What verb do you use to describe a very loud, unpleasant and quite long laughter? We use ржать for that in Russian.
In addition to Seraph's suggestions, I would offer "to bray with laughter" or "to have a braying laugh". ("To bray" literally refers to the йа-йа noise of a donkey.)

There's also the word "cackle", which refers to the loud, unpleasant, and feminine laughter characteristic of a "хабалка" sort of woman. So, in general: witches cackle; gossipy teenage girls sometimes cackle; men usually don't "cackle" unless they're голубые и женеподобные. (Literally, "cackle" is the sound of chickens.)

Women cackling in the onomatopoeic song "Pick-a-Little, Talk-a-Little", from 1962's The Music Man: