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A What was so extraordinary about Landau damping?

  1. Feb 14, 2018 #1
    I've been told Landau damping was a surprising phenomenon that many people didn't believe possible when first introduced since it permit wave damping in the absence of collisions. I appear to be missing something fairly basic and fundamental to this picture, but aren't all wave-particle interactions without collisions (e.g. electromagnetic wave moving a stationary electron)? What was so revolutionary at the time?
  2. jcsd
  3. Feb 14, 2018 #2


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    So you have marked your thread with an A tag ... post graduate level
    What specific reading/research have you done so far and what didn't you understand about anything
    in particular that you read so that people can give you good answers
  4. Feb 14, 2018 #3
    Ahh well this is a very basic question so my apologies. I've gone through multiple different derivations of this phenomenon (e.g. via Laplace transform or strictly laborious algebra), and it appears in multiple places but I've mainly read through notes for MIT OCW 22.611 (the graduate intro plasma physics). The individual steps in the derivations make sense, but I'm simply wondering why this is a unique phenomenon not previously believed possible before it was derived and then experimentally proven. What's so different about this type of wave damping not seen in other wave-particle interactions?
  5. Feb 16, 2018 #4


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    I heard that also, but have not researched it to learn if it is true. Let's assume it is true, though.

    I've never read up on the history to understand why, but it is my understanding that Vlasov was the first to point out that the collisional terms in the Boltzman equation should be negligible in a hot plasma. Landau's analysis of that collisionless Boltzman equation (now called the Vlasov equation) appeared in the literature just one year after Vlasov's work was published (at least I think it was ... could you verify/refute this for us?). So I suspect that the answer to
    is that there were no other wave-particle interactions studied in the context of collisionless kinetic theory prior to Landau's work. Collisionless fluid models of course show that waves would not be damped, and since there was not a lot of theoretical predictions based on the Vlasov equation available to compare with theory, it may not have been obvious that the Vlasov equation really was a good mathematical model at all. So it may be no surprise that when unexpected results come out of a relatively difficult mathematical analysis of an unverified model, that the community really wants to see the experiment to believe what is going on.

    Not unique in this regard at all. Perhaps a similar (and much more profound) case was when Fresnel first presented his wave theory of light. Poisson performed a mathematical analysis that showed the wave theory predicts a bright spot right in the middle of the shadow of a disk or sphere when illuminated by monochromatic light. This apparently lead some folks (including Poisson!) to dismiss the wave theory of light because this was an unexpected result that had no experimental evidence ... yet. Arago then did the experiment and found the spot.

    I would assert that in some sense the fluid theory of plasmas is analogous to the ray theory of light, and the kinetic theory of plasmas is analogous to the wave theory of light.

    Last edited: Feb 16, 2018
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