Temperature inside LHC....?

Could someone provide an ainformation what is the temperature inside the Large Hadron Collider (or similar systems) where the colision of particles happens? THANK YOU!!!!

It's a vacuum!

https://home.cern/science/engineering/vacuum-empty-interstellar-space

OK, let's paraphrase my lack of understanding...
It is written that early universe was very violent place, with high presure, high temperature, high density and high radiation. In the same time, I have read somewhere that LHC can "simulate the conditions" of early universe. So, if the reactions (collisions) in LHC happen in vacuum, how it can "simulate the coditions" of early universe? :-(

Sasho Andonov said:

OK, let's paraphrase my lack of understanding...
It is written that early universe was very violent place, with high presure, high temperature, high density and high radiation. In the same time, I have read somewhere that LHC can "simulate the conditions" of early universe. So, if the reactions (collisions) in LHC happen in vacuum, how it can "simulate the coditions" of early universe? :-(

Temperature is a collective phenomenon. The point is not to recreate the same temperature, but to have collisional energies that are comparable to what you would get were the particles in an environment at that temperature.

DrClaude said:

Temperature is a collective phenomenon. The point is not to recreate the same temperature, but to have collisional energies that are comparable to what you would get were the particles in an environment at that temperature.

I understand, but the will this temperature (energy) around affect the results of collisions? Under "results of collision", I mean new particles created by collisions.

To repeat DrClaude in different words, temperature is a proxy for the distribution of energy for the constituents of a system. It isn't some soup everything is swimming through. If we are speaking at the level of particle collisions then we don't need to talk about temperature. Interactions between particles affect particle collisions.

Sasho Andonov said:

TL;DR Summary: Large Hadron Colider temperature...

LHC produces hottest temperatures ever recorded on Earth
15 August 2012
The Large Hadron Collider (LHC) at CERN created a quark–gluon plasma whose temperature exceeded 5 gigakelvin (5 trillion °C). The LHC is primarily known for its proton collisions, which revealed the existence of a particle very like the Higgs boson. However, researchers there also use the LHC to collide lead ions. The resulting plasma, made of extremely high energy quarks and gluons, was 40% hotter than the previous record temperature, established by the Relativistic Heavy Ion Collider (RHIC) at Brookhaven National Laboratory in New York. Both the LHC and RHIC are re-creating conditions that occurred just microseconds after the Big Bang. One of the goals of the research is to determine at what energy the quark–gluon plasma settles into normal matter.
(https://pubs.aip.org/physicstoday/online/16886/)

renormalize said:

researchers there also use the LHC to collide lead ions. The resulting plasma, made of extremely high energy quarks and gluons, was 40% hotter than the previous record temperature

Since the OP will probably ask, do we know what the volume of that plasma was? It must have been confined to a pretty small region where the two beams were colliding... (compared to the total volume of the vacuum chamber around the collision volume)

We are falling into the trap of trying to stitch together popularizations and get something sensible out.

• The beampipe is at vacuum. It doesn't have a temperature.
• The pipe itself is at 4K (to keep the helium liquid). In principle, some day what little gas is in the pipe will reach this temperature, but it will take a long, long, long time.
• Ion collisions are not really in thermal equilibrium, so they don't have a temperature either. You can get something with dimensions of temperature by taking E/k (what the popularizations do) but that doesn't make it a temperature.

You can get a hand-wavy idea why this will be so when you consider the minimum time for temperature at one part of the plasma to equilibrate with the temperature at another part: a few times x/c where x is the distance. However, the collision is happening on a time scale like x/c too.

berkeman said:

Since the OP will probably ask, do we know what the volume of that plasma was? It must have been confined to a pretty small region where the two beams were colliding... (compared to the total volume of the vacuum chamber around the collision volume)

Well, here is what I would say (as a non-expert), based on the conclusions on pg. 47 of the massive (327 pages!) recent report from the ALICE collaboration at the Large Hadron Collider (https://arxiv.org/abs/2211.04384):

Head-on collisions of heavy ions in the LHC create a very short-lived quark-gluon plasma (QGP) fireball that is believed to mimic the state of the universe in the first few microseconds after the Big Bang. For the particular case of lead-lead collisions at a total center-of-mass energy ##2.76\text{ TeV}##, the fireball has an initial energy density of ##\sim12.3 \text{ GeV/fm}^{3}## and an effective temperature of ##304\pm41\text{ MeV}##, or ##\left(3.53\pm0.476\right)\times10^{12}\text{ °K}##. As the QGP fireball expands, essentially at the speed of light, its temperature rapidly drops until the fireball reaches a size on the order of ##10-13\text{ fm}##. This is the point of so-called "freeze-out", where all the quarks and gluons have recombined into hadrons (pions, protons, etc.). These hadrons are ultimately detected by the ALICE instruments monitoring the target region.

Perhaps @Vanadium 50 can weigh in?

berkeman said:

Since the OP will probably ask, do we know what the volume of that plasma was? It must have been confined to a pretty small region where the two beams were colliding... (compared to the total volume of the vacuum chamber around the collision volume)

No, effectively the volume of the nuclei colliding.
You start off with two nuclei meeting each other - if they are stable isotopes of lead then you have initially 408 to 416 nucleons in the volume of two nuclei, no exotic quarks or mesons, and the nucleons all have kinetic energy of about 7 GeV in one or other direction.
How does the thermalization from that state proceed?
How big nuclei can be thermalized? How big must a nucleus be to form an opaque target to an incoming nucleon, or nucleus?

Vanadium 50 said:

Ion collisions are not really in thermal equilibrium, so they don't have a temperature either. You can get something with dimensions of temperature by taking E/k (what the popularizations do) but that doesn't make it a temperature.

Getting something with the dimensions of temperature isn't insensible or undesirable.

People who aren't particle physicists have no frame of reference to understand electron-volt units. You may as well be quoting a highway speed limit in units of cubits per lunar cycle. You have said words but you haven't communicated meaning. But almost everyone has a frame of reference to understand temperature units.

Also, words can have more than one meaning even if the meanings have subtle differences. There is no rule that says that the word "temperature" can't sometimes mean "thermodynamic statistical mechanical temperature", and at other times mean "a quantity that can be expressed in units that have the dimension of temperature" (which is a widely used sense of the word in published articles and books about physics and cosmology), as context demands.

In the context of explaining how much energy is involved in a collision of particles at the LHC to someone with no background in particle physics notation and units, using the word temperature to mean "a quantity that can be expressed in units that have the dimension of temperature" is almost certain to improve rather than muddy understanding. And, people who are "in the know" and familiar with particle physics are unlikely to be misled by that terminology.

Similarly, while there are circumstances when it is important to distinguish between "mass" which is often measured in kilograms, and "weight" which is often measured in pounds, there are also lots of every day circumstances where making that distinction is unimportant, and no harm is done by uncritically converting kilograms to pounds without explaining that one is a unit of mass while the other is a unit of weight.

berkeman said:

Since the OP will probably ask, do we know what the volume of that plasma was? It must have been confined to a pretty small region where the two beams were colliding... (compared to the total volume of the vacuum chamber around the collision volume)

Depending on the beam energy as well as on the centrality class it's at the order of 1000-2000##\text{fm}^3##, as inferred from the statistical hadronization model, which works amazingly way to determine the particle abundancies. It's the volume at the time of thermal freeze-out, i.e., after some considerable expansion of the fireball. See, e.g.,

https://arxiv.org/abs/0812.1186