If you were to try and apply hard science to it, which I might add is a bit silly...
Beam cannons are most likely pools of plasma driven direct from the drive core of the fusion reactors. They pool at the surface of a beam cannon, aligned in an extremely powerful magnetic pinch, and then channeled. Vastly beyond our own technology, of course, since the magnetic fields required to contain that plasma would require complete enclosure. The trick would be to stop the particles dispersing quickly once they reach vacuum (plasma is basically a gas). You could minimize this by forcing them to relativistic speeds, done by exciting the particles and then projecting them through a sufficiently lengthy magnetic bottle ala a particle accelerator. By the time the dispersal effect has kicked in, the damage has already been done.
The charge up time would be the pooling procedure, bottling them up and getting them even more superheated and excited, essentially forming a kind of self sustaining fusion reaction, crushing the particles tighter and tighter. The unknown part would be after releasing the particles, how to direct them which is likely the trick the GTVA picked up from the Shivans - some form of superspace manipulation technology. Slasher beams would be easier to implement since you could produce a pool of particles and direct only those that had a specific stochastic direction producing a weaker, but mobile beam.
As for the actual effects, we already know GTVA reactors use gas giants for fuel, so any beams are likely to be pre or post-fusion helium/hydrogen nuclei with their attendant electrons contained in the flow. That's relatively easy to figure out the effects, since what you're basically doing is producing a massive stream of alpha and beta radiation together with constantly fusing particles. It's safe to assume that since the beam is magnificently directed, the GTVA have figured out some way of extending magnetic bottles to combat range, which would mean that the nuclear fusion process would still be ongoing midflight. The glow of the beam comes from the photonic effects due to faster particles smashing into slower particles, though strictly speaking it should be Bremmstrahlung radiation and simple photonic effects from the overwhelming heat radiating into space - incandescent like the sun. Which explains the extremely hot core of the beam, which is brilliant white, if not the varying colours on the outside - those may be due to plasma temperature but unlikely.
Then you've basically got a stream of light nuclei and electrons travelling at say 0.9c smashing into other nuclei and shields. Assuming no net slowdown of the beam and that dispersal is the only problem, the raw kinetic damage of a metric ton of particles travelling at a group velocity of 0.9c assuming I remember my relativistic physics (if I dropped the lambda you don't want to know what numbers would come up) right is tantamount to around 10 gigatons of TNT. Add on the additional heat damage caused by fusion elements and you arrive at around the right numbers as represented in the original game - surprisingly good of the devs I might add.
What you're looking at then is billions of relativistic electrons and protons and alpha particles all travelling at an average velocity of 0.9c with electrons travelling somewhat faster due to their lower mass which means massive surface ionization of all elements within beam width as well as seismic compression waves and atmospheric heating. Any fissionables would likely instantly fission under the bombardment of so many charged particles adding to the radiation damage. Mass ionization of the atmosphere would occur on deep layers depending on beam use.
There probably wouldn't be that much radioactive damage, but atmospheric heating alone would devastate the ecology of the planet, and the resulting seismic activity (likely as a result of sustained beam damage vapourizing through to the mantle) would render most cities and areas unhabitable for years. By comparison a Sathanas is capable of something like a 120 gigaton broadside.
