This phenomenon is a high voltage electrical breakdown in air known as corona discharge. At some critical voltage, the discharge begins and cretes streamers in air or between two electrodes. At high frequencies (above ~10 MHz) the ions get trapped near the electrode tip and promote further discharge, so the streamers tend to appear as a cohesive unit and look much like a candle flame.

By modulating the size of the flame (via power supply voltage), one can create audible sound waves of high quality.

Here's the whole setup (with Helium gas being blown on the flame). The big white bar is
actually a fluorescent tube that lights up due to the high electric fields in the area.

Here's what happens when you put it in a glass tube that still has some residue in it.

This is Helium gas. Even though the gas is coming out of the tube, the flame is sucked
into the tube because it is easier to ionize than air (and more linear since it's monoatomic).

This is how you bend the flame!

This is a nice large freestanding flame of about 3cm. Bigger than any I've made before.

This is a "pulled" corona of about 4cm in length! The screwdriver tip gets extremely hot.

Here's the circuit that caused it all!