In the left part of the picture, the fog is rather thick, as well as the right part of the picture. In the middle, there shouldn't be any fog, but at the moment we are only using the amount of light available in a certain point, and not the light absorbed in this point. This means, that the light added to a pixel in the area between the to fogs is the same as in the right most part of the left fog.
Since the extinction coefficient is very low in the middle, little light should be absorbed, and we should therefore not be able to see any light beams.
In the following picture, we multiply the light added to the pixel by the extinction coefficient in this point.
And with 50 passes of 1k beams:
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