This is actually marketed as a "Mini Tesla Lightning Machine", but you're not going to argue when u get shocked by it. The kit i got cost a little under $20 from the great people at Information Unlimited, a company that sells all sorts of crazy stuff, and are well worth a visit.
Click here for circuit diagram
The theory behind this circuit is simple, it works a lot like a camera flash:
This is advertised as being 'safe', but I assure you, you wont be saying that when you accidentally touch it, as I have 3 times so far...its bloody painful and definately makes you jump. And dont touch the capacitors when they're charged either! I added a safety switch to short out the capacitors on mine so I didnt get electrocuted every time i opened it :P
Heres a pic of mine set up as it's SUPPOSED to be, as a sparker. Once the circuit's built, it's easy to configure how you want.
The easy way to make one is to just order the kit... but if you cant be bothered thay are quite simple to make once u have all the parts.
Parts list for basic circuit:(R1) 2.2KW 1/4 Watt resistor (R2) 100W 1/4 Watt resistor (R3) 27W 1/4 Watt resistor (C1) 10 uF 30V electrolytic capacitor (C2) 0.047 uF 50V polyester cap. (C3) 4 uF 350V polyester cap. (C4) 0.47 uF 250V polyester cap. (Q1) MJE3055(npn)power transistor (D1) IN4007 1KV rectifier diode (SIDAC) 300V sidac switch (T1) Switching square wave transformer 400V (T2+3) 2x 25KV pulse transformers (S1+2+3) 3x 3A SPST switches
By speaking nicely to people at Farnell and Information Unlimited customer services, and by scrounging around, I have been able to get almost all these parts for free :P. The only problem i have had is that the pulse transformers from Info-Unlim. are a bit dodgy: 2 out of the 4 I have are slightly faulty, so you dont get the big arc between terminals, but still get fryed :).
The transistor circuitry oscillates the 12Vdc supply across the transformer, producing ~300Vac across the secondary winding. The output from the secondary charges the HV capacitors. When the capacitors are charged to around 300V the sidac switch trips and dumps all the charge in the capacitors across the primary of the pulse transformers. This creates a voltage of 25,000V across each secondary winding, and because the transformers are wired 'against' each other, this creates 50,000V between the two output terminals, which results in a spark, about 3 inches long on a good day.