A $50$ MVA, $10$ kV, $50$ Hz, star-connected, unloaded three-phase alternator has a synchronous reactance of $1$ p.u. and a sub-transient reactance of $0.2$ p.u. If a $3$-phase short circuit occurs close to the generator terminals, the ratio of initial and final values of the sinusoidal component of the short circuit current is ________.