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Avoiding breakdown

  1. Nov 4, 2013 #1
    Hello,
    1. The problem statement, all variables and given/known data
    The laser Nd:YAG can product a light impulse of λ=1064nm that lasts for 10ns and encloses an energy of 0.1 J and propagates as a cylindrical beam of uniform section in air (n=1)
    The maximum electric field that can support air before atoms' ionization is ≈30 MV/m otherwise there's breakdown
    What is the minimum diameter of the beam to avoid breakdown

    2. Relevant equations



    3. The attempt at a solution
    I don't know how I can link all these datas and which formulas will help me to

    Thanks
     
  2. jcsd
  3. Nov 5, 2013 #2
    An average flux density of EM wave can be calculated with
    $$
    I = \frac{1}{2} \sqrt{\frac{ε_0} {μ_0}} E^2,
    $$
    where ##E = 30 MV/m.##

    On the other side an energy (##W = 0.1 J##) is
    $$
    W = I S τ
    $$
    where S is a beam area and ##τ = 10^{-8} s##.

    So you can calculate a beam area S and then find a diameter of the beam.

    I don't know why data include a wave lenght.
     
  4. Nov 5, 2013 #3
    S is the area of the beam or of a section because if it is the total area it will depend on h as it is a cylinder and we don't have it. Thanks
     
  5. Nov 5, 2013 #4

    berkeman

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    Staff: Mentor

    Gregory -- please be sure to check your PMs. You received a message about how we handle Homework Help here on the PF. Thank you.
     
  6. Nov 5, 2013 #5

    berkeman

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    Staff: Mentor

    You *do* have the height of the cylinder. You are given the duration of the pulse...
     
  7. Nov 5, 2013 #6
    Is it just L=c*t ?
     
  8. Nov 5, 2013 #7

    berkeman

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    Staff: Mentor

    Yep! :smile:

    So can you show us the complete solution now?
     
  9. Nov 5, 2013 #8
    With
    μ0 = 4 π 10-7 Hm-1
    ε0= 8,85* 10-12 Fm−1
    ε=(ε0/μO)1/2

    W=0.5*ε*E²*t*2π*r*c*t
    r=W/(ε*E²*t²*2π*c)

    t=10^-8 s
    E=30*10^6 V/m
    W=0.1 J
     
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