The battery is a standard GelCell type sealed lead acid battery. These are typically cheaper than a similarly rated Ni Cad battery. It must be a 12 volt battery (because of the 12 volt halogen bulb used) and of the size (6” x 2 1/2” x 3 3/4”) as seen in the photo. Typically rated for 6.5 to 7.2 amp hours. I found mine at a local electronics flea market for about $6 used. Typically this is the standard size used in commercial emergency lights and are replaced every year to meet fire codes. That means that in general they are unused and have been on trickle charged for a year. New they are about $18 to $25 new from industrial supply houses.
Charging the Battery
You can buy a battery charger specifically for this size battery such as the Yuasa "Smart Shot 900", model 12V900, available on the internet for about $30. This charger properly limits the charging amperage to less than 1 amp and after the battery is fully charged, puts the battery on a maintainence charge rate. A standard photovoltaic solar cell array is another way to recharge the battery. They typically put out 13 - 14 volts, no load, and a square foot or so of surface area will do nicely.