high rpm (10k-19k) low hp ac motor. very loud They have to have tons of air moving by them and they're duty cycle is still low.
Most are fractional horsepower electric motors.
In household vacuum cleaners, most of them are universal, series wound brush motors. Brush less vacuum motors are available, but are generally too expensive for consumer products. Some large commercial central vacuums will use induction motors, but they need special blowers because of the lower RPM.