Put an omni light at the beam source (turn shadow casting off...the MAX renderer hates shadows!)
Go to the render dropdown menu, go to effects.
Add a new lens effects and load the "sun" preset.
Delete the outer glow and tweak the inner glow to about 10 units in size, also put the "use source colour" up to 100. make this one green...or whatever the beam colour is.
Now add in a NEW lens effects glow, set the size to 5 and put "use source colour" to 0. Make this glow white.
Now go back to your scene and tweak the colour of the beam source omni light to be green (for example), but drag the hue slider so its got some white in there (should be a slightly washed out)
With any luck, you'll get a great beam blob. Use the same technique with a cylinder for the beam itself.
This way you can also animate a convincing "warmup"
