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Collider luminosity

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  1. Jan 17, 2015 #1
    1. The problem statement, all variables and given/known data
    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 ?

    2. Relevant equations
    L=N_1 N_2/A * f
    density = N/(AT)


    3. 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!
     
  2. jcsd
  3. Jan 17, 2015 #2

    mfb

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    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?
     
  4. Jan 18, 2015 #3
    Ok so Current = Charge/ Time. So I can solve for the time?! Still a very confused on how to solve this. sorry :(
     
  5. Jan 18, 2015 #4

    mfb

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    Yes you can find the revolution time. You know the speed of the electrons/positrons and the collider geometry (ring with 100m radius).
     
  6. Jan 18, 2015 #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?!
     
  7. Jan 18, 2015 #6

    mfb

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    What did you calculate here? What are the units?

    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.
     
  8. Jan 18, 2015 #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 travelled will be 200pi Meters, I don't know the speed though......
     
  9. Jan 18, 2015 #8

    mfb

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    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.
    See post 2.
     
  10. Jan 18, 2015 #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?
     
  11. Jan 19, 2015 #10

    mfb

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    Ah... okay, that is the average time between electrons then.
     
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