damper winding help to maintain the magnitude phase shift (on load chages) between rotor an stator flux and kill some parasite currents produced by the leakage flux moving out the rotor winding to the rotor core.

It is definitely used in a turbo-generator

Damper windings:-

Most of the alternators have their pole-shoes slotted for receiving copper bars of a grid or damper winding (also known as squirrel- cage winding).the copper bars are short-circuited at both ends heavy copper rings. these dampers are useful in preventing the hunting9momentary speed fluctuations) in generators and needed in synchronous motors to provide the starting torque. Turbo- generators usually do not have these damper windings(except in special case to assist in synchronizing) because the solid field-poles themselves act as efficient dampers. It should be clearly understood that under normal running conditions, damper winding does not carry any current because rotor runs at synchronous speed.

The damper winding also tents to maintain balanced 3-phase voltage under unbalanced load conditions.