Luminosity

The luminosity is a term from the accelerator or the high-energy physics ; it describes the number of particle encounters per time and area. This, in addition to specifying the collision energy, indicates the performance of a particle accelerator . ${\displaystyle L}$

application

With the help of the luminosity, the expected event rate or the differential cross section of an experiment on a ring accelerator with two opposing particle beams can be determined: ${\displaystyle {\dot {N}}}$ ${\displaystyle {\frac {d\sigma _{\mathrm {p} }}{d\Omega }}}$

${\displaystyle {\begin{aligned}{\dot {N}}&=\sigma _{\mathrm {p} }\cdot L\\\Leftrightarrow {\frac {1}{L}}{\frac {dN}{dt}}&=\sigma _{\mathrm {p} }\\\Rightarrow {\frac {1}{L}}{\frac {d^{2}N}{d\Omega \cdot dt}}&={\frac {d\sigma _{\mathrm {p} }}{d\Omega }}\end{aligned}}}$

The event rate is the number of expected events per unit of time in a detector that is installed in the accelerator at a point of intersection of the two particle beams. ${\displaystyle {\dot {N}}}$

definition

The luminosity of a storage ring is derived from the numbers and of the particles in the clashing packets (engl bunches.) And the number of bunches, with the repetition frequency are brought into collision; the particle bunches have the cross-sectional area : ${\displaystyle N_{1}}$ ${\displaystyle N_{2}}$ ${\displaystyle n}$ ${\displaystyle f}$ ${\displaystyle A}$

${\displaystyle L={\frac {n\cdot N_{1}\cdot N_{2}\cdot f}{A}}.}$

The luminosity has the same unit as the particle flux density , namely cm ⁻² s ⁻¹ . As a rule, rays do not have a uniform particle density. If the particle density follows a Gaussian distribution with the latitudes and , the result is a luminosity of ${\displaystyle \sigma _{x}}$ ${\displaystyle \sigma _{y}}$

${\displaystyle L={\frac {n\cdot N_{1}\cdot N_{2}\cdot f}{4\pi \sigma _{x}\sigma _{y}}}.}$

If you want to examine a process as precisely as possible, i. H. with high statistical significance , a high luminosity is necessary. This depends on the structure of the accelerator and the quality of the particle beams in the accelerator.

Records

A luminosity of 1.75 · 10 ³⁴  cm ⁻² s ^{−1 was} achieved at the LHC accelerator , while luminosities of approx. 4 · 10 ³²  cm ⁻² s ⁻¹ were finally achieved at the Tevatron . The current world record is held by the electron / positron accelerator KEKB in Japan and is 2.11 · 10 ³⁴  cm ⁻² s ⁻¹ (June 7, 2009). However, due to their different designs and types of accelerated particles, the different accelerators are difficult to compare: The LHC holds the world record for proton accelerators.

Web links

• “What actually is luminosity?” At www.weltmaschine.de

Individual evidence

1. ↑ Bogdan Povh , Klaus Rith, Christoph Scholz, Frank Zetsche: Particles and nuclei ("Particles and nuclei"). 5th edition Springer, Berlin 2006, ISBN 978-3-540-36683-6
2. ↑ DA Edwards and MJ Syphers: ACCELERATOR PHYSICS OF COLLIDERS. Particle Data Group, July 2011, accessed February 13, 2017 . 
3. ↑ Performance plots , accessed October 10, 2017
4. ↑ fnal.gov: Tevatron Luminosity ( Memento of the original from March 23, 2010 in the Internet Archive ) Info: The archive link was inserted automatically and has not yet been checked. Please check the original and archive link according to the instructions and then remove this notice. 
5. ^ Tetsuo Abe et al .: Achievements of KEKB. In: Prog. Theor. Exp. Phys. 03A001, 2013, pp. 1–18, doi : 10.1093 / ptep / pts102 .