Flashing a fluorescent light bulb with high voltage My son and I built a Wimshurst machine (our second try) over the last couple of weekends.  It works -- not terribly well, as it only makes 2cm sparks with 20 cm disks (something like 60 kVolt when it should be capable of 5 cm or over 100 kVolt), but we were happy to get it going at all since our first machine failed completely.
With a source of high voltage to play with, we've done a few of the simpler electrostatic experiments.  Paper strips that stand up when charged, electroscopes, etc.  One of the things we did was to hold a fluorescent light bulb close to one of the discharge terminals on the machine.  Since a fluorescent bulb will light up if you rub it on wool to generate static electricity, I figured it would light up while the disks were turning.
Well, sort of.  It flashes when a spark jumps the spark gap on the machine -- that is not a spark from the machine to the bulb, but just a normal spark between the terminals on the machine itself.  The bulb will flash when held anywhere close to the machine -- say, within 1 meter.  It doesn't light up continuously as I expected it to.  If I open the spark gap far enough to prevent sparks all together, then the bulb doesn't light at all.
Why does the bulb flash when the machine sparks?
Why doesn't the bulb light up continuously when the machine is running?
Why does the bulb flash even though there's no contact with the discharge terminals?

Update:
I've investigated the suggestions from 
WetSavannaAnimal aka Rod Vance as well as I could.  I couldn't put the generator in a screen cage - it simply isn't practical to build a screen cage large enough and solid enough and still be able to crank the machine through it.
Since the heart of WetSavannaAnimal aka Rod Vance answer was that the flashing was caused by x-rays, I tried to prove that it really is from x-rays.  X-rays should cause other fluorescent stuff to flash as well, or so I would think.  I dug up some of the glow in the dark stars that used to be on the walls in the kids room.  Those contain either zinc sulfide or strontium aluminate (both types can glow the same faded green, so I can't tell which I've got,) and should also glow in the presence of x-rays.  No matter how close they were to the spark, they would not flash or even glow brighter.
I then got hold of another fluorescent tube.  This is a straight tube about 15cm long and less than 1cm in diameter.  I hung this tube on some strings above the work bench, and cranked the generator.  This tube flashes as well, but with it held stationary, I could move the machine and the spark terminals and see what effect various orientations and distances had.
It comes down to the distance from the discharge terminal of the machine to the contact on the end of the tube.  If I keep the tube the same distance away from the terminal but arrange it so that the contact on the tube is further away, then it doesn't flash as brightly.  It doesn't matter whether the terminal (a solid metal ball) is between the spark and the tube.  Only the distance to the contact matters.
It seems to be an electrical effect.  It also happens if I charge up the machine and tough the discharge terminal with my finger - crank the machine until it is just short of making a spark, touch the terminal with a finger.  A spark jumps from the terminal to my finger, and the fluorescent tube flashes.
I am guessing there is some kind of capacitive coupling between the generator and the tube.  Any suggestions on how to verify that?
 A: Fluorescent tubes normally light when a electron, produced by thermionic emission at a filament, inelastically collides with a mercury atom and raises the latter to a metastable state, which decays and emits UV light. The fluorescent coating on the lamp then absorbs this UV and fluoresces.
In very high electric fields, the filler gas in the tube can become ionised without heating from the filament and the electric field accelerates the electrons freed by this process. Again, they will crash into the mercury atoms, thus begetting fluorescence as described above.
I am guessing what is happenning in your situation is that the DC electric field around the Wimshurst machine is not enough for the effect in the last paragraph, but that one or both of the following is happenning when the spark happens:


*

*An extremely swiftly changing current in the spark produces an extremely swiftly changing magnetic field, which through Faraday's law begets high electic fields and launches a pulse of relatively intense EM radiation: it is the electric field of this propagating radiation that may be ionising the tube's gas and giving rise to electron - mercury atom collisions;

*The spark comprises high energy ions and electrons, accelerated to 60keV, which then crash into the positive electrode, giving rise to ionising bremstrahlung (soft X-rays) of enough intensity to ionise and accelerate the tube gas and cause collisions. 
One could differentiate between the two by seeing whether a fine copper wire mesh around the Wimshurst machine will stop the tube fluorescing: such a fine wire mesh will significantly absorb the pulse produced in 1. but will not absorb X-rays significantly.
Another test to do to check that could falsify or confirm either of the above hypotheses is to check which orientations the fluorescent tube lights must have and also where it is relative to the spark gap for it to light. Any X-ray bremstrahlung will be emitted roughly normal to the spark's flow direction from the anode. Likewise, the spark with its two electrodes will behave as a capacitively loaded short dipole antenna. Both of these statements mean that:


*

*There is very little field along the line of the spark at any appreciable distance from the spark. Therefore, if you align the fluorescent tube with the spark's flow (i.e. lie it along the axis joining the centres of the two electrodes) (i.e. you align it along the $\hat{Z}$ vector and put $\theta=0$ in the discussions below), you should be able to bring its end quite near to the spark without lighting the tube;

*On the other hand, if you keep the tube in this orientation (aligned along $\hat{Z}$), but bring it alongside the spark (put $\theta = \pi/2$), you should see the tube lighting at even a considerable distance from the spark;
The electric field for the dipole is as follows. If $\hat{Z}$ is a unit vector aligned with the spark's current flow, then we have:
$$E(r,\,\theta,\,t) \approx \frac{\mu_0\,L}{4\,\pi}\, \frac{\left[\frac{{\rm d}}{{\rm d}\,t}I(t)\right]\,\sin\theta}{r}\,\hat{Z}$$
where $\left[I(t)\right]$ is the retarded spark current and $r$ the distance from the midpoint between the electrodes and $L$ the length of the spark. Because there is a time derivative of the current in this expression, the electric field can be very high. If we assume the capacitance of the two electrodes is $10{\rm pF}$, then they build up a charge of $6\times 10^{-6}{\rm C}$ when the spark begins. If we assume a discharge time of one nanosecond, then we have a peak current of about $6000A$, If we assume the establishment of this current takes a nanosecond, then $\frac{{\rm d}}{{\rm d}\,t}I(t)\approx 6\times 10^{12}{\rm A\,s^{-1}}$ and the above electric field expression yields a peak field of about $12000{\rm V\,m^{-1}}$. This would probably not be enough to ionise the gas in the fluorescent tube, and so I think the soft X-ray explanation is the likelier.
