Still don't know the power input, I can only guess. My ballpark guess is 5kW.
Given that one of the only claims in the video posting is that it's running off a different power source (capacitors), of what value is your guess? Capacitors are typically used to deliver short bursts of very high power levels.
Yes it is running at the start of the video ; the liquid gallium is being pumped. But there is no hydrogen. Only when the hydrogen is added does the reaction proceed and the temperature start to rise.
At what time mark in the video is the hydrogen added? What in the video (or audio) indicates the addition of the hydrogen?
Or is that another of your guesses?
A key to understanding how we can know it starts near room temperature is to see how quickly the shade of red changes. One can tell the temperature by the shade of red. 500C is a dark dull red. 800 is a bright glowing red.
See
https://commons.wikimedia.org/wiki/...e_colors_(temperature_range_550_-_1300_C).svg
The video shows the top of the sphere going from about 500C to 800C in just 6 seconds or so. A temperature rise from 20C to 500C would take about 6*(500-20)/(800-500) =~ 10 seconds, which is roughly the time it takes to achieve a dull dark red at 500C once the hydrogen is turned on.
The dull dark red of 500C would not be visible in lighted conditions. So it's starting at higher than 500C. Your 800C estimate based on the shades of red viewed in a browser is equally questionable. Also, we don't know how hot the interior surface of the sphere is at the start (or at any other time). We could be seeing mostly the passive conduction of heat from the interior to the exterior surface during those 6 seconds, which wouldn't necessarily require
any power (input or generated) at all during those 6 seconds.
If only there were devices BLP could use to actually measure and display the power inputs, temperatures, mass flows and other relevant parameters of the run. Then you wouldn't have to guess.
Oh, well. As the old saying goes, if wishes were horses, we'd all have to spend a lot of time shoveling wish manure.
Capacitors can do low voltage high current. See for instance
https://www.maxwell.com/products/ultracapacitors/cells
Of course they can. But why are they being used in this setup, instead of whatever power supply BLP has been using for its arcs in all previous "tests"?
Could it be because they needed a higher power level for their "ignition" system? If so, congratulations, they've shown that a lot of power can make something heat up fast. If they had a time machine, maybe they could amaze Aristotle with that finding. But probably not.