It's a Gauss Weapon.
The difference between TL-10 and TL-12 is TL-12 is about 0.625 shorter for the same acceleration (based on the table provided).
And our normal CPR pistol (Say an M-9) has a 4.9" barrel (12.5 cm) to get 381 m/s at TL-8 (494 Joules). Weights about 7.5 grams.
TNE suggests the minimum m/s for a Gauss weapon is 1500 m/s and some head up to 5000m/s and TL-10 is the least.
If we assumed you could build a Gauss weapon at 400 m/s at TL-8, I'd extrapolate the table value to about 2.3.
So 400 m/s at TL-8:
Lb(cm) = (400/100) * (2.3) = 9.2 cm (= 3.6").
For a 4mm Gauss projectile, the projectile has has a diameter of 20mm.
Wt = 0.02 * pi * radius^3 (radius in mm)
= 0.02 * 3.1415 * 8
= 0.5 grams
Muzzle Energy in KiloJoules = 0.5 * (Wt * Vel^2) / 1000
Muzzle Energy = 0.5 * (0.5 * 400^2) / 1000 = 400/1000 = 0.4 KJ = 400 Joules
So the lighter round seems to liberate about 80% of the damage doing of the 9mm with a 3.6" barrel. Maybe with a 5" barrel, it could have about the same results.
I didn't write the tables. I know the one original one I quoted was broken (because the way they wrote the barrel length, it got longer as you got higher tech which is the opposite of what they say should happen) but otherwise, I have no idea where they pulled most of the equations from.
I suppose if I still had my copy of Guns! Guns! Guns!, I could design a Gauss PDS or a Gauss Railgun for a ship if I had the MT conversion notes...
Anyway, they use one set of equations for Gauss Small Arms, available TL-10, sizes up to 2 cm, then a different set starting maybe as low as TL-8 for Mass Drivers down to 2 cm. I imagine a 2 cm design in each system will not line up.... and no length is involved for a Gauss Cannon - but there is some length calculations about the Bay you might put it in and the tunnel it is installed in....
TomB