Thanks. But I must say that many of the properties you've mentioned (such as impurities, mixture ratio, effective refractive index, pressure, wavelength, etc) are already accounted for in γ(ν). Of course my calculation is not accurate, I was looking for a rough idea as to how small these things can be made. 
Also, widening the bore doesn't necessarily make it multimode. In fact shortening the tube length (L) is more likely to make the laser Single-mode, because you can increase the mode spacing ω = πc/L until only one mode has sufficient gain to oscillate.
Also, widening the bore doesn't necessarily make it multimode. In fact shortening the tube length (L) is more likely to make the laser Single-mode, because you can increase the mode spacing ω = πc/L until only one mode has sufficient gain to oscillate.
