If you someway managed to straighten a circline and make it linear, would it increase its efficiency? Looks so.
And if you unwove a spiral CFL and make it linear, the efficiency rise would be even bigger.
Vice versa - bending a linear tube would make it less efficient.
Is this theory correct?

So called "hot kisses" on 2U, 3U, ... CFLs seem to make things even worse. Not only there are sharp turning points for the arc, they're also bottlenecks for it. The strange thing is that some PL lamps aren't a clean "U" shape, but there's a "hot kiss" in about 95% of tubes length. But this probably makes these lamps manufacture easier/cheaper.

This topic might also be called "why CFLs are less efficient than equivalent linear tubes and why spirals are a bit better". It must have something to do with electron trajectories and collisions...? I'd be interested to find out more on this...

I doubt there is anything bad about bent arcs. Maybe except the current density getting higher inside the kiss joints, but those areas are insignificant compared to the overall length of the arc. Actually from the arc point of view, i see reasons why CFLs would be more efficient than a "bigger" FL lamp of same wattage would be :

Electrically - Cathode loss power is V*I. V is the work function of the metal, with the emitting coating, when preheated and so on - Not much there can be changed, unless some better emitter coating is invented. I is the lamp current, lower lamp current, lower losses. So for the same overall lamp power, it is better to make high voltage, low current arc. That is exactly what most CFLs are

UV utilization - Gases have significant self absorption : UV Photon originating somewhere deep in the lamp volume may be lost while hitting another Mercury atom, before making it to the Phosphor at all. Thinner lamp is shorter path from any point inside the lamp to the Phosphor, so less losses at the UV stage

In the US they made T12 and T17 lamps with dents along the lamp, in order to make the lamp volume thinner along the center part of it - Shorter way for UV to travel to the Phosphor. Same effect happens with Sodium discharge, there it is really bad as Sodium (at low pressure) emits only one thin line, and absorbs the exact same line. The highest efficiency Low Pressure Sodium lamps were made in the form of a straight tube, either with dents as with the Fluorescents, or the entire tube was made with a * shaped cross section - To minimize the path any Amber Photon goes through the vapor. That indeed showed some big improvement over the standard U bent round tube

Actualy, the same factors would hold for a straightened out CFL as well

There are other big factors that let the CFLs down :

 - It is harder to properly coat a bent tube of complex shape with Phosphor. Spirals are the worst (2U/3U CFLs are kissed after coating i think). The lamp ends up with places where the Phosphor is too thick and obscures the light. If less Phosphor would be used, then in other spots it would be too thin. Coating the tube before bending it is not possible either, as the heat for bending the glass would burn up the Phosphor

 - Big part of the surface area of the CFL emits light that is obscured by another part of the tube, so never makes it out of the lamp

 - Big part of the surface area of the CFL emits light that is obscured by another part of the tube, so never makes it out of the lamp

That's a big flaw in CFLs.
If only they had a reflector or something like that.

There are more details, why circular or more complex shape lamps use to be less efficient:
- Straight tubes do not obstruct it's own light
- The area between the two electrodes is not obstructed by anything, so the gas mix does not have to be tweaked for better starting, so may remain better optimized for the efficacy and life
- The straight tubes allow easy application of the phosphor coat. That means it yields more uniform layer, with more room for the the auxiliary materials to not interfere with the main phosphor operation.
- Cheaper glass forming, leaves more of the budget to reach better performance elsewhere.

- The area between the two electrodes is not obstructed by anything, so the gas mix does not have to be tweaked for better starting, so may remain better optimized for the efficacy and life

Is that the reason why circline (22w, 32W and 40W) lamps still uses argon and not more modern gas mixes used in T8's?

Thanks. OK, I focused on one thing only and forget the others...

It is harder to properly coat a bent tube of complex shape with Phosphor. Spirals are the worst...

Actually, spirals are probably more efficient than 3U designs:
Osram Energy Saver Superstar Quick Light, both in WW 2700K.
3U: 23W/1400lm = 60.9 lm/W
Spiral: 21W/1400lm = 66.7 lm/W.

That's a big flaw in CFLs.
If only they had a reflector or something like that.

There are linear fluorescents that have a part (I think 1/3 of the surface) coated with an internal mirror. It reflects the light that would go to the fitting behind the tube otherwise. Might be extremely complicated to do so in case of complex shapes though.

The area between the two electrodes is not obstructed by anything, so the gas mix does not have to be tweaked for better starting, so may remain better optimized for the efficacy and life

That's not so far from my theory but I didn't know it's just a problem of starting. Wouldn't modern HF ballasts capable of starting it without that chemical tweak? I mean something like boosted starting voltage etc. ...? Isn't it also about keeping the arc during operation?

Actually, 2D and circline lamps don't self-obstruct too much light and yet they're less efficient than linear lamps.
And I forgot one important thing: Induction lamps are usually small thick circular tubes so there should be both problems with phosphor coating and a partial self-shadowing and yet their efficacies are very good.

Advantage of the spiral in your example may be coming from how the light leaves the tube near its base : In spiral lamp the coil is sorta open at the end near the ballast, so more light that was emitted into the center space of the spiral can come out. Maybe this have bigger effect than the Phosphor coating disadvantage

The starting problem can be overcome in many ways other than tweaking the gas contents - Starting strip, and changing the ballast starting behavior. This may actually have less to do with voltage alone, but with density of starting pulses - A HF or Electronically started Magnetic would have advantage over Switch start if thats the case, as the next pulse arrives before the ionization from the previous one had the time to die completely

I dont think the arc shape have effect after the lamp is allready working, but thats a guess

With Circlines maybe it is indeed the chemical tweaking at play - Circlines are used itn the US too, and there they are used on Rapid Start ballasts with very limited starting voltage on the order of 300..400V. The 2D lamp was designed with Switch Start in mind and possibly Electronically started Magnetic, so available starting impulse on the order of 1KV - Maybe they aresimply not tweaked as bad as circlines

IIRC 2D's are about as efficient as PL-L. Thats only some 10% less efficient than a T8, and that i think can be attributed to the Phosphor coating problem (PL-L being better on the Phosphor part and worse on the self obstruction part, so all in all coming out equal)