Collider Luminosity Calculation

In summary, the current given for the electron beam is 0.01 Amps and the charge of an electron is 1.602X10^-19. This means that the average time between electrons is 1.6x10^-17 seconds.
  • #1
renegade05
52
0

Homework Statement


A collider has an average electron current of 10 milliAmps and an average positron current of
5 milliAmps.If the ring radius is 100 m and there is one electron bunch and one positron bunch
with uniform density, radius 1 µ and length 2 mm, what is the average luminosity in cm–2s–1 ?

Homework Equations


L=N_1 N_2/A * f
density = N/(AT)

The Attempt at a Solution


Ok so I know the target thickness (T) is 2mm with and Area (A) of pi * (1µ)^2
The density I am having a problem with.
I don't know how to incorporate the current given or the ring radius.

Just having a hard time with this question in general. Not sure where to start or where to plug everything in. Please help - thanks!
 
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  • #2
You don't need a density.

How frequent do the electrons pass your collision point? You can assume that they are high-energetic and move with roughly the speed of light.
Which current does a specific amount of charge give, using the information calculated above?
 
  • #3
Ok so Current = Charge/ Time. So I can solve for the time?! Still a very confused on how to solve this. sorry :(
 
  • #4
Yes you can find the revolution time. You know the speed of the electrons/positrons and the collider geometry (ring with 100m radius).
 
  • #5
Ok so for the electrons I get a time of... Time = 1.602X10^-19 / 0.01 = 1.6x10^-17 seconds ?
and Distance traveled will be R=2pi*100 = 200pi
NOW WHAT?!
 
  • #6
renegade05 said:
Ok so for the electrons I get a time of... Time = 1.602X10^-19 / 0.01 = 1.6x10^-17 seconds ?
What did you calculate here? What are the units?

renegade05 said:
and Distance traveled will be R=2pi*100 = 200pi
Don't forget the units.
You know distance and speed, that allows to calculate how long the electrons need for one round in the ring.
 
  • #7
Ya I have the units for the first one. They are seconds. I am not sure what that time is referring to though or how to use it.

The distance traveled will be 200pi Meters, I don't know the speed though...
 
  • #8
renegade05 said:
Ya I have the units for the first one. They are seconds.
No they are not. The first value seems to be the elementary charge, which has units of a charge (Coulomb), and I have no idea what the 0.01 is supposed to represent. It is hard to help if you throw in completely unexplained calculations.
The distance traveled will be 200pi Meters, I don't know the speed though...
See post 2.
 
  • #9
Current = Charge/ Time
The current given for the electron beam is 0.01 Amps
The charge of an electron is 1.602X10^-19
Thus Charge/Current = Time
right?
 
  • #10
Ah... okay, that is the average time between electrons then.
 

1. What is collider luminosity?

Collider luminosity is a measure of the number of particle collisions that occur within a given amount of time. It is an important factor in determining the efficiency and productivity of a particle accelerator or collider.

2. How is collider luminosity calculated?

Collider luminosity is calculated by multiplying the number of particles in the colliding beams by the frequency at which they collide. This results in a unit of inverse area-time, typically measured in inverse femtobarns (fb^-1).

3. Why is collider luminosity important?

Collider luminosity is important because it directly affects the rate at which rare particle collisions occur, which in turn allows scientists to study fundamental particles and their interactions. Higher collider luminosity also increases the chances of discovering new particles or phenomena.

4. What factors can affect collider luminosity?

The main factors that affect collider luminosity are the number of particles in the beams, the size of the beams, and the frequency at which they collide. Other factors such as beam stability, beam overlap, and detector efficiency can also have an impact.

5. What is the current state of collider luminosity in the Large Hadron Collider (LHC)?

The current state of collider luminosity in the LHC is around 2.06 x 10^34 cm^-2s^-1, which is the highest achieved in any particle collider to date. This high luminosity has allowed for the discovery of the Higgs boson and continues to provide valuable data for research in particle physics.

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