Ulrich reported minor problems with the rf choke RFC in the above. With a little experimentation I found that the inductance of this component is not important, but that if a second Tesla coil TC is wound, this serves perfectly as the choke. This Tesla coil/choke should be say 25-40 turns of thick (0,9mm - 2,2mm) wire wound to a diameter of 25 - 35mm, the thing is completely non-critical, so long as both are the same. Apparently the self-resonance of this choke at the operating frequency performs admirably to keep the oscillations from escaping into the power supply (and no, the HT side isn't earthed to anything, I simply threw it all together breadboard fashion!) The first choke I used was 164uH and physically rather large. It can be seen lying horizontally behind the Tesla coil and valve (EL37) which are at the front of the layout. It was not resonant at the operating frequency, and though it is made of 1,6mm wire and carries only 160mA, it got warm in use! The second Tesla coil I wound, which I used in place of this choke, remains stone cold. A later photo shows this component.
At
the rear left is the HT transformer, on top of which is perched the
10H choke, which is essential when using a mercury rectifier. This
valve, type 83, is to the right of the HT transformer, centre rear.
At the right rear with its LT centre tap sticking straight up is a
homebrew filament transformer for the 83. Despite only putting out
5V at 3A, this secondary needs high voltage insulation because it
forms the positive HT terminal and can be at up to 400V. In front of
that, right midfield, is the LT heater transformer (6,3V) for the
EL37. Left midfield is the 4uF smoothing capacitor on top of which
is a very large 30k resistor. The front row shows the Tesla coil on
the left, atop which is the plasma, barely visible against a steel
band of the HT transformer (bad siting on my part for the photo.)
Near the valve base of the EL37 to the left is a parallel pair of
4,5nF 4kV ceramic capacitors. The value isn't very important, but a
high voltage rating is, as the "hot" side is connected to
the loop L, seen at the top and outside of the Tesla coil as a thick
brown wire. In front of the valve base is the 15k grid resistor
(read it right to left - brown, green, orange) and to the right of
the valve base the 0,5uF screen bypass capacitor. The white blob
apparently hovering in mid air at the left shoulder of the EL37 is
the screen resistor of 4,3k (actually a 3,3k resistor in series with
a 1k which is out of sight).
The
blue glow from the mercury vapour inside the two anodes of the 83
contrasts nicely with the bright orange filaments, though the
filaments haven't really shown up too well in this photo. The
unaided eye sees them much better.
The
plasma is now clearly visible as a bright white "flame" to
the left. To the eye it appears blue with a green tip from the
copper wire. Far right is the orange glow of the EL37 heater, and to
its left a blue light from the 83, plus an orange-red blur above
from the 83 filament. The blue fluorescence of the
EL37 glass (due to very high vacuum in the valve) is also seen,
thanks to another photo-shoot with faster film (Jessop's 200ASA). Mid-way up the coil is the bright light of a neon bulb held nearby, the gas is ionised by the rf field of the coil. 
In this photo, a small filament lamp connected across a few turns of wire is being held at the top of the Tesla coil. Rf energy from the Tesla coil is then induced in the coil across the lamp and lights it, demonstrating the presence of inductively-coupled energy. The lamp used to perform another trick, until I got it too close and cooked it . . . the gas in the lamp would light up blue and it was possible, once the filament had lit (electron emission produced thermionically helps ionise the gas filling) and the gas had ignited, to raise the lamp with its coil just above the plasma flame, rotate the plane of the coil on the lamp through 90 degrees to reduce inductive coupling to near zero, and the blue glow from the gas would remain due to capacitive coupling of rf from the Tesla coil. Unfortunately, as I said, I got a bit carried away with this neat trick and it wouldn't do it for the camera! Another shot on Jessop's 200ASA.
Here's a closeup of the plasma flame, on Jessop's ASA200, the blue glow from the 83 is visible in the right background. This has been an interesting illustration of the differing sensitivities of the eye and film to different wavelengths at low levels of illumination. The plasma flame is distinctly blue to the eye, but less so to the film, also the tip of the flame is greenish, whereas the film sees it as yellow! I've also noted that weak Tesla streamers from the induction coil setup elsewhere on these pages are very blue to the film, but purple to the eye! This coil has now been dismantled and the bits recycled for other experiments. Most of my projects tend to go that way, only a very few things end up as keepers. It's interesting to note that, despite the resonant frequency of this coil being around 29Mc/s the amount of radio interference was low - nice one for the law of conservation of energy - you can either radiate it as radio waves, or use it to ionise the air and make it hot, but not both at once.