. I'm not arguing against caps completely, I'm saying that most people are too quick to add one to their system thinking it's the "fix all" solution. I agree that a larger or second battery is not the solution. In fact more electrical storage, of what ever kind, is not the true solution. It's a band aid.
An alternator can only produce so much current at a given voltage. When the current requirements exceed that limit, the current will flow, but the voltage will drop. It has nothing to do with wire gauge, length etc. You could have the amp connected to the alternator with a 2" solid copper bus bar. When the amp needs more current than the alternator can produce at 13-14v the current flows, but the voltage drops.
A capacitor can help lengthen the life of your alternator and battery by smoothing out the current spikes in your system. But the bottom line is that your alternator it self must be capable of producing the amount of current required for your system at 13-14v.
Moderator Car Audio/Video
2001 Black R/T
All the options
Toyo Proxes T1-S 245/45-17 (worn out)
Continental ContiExtremeContact 245/45-17
Brembo Front Brake Rotors
Hawk HPS Front and Rear Pads