If all you have for your stereo is a normal head unit (stock or common aftermarket) and this 1,000 watt amplifier, you will probably be okay with your stock alternator. Adding a capacitor will eliminate the light dimming issue you are having. Adding a high output alternator probably will not, but it would help keep up with the power demand if you add on to what you currently have. A high output alternator that is working correctly will not damage any part of your car’s electrical system. The only reason to add a high output alternator is if you want bragging rights for installing one, and those would be pricey bragging rights. For what it’s worth, when I went through this phase as a teenager (and it didn’t last more than a year and a half or so, then a window-rattling, thief-attracting stereo no longer seemed like a life necessity), I had a 600 watt RMS amplifier for a pair of subs in a Cavalier with a 95 amp alternator. If I turned the volume way up, the headlights would dim with the bass. I didn’t do anything about it other than keep the volume at a level such that I did not attract police attention. At normal volumes, the headlights would not dim. I never added a capacitor and never had a problem with the charging system or battery due to the amplifier’s power demands. My father continued driving that car when I was done with it for another ten years, and it went to the junkyard rusted out with the same alternator and its reman date tag from 1997 attached to it (the car was a 1990 model year).