Tesla Coils and Fluorescent tubes I was recently at the Nikola Tesla Museum in Serbia. I found it a bit lacking on the science aspects of Mr Tesla - but it held a remarkable collection of his personal belongings (he was evidentially an exceptionally well-dressed man). 
Anyway one of their exhibits was a Tesla coil which discharged to a grounded sphere (on the ceiling). People were asked to hold fluorescent tubes which glowed. See image from the museum website. 

The explanation given at the museum was that the electrons from ionised air travelled down from the "lightning" to the tube, completing the circuit and thus the tubes light up. 
Reasons why I think the explanation may be flawed: 


*

*The mean free path of electrons is too small in air to travel to the fluorescent tubes. I haven't done the calculations - but I have a feeling of it being on the order of nm to cm - not metres as is required. 

*The "turn on" was instant when the lightning started - this suggests, for me, that something with the E field is much more likely than charged particles. 

*Electrons would ionise the air before travelling to the tubes. 

*The ions/electrons and plasma would be contained very close to the lightning (this is really a restatement of the above points). 


So, does anyone have a better explanation? 
 A: Addressing each of your remarks below

The mean free path of electrons is too small in air to travel to the
  fluorescent tubes. I haven't done the calculations - but I have a
  feeling of it being on the order of nm to cm - not metres as is
  required.

The Tesla coil is properly classified as a high frequency, air gap transformer. The secondary coil can generate over 1 Million volts, however very low, high frequency current. The reason the tubes light up is that current indeed from this high potential is flowing all around the coil, trying to make its way to ground. In the vicinity of the top load the voltage, energy is great enough to ionize the air and you see streamers. But that doesn't mean there is no electric field, current flow outside of this area. There is still enough potential to excite the zinc sulfide inside the tubes to cause them to glow.

The "turn on" was instant when the lightning started - this suggests,
  for me, that something with the E field is much more likely than
  charged particles.

Yes - electrical current travels near the speed of light.

Electrons would ionise the air before travelling to the tubes.

They do in the immediate area of the top load, but the potential field exists beyond this area.

The ions/electrons and plasma would be contained very close to the
  lightning (this is really a restatement of the above points)

Not true. Even without Tesla coils there are free electrons all around us. The Tesla coil generates more than usual in its vicinity and creates current flows through local antennas (people and tubes).
A: I built a small slayer circuit telsa coil that is powered by a 9 volt 280mAh rechargable battery. It will power a 4 foot standard flourencent tube at about 1/4 light output for maybe 30 minutes. The BD135 transistor has to be well heat sinked as it gets pretty warm. It seems to use most of the battery power. The coil used is 650 turns and the pancake coil is 5 turns. If one was to reduce the pancake coil resistance and optimize it for lighting the tube it could be pretty efficient compared to a standard ballast. I have not done any calculations, but the concept seems to be valid and should be investigated further. 
