How does the NerveGear fallback battery work? On the first episode of Sword Art Online we know about a microwaves device installed on the helmet. We learn that this device can damage to death the user's brain removing the limiter. Unplugging the device causes the battery to activate as fallback, using the remaining power on the battery to damage the brain of the user.

The main device of a today microwave oven is magnetron, I cannot find any example of a magnetron consuming less than 1kWh as now (I accept correction), emitting more than 600W in microwaves. As of current technology, can a portable battery provide enough power to burn a brain? Are there more details about this issue described later in the anime or in the novels?
Lets say the magnetron indeed has a power requirement of 1kW (I never tried, so I might be off with this value and 1kW is not enough to burn a brain. On the other hand, I guess it also depends on the duration the magnetron is turned on.)

Lets also say a mobile(-ish) battery of 50V is used (I do have to pick some value, right).

P = V * I , so it would draw 1000W / 50V = 20A.

Now, lets say a brain is fried in 1 minute (maybe this assumption is too high: if it takes too long the 'immediate dying' effect would be gone? Although some agony is a pro in the eyes of an evil mastermind)

So this battery for example (disclaimer: first one I found; I do not own stock for this company) seems to be sufficient. As it should be able to power it for about 1 hour (19.5Ah)...
It is a bit heavy with its 8.8kg, but we do probably not need power for one hours, so a smaller battery should be sufficient, weighing a lot less.



So in short the answer is (with these crude estimates and calculations): Yes it is possible to power a (mobile-ish, the magnetron you linked to did not look too mobile as well) device with our current technology.

I did not read the manga or anime, but I guess the complete system needs to be scaled down to match the description and fit in a helmet...