I'm gonna neglect the following aspects:
- aerodynamic drag - since you are in space
- cooling - I'm gonna assume ideal cooling
- heating/melting of the projectile - I have no idea how to calculate that
Take a nuclear reactor: e.g. Turkey Point U.S. with a nominal output power of 1000MW.
The kinetic energy of a moving mass is $0.5*m*v^2$
The question is, how much energy can the projectile gather with the given barrel length?
The velocity over time is $v(t)=a*t$ (with constant acceleration $a$)
If you integrate it over time, the travelled distance is $s(t) = 0.5*a*t^2$
You can only accelerate in the barrel with length $L$, so $L = 0.5*a*t^2$. $a = 2L/t^2$
Power is work (energy) over time ($P=E/t$), or force times distance ($P=F*s$): $P = 1000MW = F*L = m*a*L$. So $a = 1000MW/(m*L)$
$1000MW/(m*L) = 2L/t^2$
$t= sqrt((2L*mL)/1000MW) = sqrt((2*m*L^3)/10^9W)$
So the kinetic energy is (btw. I think this is the part, that is most interesting for you): $E = P*t = 10^9W * sqrt((2*m*L^3)/10^9W)$
And the velocity: $v= sqrt(2*E/m) = sqrt(2*(10^9W * sqrt((2*m*L^3)/10^9W))/m)$
Estimated projectile velocities with a 1000MW reactor.
You have to consider, that the damage done by the projectile is mostly dependent on the kinetic energy.
These are the ideal conditions. You would have thermal losses in the coils/conductors (you could minimize them with superconductors).
You could increase the power with very large (I mean huge) capacitors. They need to store energy, and discharge, while the projectile is accelerating. This would mean higher projectile energy, but also a recharge time for your vessels.