Capacitors.

    A capacitor is a device which "stores" up an electrical charge produced by a power source, by spreading electrons over a surface, creating a "negative" on one plate and a "positive" charge on the other.  This charge differance is described by it's voltage, and it's capacitance, measured in farads.  The capacitor forms a resonant circuit with the primary coil inductor.
    There are several types of capacitors used by Tesla coilers, professional pulse caps, MMC, poly-plate, and Leyden jar (beer bottle or salt-water caps).  The professional pulse capacitors are generally prohibitively expensive, and hard to find, so one might say they are not ideal, however, I use one with my 6-in coil and it works well.  MMC (multi-mini-cap) are series strings of smaller caps to obtain the proper voltage requirement of the system, then stringed in parallel to get the proper capacitance.  I am told these are quite reliable, and give excellent results, but are somewhat costly to build (a cap of this type for my 6in coil would cost over one hundred dollars).  Poly-plate caps, are stacks of dielectric (usually poly-ethylene plastic) separating alternating polarity sheets of conductor (aluminum foil or sheet metal), the entire assembly is usually squeezed between two flat hard objects (wood or fiber-glass) and then planted in some non-conductor (mineral oil) to suppress loss of power, and dielectric damage through corona.  I have built several experimental caps of this fashion, the first using .06 mil polyethylene stacked with aluminum flashing, it did not work as a short developed inside immediatly and the plastic was easily punctured by the aluminum (next time, go for a thicker dielectric).  Prototype two used glass greenhouse panes, and foil tape, and initial tests gave tremendous results.  My spark gap lit like I have never seen it light before, but because my cap was not under oil both terminals arced like crazy to their opposite plate (essentially the capacitor was so powerful it shorted itself  and ran the sparkgap at the same time, like running three sparkgaps simultaneously).  The glass plates would have worked extremely well, had I not accidentally cracked the glass before imbedding them in molten wax.  The poly plate is said to give excellent results, but they seem to be a pain to build for me (it is a pain, but if it would make my coil better and it is cheap, who cares how difficult it is, right?  Wrong!  I am fed up with torn plastic and cracked glass, so for the time being I will stick with my salt caps, and off the shelf parts!).  Another variation of the poly-plate cap is the rolled cap, which is basically a strip of dielectric between two flexible electrodes, and the entire assembly is rolled in a tight spiral (this is how a lot of real capacitors are designed), this saves on space but it does now work quite as well as it's flat plate counterpart, because some power is transferred directly by inductance because the electrodes are so long.  I built a prototype rolled capacitor, but have never tested it, the plastic is only good to about 6000 volts, so I would need to make several in series, and I found a better deal before I got around to finishing all of them.  I may use them on my smaller coil someday. 
    Lastly is the Leyden jar or "beer-bottle-cap" which is a slang term because these bottles are employed so often.  A jar or bottle or whatever is filled with a conducting fluid (saltwater or any ionic compound, the hydronium (H3O+ or just H+ like in H+Cl-) and hydroxide (OH-) ions conduct the best, but are caustic to use) and the outside is surrounded by a conductor (aluminum foil or I use foil tape), a conducting rod or plate like a copper pipe in the fluid is one "pole" and the outside conductor is the other, usually it is then wrapped in an insulator (like electrical tape) and oil is poured on top of the fluid to prevent corona loss.  These are by far the easiest cap to build (I made my first in about two minutes) and there are tons of variations.  I use huge pickle jars that hold a gallon, some people use tons of little bottles (I don't drink, so I have no beer bottles, but canning jars worked good, or even jelly jars) some people surround the container with another conducting fluid in place of metal foil, so less energy is lost to corona, and glass degeneration because of sparks generating heat (my caps glow purple when I am using them, and the water solution would stop that because corona is formed when air is between your two "poles").  These caps are super cheap and easy, but they are not as good as poly-plate performance wise, and mine have been known to "stall" which means contact is poor and not enough power is getting through, and therefore the system stops working.  Much of my problems are self-inflicted, a well built bottle cap should be very reliable, after all, Tesla used them almost exclusively. 
    For my new tesla coil, I am using a professionally built Maxwell pulse capacitor.  I got a great deal on the thing, 125 dollars, the company that manufactures them said to buy one new would cost about $800, but another tesla coil enthusiast came through for me.  Needless to say it works great, especially with a synchronous rotary spark gap.  Here are some pictures.

 
Tesla coil high voltage capacitorsleyden caps 2Maxwell 1maxwell 2

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Scott Bogard. 2007