The issue here of course is that the light beam sweeps the sky and that alone completely sets the rules for capturing the image. A very quick shutter speed gives you a low intensity thin streak of light. A long shutter speed sees all the beams merge together as the beam sweep is faster than your shutter speed. You might already guess that on this occasion, you simply have to use the manual mode on your camera because the Auto modes simply wont know what you are trying to achieve here. And of course, with shutter speeds measured in seconds, a tripod is essential.
So, to get the beams of light in the most satisfactory aspect, trial and error revealed that a one second exposure was optimal - remember, shutter speed controls motion and here the light is moving across the sky, hence, a one second exposure allows the movement to come through giving those beautiful wide beams. Now, I am already shooting wide open (f/2.8) so my only other variable here is my ISO (and I want that to be as low as possible) and I found that ISO500 gave a satisfactory, especially as I know what I'm going to do next.
What I am going to do next is to take a 4 second exposure allowing for a much brighter lighthouse. Remember also, the camera is on a tripod so the images exactly fit on top of each other. In Photoshop then, I selected the ground and the lighthouse building from the long exposure and place it over the perfect light beams. Overall then, the final picture is balanced between the bright beams and the lighthouse itself.