Half Wave Power Control
This is similar to the DC control circuit but the thyristor turns off every half cycle because the AC voltage drops to zero.
The switch on is timed with an adjustable RC timing circuit.
If R is larger, it takes longer to charge C enough to trigger the thyristor.
If R is smaller, C charges more quickly and the thyristor is triggered almost immediately.
This is called phase control.
This method is very simple.
Better control can be achieved by generating the control pulses in other ways like
using a microcontroller to do the timing
using a 555 timer to position the trigger pulses with greater accuracy.
Full Wave Power Control
By adding four diodes as a full wave or bridge rectifier, this circuit can be converted to full wave control.
In other respects it's the same as the half wave version.