LM317 oscillating in cathode circuit

[bigwill]

Dids you use high-efficiency LED's ?
They may cause the oscillation-problem , because they have some regulator circuitry inside that make some HF-switching-noise.
LM317 should perform well without the output biassing capacitor on a reactive load. The capacitor is only nescessary with an inductive load.
biassing of the tube needs a negative voltage on the grid , in case of automatic bias that means you want a positive voltage on the cathode by a cathode resistor. So why the hell did you use a CCS ? You need a constant voltage device !

They are just normal Green LEDs. I did try the circuit without them and it exhibits the same behaviour.

 

[bigwill]

Just make your own heatsink - take two pieces of metal (preferrably black electroplated aluminium) sheet as large as you can fit inside your enclosure without actually touching any other metallic part, screw them onto the tab of LM317 (one on each side - you'll have to cut a small portion away for the front part) and bend them outwards so they form an 'X' when viewed from the top in order to improve the airflow around them.

If 4 tabs can dissipate all the heat generated, it should take much in the way of heatsink to accomplish the same.

This is a surprisingly simple idea I didn't think of!

 

[ChrisA]

This is a surprisingly simple idea I didn't think of!

I was going to suggest almost the same. Just use a short section of copper plumbing pipe about 1 inch long, slightly flatten one side and place the regulator inside then screw it to the inside of the pipe.

Another even easier heat sink is a large brass fender washer, (they even come with a hole in them pre drilled.)

 

[Merlinb]

No doubt this is going to sound stupid, but surely the reason it is oscillating is that all the CCSs are in parallel. Since each one is not identical, each needs a slightly different voltage across itself to maintain the correct current (the adj' currents won't be identical), so they are all fighting for control simultaneously.