Assuming you know how to use the particle system to create a laser beam.
Place an empty behind the particle emitter. Select the empty and create a wind generator. Then have the Empty track the target using COntrol+T. You may have to play with the tracking axis to get it to work correctly. Again you’ll have to play with wind speed, etc.
Here is my slow demo (looks more like I’m hitting something with oozing Aquafresh toothpaste).
Format: QT/Sorenson 3.
This works for “trek” style phasers. The movie is only 15 FPS just to reduce file size and show a demo.