I don't think a tesla is what you want. A flyback transformer is suitable for this kind of experiment, but obviously take suitable safety precautions! Only run if from a battery, using a simple transistor oscillator to generate the AC. Actually, the stun gun project posted on this site might work :?: , mabye would need a bigger stepup ratio for 2cm arc though.
ALL transformers need AC to work, but you sometimes switch a DC supply to create the AC.
A flyback transformer is the transformer inside a TV that generates the EHT for the tube, usually around 25Kv in a colour TV. It's often called the LOPTX (Line Output Transformer).
It's called a 'flyback' transformer because they work by switching the DC supply through them ON and OFF, as it's switched OFF you get a large 'flyback' pulse, this is what creates the high voltages - in the same basic way as a relay coil does. The LOPTX though is tuned (by capacitors), and this makes it work even better.
i built a telsa coil in eletronics in high school it took 4 hours to wind the coil on a lathe could be done with a drill an some help used a 1ft peice of glass with to steel plates on each side for a cap. an a 7k transformer from a neon sign to fire it. it would light a florence tube at 20' if you stated it off next to the coil. man it was something to see though amprereage was low.
Yeah, an actual tesla coil is a more interesting project, and so long as you insulate the parts that are capable of supplying dengerous currents (ie the primary of neon sign transformer), then it is fairly safe.