Satsuma is also the name of a variety of Japanese sweet potato, satsuma-imo (薩摩芋). It is long, skinny, and has slightly pointed ends, with purple skin and yellow-orange flesh.
It is very popular in autumn, although it is thought to be fattening. (Really, it is no more fattening than, say, white rice.) A rarity in Japanese food, it is also a good source of fibre. Most of the fibre is found within 3mm of the skin, so it is best eaten unpeeled. The skin and outer flesh also contain the digestive enzyme yarapin. As a result, including this potato in your Japanese diet can greatly help to prevent constipation.
It is commonly roasted whole or served as tempura. You can also find it in the form of sweet potato chips, or some breakfast cereals such as Calbee's Osatsu.
It's also not uncommon to see the roasted satsuma-imo being sold by street vendors in cities. You can locate these vendors by following the wail of their continuous steam whistle. The unmatched heat-retention properties of this treat will keep your hands warm during those long autumn evening walks. Once cooked, it will easily break in half to share with your friends. Accordingly, satsuma-imo is also an autumn kigo in haiku.
Source: My girlfriend. (She's a nutritionist.)