With low pressure lamps their designer have to solve a dilemma: - Make the arc current density as low as possible, because high density lower the efficiency in generating the useful radiation (660nm orange for LPS, UV for fluorescent). Therefore the tube would have to be as thick as possible. - Make the distance the generated radiation to travel through the plasma as short as possible, because the plasma is opaque to the radiation it generate (sodium to the 660nm orange, mercury to the UV). This would ask for as thin as possible tube.
So you have to make the tube both large, as well as small at the same time, quite an impossible problem...
But someone got an idea: If the tube won't be of the simple circular cross-section, but a kind of profile (C, X, *), the overall cross-section would be still large (so current density low), while the path to the wall (where the phosphor convert the UV to the visible) would be still short. And viola, you a solution for the "impossible problem" from above...
These modifications are most effective with fluorescent, as once the UV is converted, the visible could pass through the tube without any issues, even from the walls deep in the tube outer perimeter. Of course these modifications are not as efficient when there is no conversion involved, but still bring at least some extra efficacy (utilized on linear LPS)
And of course these modifications have their drawbacks: Complex shaping mean the tube become costly and fragile, so it make sense to do that only on tubes of large power, where the energy saving gain would justify that. Second the phosphor deposition become a problem: More complex shape mean worse uniformity, so the optimum thickness is not reached on larger tube size. And as the lamp technology (phosphor deposition on the circular tube wall was possible to control way better, the high current density efficacy loss was reduced by modified gas composition), the extra gain from the complex shape was nearly all lost by the far from optimal phosphor thickness, mainly when compared to lower wattage lamps. And as the cost of fluorescent control gear fell, higher number of smaller lamps was not a problem anymore (it was rather a plus, when something was about to fail - only small fraction went out), there was no interest to pay the extra cost for such complex shape tubes.
And the patterned phosphor disappeared, because the improved accuracy of the phosphor thickness (so the ability to make it way closer to the optimum) make the efficacy gain rather small, so it wasn't worth the extra cost.
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