Driving 12V halogen lamps (downlights)
For full brightness they can be driven either with (about) 12 VDC or 12 VAC RMS.

Use of half wave rectified AC will operate them at somewhat less than half power but they may flicker and will have a lower color temperature. I've never seen them operated with half wave AC. If this works for some application and meets some purpose then that's fine - but I would have expected it to be less than satisfactory. 

The above is at 50 or 60 Hz. If operated at 1/2 wave AC at switch mode power supply frequencies you would get reduced power but no flicker. Many commercial "ballasts" are very basic high frequency oscillators with a few turns driving the bulb. These are not half wave feed BUT the output usually reduces to zero at the mains zero crossings. You get full wave modulated wavetrains at 10's of kHz. The voltage of this composite waveform is adjusted to be about 12V RMS. 

Only somewhat like this - gives the general idea. Peaks at 120 Hz in 60 Hz system.
 (May improve diagram later.)



Notes:


I mentioned half wave AC as producing "somewhat less than half power" as the filament has time to cool somewhat between half cycles. A cooler filament has a noticeably higher resistance so will draw less current so will not produce half of full power in half a cycle. How much less than half depends on thermal time constants and bulb environment so ill vary 'somewhat'.
A bulb powered with half wave AC will have a "different" lifetime. Lower voltage will produce an increase in lifetime. The greater thermal cycling will perhaps shorten lifetime. The two effects will compete. I'd expect the overall lifetime to be longer.
I say "about" 12 VDC as a "12V" bulb may have been designed as a 13.6V bulb if it is for automotive purposes. Small changes in voltage make a significant difference to lifetime. More anon on this if of interest. 




Filament time constants:

Lamp filament thermal time constant (~= rate of cooling or heating) will be relevant if the filament changes temperature during off periods in a switched AC waveform or if it tracks the AC variations.

Most documents that mention filament thermal time constants simply say that they are long compared to AC mains cycle times. No references or absolute values are usually offered. This document   "Flicker Metrology" (Helsinki University of Technology, 2006) offers some insight. 


The time constants suggested are much lower than may be expected from normal comments on the subject.
Thermal time constant is approximately inversely proportional to bulb rated voltage. That is decreasing bulb rated voltage increases time constant. This is a consequence of filaments thickening with decreasing voltage and increasing current in order to maintain the same power  - eg given  230V and 120 V lamps of the same power rating, the 230V lamp will have about half the thermal time constant.
At 120V, thermal time constant ~= (0.5 x Watts) - 3  millisecond.
Applying their inverse relationship of rated voltage and time constant (possibly dangerously) gives

        Thermal time constant = Tth ~~= (0.5 x Watts -3 ) x 120/Vrated  milliseconds


It is not certain how well this works for voltages much different than 120V, but applying it to a 12V bulb anyway.


Power = 25 Watt. Rated Voltage = 12V.


Tthermal = (0.5 x 25 -3) * 120/12 = 95 mS


Similarly you'd get about 40 mS for a 10 Watt bulb and 190 mS for a 50 Watt bulb.

Using mains Voltage rated halogen bulbs the time constants would be expected to be about 10 times lower at 110 VAC and 20 times lower at 230 VAC !!!

Note that even with a time constant of 95mS, some filament cooling would be expected in the 8.3 mS off period in half wave rectified AC but it would be very small. 

For interest, this useful application note from Micrel Driving halogen lamps gives information on both driving and flashing aspects and discusses longevity factors caused by filament cooling during flashing. Their notes to figure 1 re inrush current times implies a heating time constant of well under 10 mA. This will be much shorter than the turnoff time constant as turn on is affected by applied electrical energy while turn off relates only to thermal energy stored in the filament.