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There are three common types of Tesla coils; the monopolar 1/4 wave, the bipolar 1/2 wave, and the Tesla magnifier. I have built the bipolar type and am currently working on a 4"x20" monopolar.
Here are some pictures and construction information on this bipolar Tesla coil:
This is the basic setup of my small bipolar coil. At the top the two spheres were constructed from two softballs covered in aluminum foil. Below the output terminals is the secondary and primary. The secondary is wound with about 1100 turns of 27 guage magnet wire on a 1 1/2" piece of PVC pipe. The winding length is 18 1/2" long. The primary is about 7" in diameter and is wound with 6 gauge solid ground wire. It has a total of 14 turns spaced 3/8" apart. The primary coil is held in place with six plywood spacers with notches for the heavy wire cut in them. The spacers are made from 1/2" thick plywood which is cut 8" long by 2 1/2" wide. The stand for this coil is very simple. It has a plywood base and the coil is supported by some PVC "tee" connectors. Below the primary on the left is two neon sign transformers. These transformers are rated 5kV at 60mA each. They are connected in series for 10kV at 60mA. To the right of the transformers is a "Richard Quick cylinder spark gap" which consists of 7 3/4" hard copper water pipes mounted .03" from away eachother. This forms 6 series gaps. To the right of the spark gap is 6 beer bottle capacitors which have a capacitance of about 800pF per bottle. The are connected in parallel for about .0048uF. There is no transformer protection circuits on this coil, but they are planned to be added.
This is an arc about 12" long. Arcs like this are loud and can even drown out the sound of the spark gap.
Here is a closeup of an arc. It is just a little longer than 12". The day this picture was taken it was very humid outside so I suspect longer arcs on dry days. Maybe arcs as long as 14".
Here are some pictures of my monopolar coil which is under construction: