[FT] Multiple Turn Weapons

I was just thinking (dangerous thing that), and was wondering about 
multi-turn weapons. By this I don't mean weapons that take more than 
one turn to arm, but weapons whose affect changes according to haw 
many turns in a row they hit (up to a certain limit).

For example: a weapon that, hitting target A on turn 1, does 1 point 
if it hits; on turn 2, if it hits the same target (A), it does 2 
points; and so on.

Any miss resets, as does switching targets.

Once the maximum damage is reached (let's say 3 for argument's sake), 
the weapon must cool for a turn.

You could use the std. Beam mechanic, but no re-rolls and all hits, 
regardless of the number on the die, only cause 1 point (or 2 for the 
2nd consecutive hit, etc.).

Comments?