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Homework Help: Free Electron Laser

  1. Sep 10, 2014 #1
    1. The problem statement, all variables and given/known data

    2. Relevant equations
    2. (b)

    I didn't understand how can I find the app. wavelength

    3. The attempt at a solution

    I tried : the electron move over λu with velocity β so the wavelength is λ≈λu
    but its not the right answer.

    my lecturer told me I should consider also the dopler

    I only know that the answer is :
    λ≈λu /(2*γ2)

    γ= gamma

    Attached Files:

  2. jcsd
  3. Sep 11, 2014 #2


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    Staff: Mentor

    This is the distance the light can travel while the electrons move by 1 structure length - but then the electrons moved forwards as well. What is the difference between those two distances?
  4. Sep 11, 2014 #3
    the electron moves λu while the light moves λ≈λu /β
    so the difference is λu [1/β-1]

    so how can I use this fact to find the wave length?

    I tried use the approximation β≈1-1q/(2*γ^2) for ultra-relativistic electrons
    but still didnt get the right answer....

    thank you
  5. Sep 11, 2014 #4


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    Staff: Mentor

    1/β is also 1/(1+β-1) where β-1 is small, so you can express that fraction as ~1-β+1
    That should lead to the right answer.
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