What is luminosity and how does it affect particle collisions?

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Discussion Overview

The discussion centers on the concept of luminosity in particle accelerators and its role in facilitating particle collisions, particularly focusing on how protons are made to collide despite their mutual repulsion and small size. The scope includes theoretical aspects of particle physics and practical considerations in accelerator design.

Discussion Character

  • Technical explanation
  • Conceptual clarification
  • Debate/contested

Main Points Raised

  • One participant questions how protons can be made to collide given their small size and positive charge, which leads to repulsion.
  • Another participant suggests that collisions are based on a finite probability and that increasing this probability is a key design concern for colliders.
  • A different viewpoint mentions that colliders contain many photons in each bunch, with most missing their targets, which is beneficial for operational efficiency.
  • One participant introduces the concept of luminosity, defining it as the number of particles per unit area per unit time multiplied by the opacity of the target, and notes its importance in estimating collision probabilities.
  • There is a historical reference to the Tevatron's Run II, where insufficient luminosity hindered the detection of the Higgs boson, which has since been addressed with improved techniques.

Areas of Agreement / Disagreement

Participants express varying perspectives on the mechanisms of particle collisions and the role of luminosity, indicating that multiple competing views remain without a clear consensus on the best explanation.

Contextual Notes

The discussion does not resolve the complexities of how luminosity is calculated or its implications for different experimental setups, leaving some assumptions and definitions open to interpretation.

nesp
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In a particle accelerator where, say, protons are accelerated in opposite directions and made to collide, how are the particles brought close enough to actually collide? Protons are extremely small, and their mutual positive charges repel. How does the collider manage to target protons so precisely that they collide?
 
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They don't. Rather they rely on the fact that there is a finite probability that a collision will take place -- think of beam density as an unnormalized probability distribution. I'm far from expert in this topic, but I suspect making the probability of collisions as high as is practically possible is a major design concern.
Regards,
Reilly Atkinson
 
Simply put, they have lot and lots of photons in each bunch. Most of them miss (which is actually good because if they all hit it would take a while to clean up the mess).
 
There is something in beam physics called the "luminosity". It is roughly defined as the number of particles per unit area per unit time times the opacity of the target or colliding particle, usually expressed in either the cgs units cm-2 s-1 or b-1 s-1. The integrated luminosity is the integral of the luminosity with respect to time. What this number tells you is roughly the probability of collision between the particle.

This was the main problem of Run II of the Tevatron a while ago - they didn't have the expected luminosity that was needed if they were to have any chance of detecting a Higgs boson. That problem right now appears to have been solved with the help of a better electron cooling technique on the proton beams.

Zz.
 

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