just because someone says a cap works doesn't mean it does. i prefer to do research before i recommend anything and i would hope the rest of you would do the same...let me explain...
caps don't work the extremely short and basic version:
Let'* imagine a car with a 12v battery and an alternator putting out 14v. This car also has a 1000watt amp powering some random sub.
We now add a 1 farad capacitor.
A 1 farad cap charged to 14v stores about 84 joules.
Since we have the battery sitting at 12v, the potential (useable power) of the cap is 2v or 12 joules.
We CANNOT use more than the 12 joules, since that would put the cap below the magical 12v where the battery kicks in.
In order to use the power stored in the cap, we would have to turn off the alternator, or the power it outputs would somehow have to drop - like if it'* overloaded (BAD).
Note: 1 joule = 1 watt-second. 1000w for one second is 1000 joule.
Anyway, our 1 farad cap has 12 joules of power we can actually use. this translates into 12 watt-seconds. This can power our 1000w amp for 12/1000s of a second, or 0.012seconds.
This means that if we charge the cap to 14v, and turn off the alternator, we can play a single test tone of 83hz one single time before the cap becomes useless.
Since I'm not at all an expert on this, I have neglected to mention ESR and ESL, which would significantly reduce the benefit we get from the cap.
Because of ESR (ElectroStatic Resistance), an amount of power will be converted into heat in the cap. The more power you try to pull, the more heat and the less useful it is.
Additionally, the amp will convert some amount of power into heat - alle depending on the amp.
In the end, the cap may give us as much as .005 seconds (single 200hz tone) of power at 1000w amp output, IF the alternator suddenly dies or for some magical reason (it'* overloaded, duh) it drops it'* output to 12v. If you only run 500W, it would be about 0.01 second or a single 100hz test tone."
next on the list don't mess with extra batteries or any of that crap YET:
do the big 3 with 0 gauge. Replacing/adding larger wire to these three critical spots can reduce or rid your electrical system of dimming and voltage drops. Overall, giving your charging system a larger surface area to travel over, will stabilize power and relieve strain on the alternator and battery.
<--how to do it, what it is etc.
if the big 3 doesn't solve your problem, which it will mind you, adding in more batteries is your only 'real' hope. you need to stabilize your voltage. the big 3 does this in a HUGE way. but when that isn't enough: ok so your system makes a big 'boom' your batt will drop from 14.v to around 12v. then your alty turns on because of the v drop and brings the whole system back up to 14, or tries. whole problem is that the alt can't prevent the initial voltage drop no matter what you do and the time it takes for it to raise the voltage is what you notice in your lights dimming. so your lights will dim slightly. the more batteries the less your voltage will drop in theory so when your big 'boom' hits hopefully your voltage will not drop down to 12 or lower which means your lights will dim significantly less. again the big 3 has the best chance of fixing your problems. you could get into voltage regulators and other crap but none of it is needed or honestly practical for ca.
Now the idea of a high output alt is nice and all but to get one for your car it will have to be custom built, is going to cost over well over $400 when shipped to your door, and will not be NEARLY as reliable as your stock one. the people who compete professionally usually run off 17v not 14.4v systems so they really need a high output alty. so basically put the idea of a HO alty out of your mind as it'* not practical and you arn't drawing nearly enough to necessitate the need for one.
or install HIDs and never have to worry about dimming headlights ever again.