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Super LHC Proposed

lpetrich

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Cern plans even larger hadron collider for physics search - BBC News

Currently called the Future Circular Collider (FCC), it will be built in CERN's Geneva site along with the Large Hadron Collider and its predecessors, it will have four times the LHC's size and accelerate particles to ten times the LHC's energy. An electron-positron version may go online in 2040 and a proton version in the 2050's.
The Future Circular Collider | CERN
Future Circular Collider Study Default
Future Circular Collider Study FCC publishes concept design for a post-LHC future circular collider at CERN

It will have a circumference of around 100 km, giving a radius of around 16 km.

It may first be used for electron-positron collisions at 90 to 365 GeV per particle at high luminosity. It will be a "Higgs factory", a maker of lots of Higgs particles.

After some years of runs, it will be turned into a proton-proton collider, much like the LHC, but going up to 100 TeV per particle. That will be good for looking for Beyond-Standard-Model particles like supersymmetric ones, particles that the LHC has yet to make in recognizable fashion.

This upgrade will thus be much like LHC itself, which replaced the previous user of its tunnels, the The Large Electron-Positron Collider | CERN. The LEP accelerated these particles up to about 110 GeV of energy, thus giving them a relativistic energy factor of over 200,000. That meant that they traveled at 10^(-11) less than the speed of light in a vacuum, or 3 mm/s less.

This new accelerator would get them to a REF or gamma factor of over 700,000, making them travel at 10^(-12) less than c, or 0.3 mm/s slower.

Turning to protons, they won't quite go that fast, but their much greater energies allow possibly making more massive particles. Protons are composite, reducing the available energy by a factor of 3 or 4. That means about 2 GeV for the LHC, and a possible 30 GeV for the FCC.
 
Accelerators | CERN A proton currently gets accelerated with this sequence of accelerators:
  • Linac 2 - E = 50 MeV
  • Proton Synchrotron Booster - four rings with r = 25 m, c = 160 m, E = 1.4 GeV
  • Proton Synchrotron - one ring with r = 72 m, c = 450 m, E = 25 GeV
  • Super Proton Synchrotron - one ring with r = 1.1 km, c = 6.9 km, E = 450 GeV
  • Large Hadron Collider - two rings with r = 4.3 km, c = 27 km, E = 6.5 TeV
E = energy, r = radius, c = circumference
Linac = linear accelerator. CERN has a second one, Linac 3, for accelerating heavy ions. It lives in the tunnel built for CERN's first one. A replacement for Linac 2, Linac 4, is to be built in its tunnel.

Work starts to upgrade Large Hadron Collider - BBC News making what's called the HL-LHC, the HL meaning high luminosity or particle flux, about 10 times previous values. This will improve its ability to detect rare events, by making them more probable.
High-Luminosity LHC | CERN
The HL-LHC Project | High Luminosity Large Hadron Collider

Why the Large Hadron Collider Is Shutting Down for Two Years -- the LHC is currently in Long Shutdown 2 (LS2), for lots of upgrades, and it will be restarted in 2021. It will take more data, then be shut down again to upgrade to full HL-LHC status.
 
An alternative to the FCC is the Compact Linear Collider or CLiC:
The Compact Linear Collider | CERN
Welcome to the Compact Linear Collider Website | clic-study.web.cern.ch
From the first link, about how the electrons and positrons will be accelerated,
The aim is to use radiofrequency (RF) structures and a two-beam concept to produce accelerating fields as high as 100 MV per metre to reach a nominal total energy of 3 TeV, keeping the size and cost of the project within reach. The CLIC test facility, CTF3, provides the electron beam for the studies.

In the two-beam acceleration concept, the high RF power needed to accelerate the main beam is extracted from a second high-intensity electron beam – the “drive beam” – that runs parallel to the main beam. This drive beam is decelerated in special power extraction structures and the generated RF power is used to accelerate the main beam.
 
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