This is almost exactly what the "Tube" particle render type is for.

To set the Tube (s/w) render type:

1. Select the particle object.
2. In the Attribute Editor, set Particle Render Type to Tube.
3. To add default Particle Render Type attributes that let
you tune the appearance, click the Add Attributes For
Current Render Type button.
4. Adjust the head and tail sliders.
5. Apply a particleCloud shader to it with a little bit of glow, or add glow to them n post

To get your particle lasers to start and stop, simply key the rate.

I know this is not very detailed, but try those few things first, and remember it is trial and error, so keep trying