| Depends how the lamp arc voltage varies with arctube temperature, so wheather the lamp uses saturated or unsaturated vapor pressure of the main components dictating the arc voltage.
MV is far unsaturated vapor lamp (so the whole Hg content evaporates completely way before the arctube fully warms up, so the vapor density is then fixed), so its arc voltage virtually does not change at all.
On the other hand e.g. HPS are saturated vapor, where the amount of evaporated Na (and to a big extend Hg too, as it tends to remain with the Na) varies with the amalgam reservoir temperature, making the arc voltage higher at higher arctube temperature.
When you feed such lamp from a current source, you have a positive thermal feedback: Increased temperature means higher voltage drop, higher voltage drop with a constant current means higher power being delivered to the arc, that means the arctube will warmup even further, increasing the voltage further,... - a positive feedback loop. The only thing against is the radiation power dissipation, increasing with T^4. And this may not be enough to compensate the whole positive loop effect, yielding thermal instabilities (either the lamp "refuses" to warmup, or starts a thermal runaway, leading to lamp arc extinction aka cycling, or plain lamp destruction).
Now MV is one extreme (far unsaturated), HPS the other extreme (all components saturated), the MH are just somewhere between.
Now with an inductor ballast (virtually the exclusive magnetic ballast in the 230V world), mainly when slightly saturated, the current tends to drop when the arc voltage (so the arctube temperature) increases, so redducing the strength of the positive feedback.
The HX will then likely behave in similar manner (there the magnetic shunt does exactly the same as the ballastcore with the series inductor).
The CWA however maintains rather solid current level, so may provoke the thermal instability in lamps not designed for it.
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