Why are there fewer stages in the turbine than in the compressor of a turbine engine? I'm a student interested in aviation. I'd like to understand why the turbine section has fewer stages than the compressor section in a jet engine.

What would be the effects of adding stages to the turbine, or to the compressor? How is the optimal number of stages determined?
Very simply, a turbine has fewer stages than the compressor, because the flow in the turbine is going in the direction of reducing pressure - the air wants to go that way naturally. But a compressor has to make the air flow in the direction of increasing pressure. If this is done too aggressively (attempting too much pressure rise per stage), the air flow on the blade seperates, and stalls. In severe situations, the flow can completely reverse direction and exit the intake.