Calculating Centre of Mass Energy in Fixed Target Interactions with the LHC

In summary, the proposed maximum colliding beam energy in the Large Hadron Collider is 7TeV per beam. To produce the same center of mass energy in a 'fixed target' interaction, the beam energy would have to be \frac{2E^{2}_{c}}{M_{p}}, where mp is the proton mass and it is assumed that the beam energy is much greater than MpC2. The key concept to remember is that E2-c2p2 is a scalar and you need to work in both the center of mass frame and the frame where one beam is at rest. By equating the invariant rest energy for each single beam and for the whole system in each frame, the solution can be found.
  • #1
leoflindall
41
0

Homework Statement



The proposed maximum colliding beam energy, Ec, in the Large Hadron Collider is 7TeV per beam (proton-proton collisions). By a Lorenz transformation, show clearly that to produce the same centre of mass energy in a 'fixed target' interaction, the beam energy woulr have to be [tex]\frac{2E^{2}_{c}}{M_{p}}[/tex], where mp is the proton mass and it is assumed that the beam energy is very much greater then MpC2.

Homework Equations



E=mc2

E=pc

E2=p2c2 + (mc2)2



The Attempt at a Solution




I don't think this is particularly hard but I can't see how to approach this problem. I though maybe take the total relativistic energy to be equal to the kinetic energy + the rest energy, and then rearrange for the required equation but I can't get it to work for me.

I would appreciate if anyone could tell em how to approach this problem?

Many Thanks

Leo
 
Physics news on Phys.org
  • #2


The key thing to remember is that for any system with total energy E and momentum p, the quantity E2-c2p2 is a scalar (frame independent): the squared rest energy.

You need to work in two frames: the centre of mass frame, and the frame in which one beam is at rest. Equate the invariant rest energy for each single beam and for the whole system in each frame.
 
  • #3


Cheers for the help! Worked it out now!

Many thanks

Leo
 

Related to Calculating Centre of Mass Energy in Fixed Target Interactions with the LHC

1. What is the LHC and how does it calculate center of mass energy in fixed target interactions?

The LHC, or Large Hadron Collider, is a particle accelerator located at CERN in Geneva, Switzerland. It is used to accelerate particles to high energies and then collide them to study the fundamental nature of matter. The center of mass energy is calculated by measuring the energy of the colliding particles and using the equation E=mc², where E is the energy, m is the mass, and c is the speed of light.

2. Why is calculating center of mass energy important in fixed target interactions?

The center of mass energy is important because it determines the maximum energy available for the creation of new particles in the collision. This allows scientists to study the properties of these particles and potentially discover new ones, which can provide valuable insights into the fundamental laws of physics.

3. How is the center of mass energy calculated in fixed target interactions with the LHC?

The center of mass energy is calculated by measuring the energy of the incoming particles, which are typically protons, and the target particles. The LHC uses powerful magnets to accelerate the protons to high speeds and then collides them with a fixed target, such as a block of metal. By measuring the energy of the protons and the target particles before and after the collision, the total energy can be calculated and the center of mass energy can be determined.

4. What factors can affect the accuracy of center of mass energy calculations in fixed target interactions with the LHC?

There are several factors that can affect the accuracy of center of mass energy calculations, including the precision of the energy measurements, the stability of the LHC's magnetic fields, and the composition and density of the target material. Any error in these measurements can result in a deviation from the expected center of mass energy.

5. How does the center of mass energy in fixed target interactions with the LHC compare to other collision methods?

The LHC is currently the most powerful particle accelerator in the world, capable of reaching center of mass energies of up to 13 TeV (tera-electronvolts). This is significantly higher than other fixed target collision methods, such as those used at the Fermilab Tevatron, which had a maximum center of mass energy of 2 TeV. However, the LHC's center of mass energy is lower than that of other collider experiments, such as the Large Electron-Positron Collider and the future International Linear Collider, which can reach energies in the hundreds of GeV (giga-electronvolts) range.

Similar threads

Calculating Invariant Mass in LHC Collisions: A Proton Beam Energy Question
    • Advanced Physics Homework Help
Replies
17
Views
2K
Understanding the Center of Mass Energy in Fixed Target vs. Collider Experiments
    • Advanced Physics Homework Help
Replies
1
Views
1K
Calculate the particle energy in a collision
    • Advanced Physics Homework Help
Replies
21
Views
4K
Fixed Target & CoM Energy of colliding protons
    • Advanced Physics Homework Help
Replies
2
Views
2K
Threshold energy of proton beam?
    • Advanced Physics Homework Help
Replies
2
Views
2K
I How powerful would a collider have to be to observe a sphaleron?
    • High Energy, Nuclear, Particle Physics
Replies
2
Views
2K
Derive an expression for the rate of interactions in a fixed target experiment
    • Advanced Physics Homework Help
Replies
1
Views
2K
Centre-of-mass Energy of Colliding protons
    • Introductory Physics Homework Help
Replies
1
Views
6K
Energy & Time Dilation in Large Hadron Collider (LHC)
    • Special and General Relativity
Replies
1
Views
2K
Is a Small Space Hadron Collider More Efficient than a Large One?
    • High Energy, Nuclear, Particle Physics
Replies
26
Views
3K

Hot Threads

Recent Insights

Back
Top