Class E: External Pulse Source for Commutation
1) The transformer is manufactured with sufficient iron and air space so as not to saturate ever. It is effective at holding the load current with a voltage that is small weighed against the supply voltage.
2) When SCR1 is triggered, current flows through force and pulse transformer.
3) To turn SCR1 off a pulse that is great added to the cathode associated with SCR from an pulse that is external through the pulse transformer.
4) The capacitor C is merely charged to about 1 volt and for the amount of this turn-off pulse it could be considered to have zero impedance.
5) Therefore the pulse through the transformer reverses the voltage throughout the SCR, and yes it supplies the reverse recovery current and holds the voltage negative for the turn-off time that's required.