At my community college, which may be the best for welding in the country, we use a drill and a "for tungsten only" bench grinder to bring our tungsten to a point.
By the way, there is some good information on the Miller website relating to length of the taper, whether to flatten the tip, and whether to arc to copper first (to form a ball) depending on the kind of material you are welding. There is also a good explanation of pure, thoriated, and ceriated tungsten.
Also I just noticed today that 5356 filler rod balls up pure tungsten much faster than 4043, and there is less silicon in 5356, so the bead is less "shiny."
Learning welding is fun. Who knows, maybe I'll become a welder...
Return to tungsten sharpeners.