BVH, the ballast doesn't control voltage, it's determined by the amount of and excitation of the lamp gas (Xenon in this case) between the electrodes. Voltage increases as the gas vapor heats up.
I'm confused about this configuration. I wouldn't think a 600W Xenon ballast would fit inside that housing because the current regulator circuit would be too large. Maybe just the high voltage ignition components are in the housing so as to not have to run potentially unsafe thick cables and connections. In the early stages of planning for my light I considered such a configuration to safely reduce the hand-held weight, but since Mercury-based lights operate at much lower current than Xenon and thus require a much smaller and lighter current regulator circuit, it didn't make sense to separate the circuit from the housing in my case.
Fortunately, there is a plus side to coping with the mass of the high current circuit for Xenon lamps over Mercury; the higher current better concentrates the light to a smaller point between the electrodes.