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Nice post Orion

A picture is worth a 1000 words....well done

You are more than welcome

But it also shows that the beta doesn't necessarily say anything about the real concentration of protons at the colissionpoint rather about the angle they collide in.
But I still belive that there is some relationship which makes beta something like a good guess for the proton-densety at the collisionpoint, but it also depends on the overall aperture of the rest of the beam. (I hope I used the right words)

Yes, if you halve beta*, you double the luminance.

Do you have the math for that?
At least it is not trivial.

Tau wrote:Yes, if you halve beta*, you double the luminance.

This is only true if you apply some more constraints, such as that the cross-section of the beam stays the same at both ends of the cavity in the middle of which is the focus point.
Otherwise I can imagine scenarios involving changes to beta* without any effect on luminance.

Indeed, I assume emittance stays the same, and the beams stay nicely focused exactly on each other. It is all in "accelerators for pedestrians", but I admit I have a hard time reading it.
The basic idea is that the particles in the beam do not all have the same sideways (transverse, they say) speed. When steering the beam, you have the choice between steering them very accurately to a point (so that the speeds differ by a lot), or a more "relaxed" steering where the speeds are more equal, but the beam is wider.
A wide beam with almost equal speeds has high beta*, where a narrow beam with lots of speeds difference (variance, they say) has a low beta*.