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Relativistic particles

  1. Nov 10, 2008 #1
    "The free electron laser uses a beam of relativistic electrons passing through a periodic, transverse magnetic field to produce coherent radiation."

    The above is a quote from an online book, could anyone tell me what is the minimum velocity of an electron that is relativistic, ie its fraction of the speed of light. thx
  2. jcsd
  3. Nov 10, 2008 #2


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    Once the energy gets to the MeV range, ALL theoretical calculations for such electrons assume that the speed is c without loss of much accuracy.

  4. Nov 10, 2008 #3
    Thx ZapperZ, but your reply doesn't help much. maybe i should have asked , is there such thing as a non relativistic electron and if so at what point (speed) does it become relativistic, thx
  5. Nov 10, 2008 #4


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    When the kinetic energy is comparable to the rest mass energy.

  6. Nov 10, 2008 #5
    In a sense everything is relativistic.(of course the relativistic effects for particles with very small velocity comparing to c are very small).it depends how precise one wants to be.the classical energy (p^2/2m) can be obtained from the relativistic energy expanding for a small veloity.then you have as well other terms including higher powers of the fraction of u/c but it's up to you where you will stop it...
  7. Nov 11, 2008 #6
    Very true, if your measurement is accurate enough, very low speeds are relativistic.

    With the atomic clocks we have nowadays, a moderate car speed is relativistic. A running man is almost relativistic. Funny notion.

    A free electron laser needs highly relativistic electrons because their speed must almost match the one of the emitted photons so the field emitted at each deviation adds up over the whole wiggler. So take much more than 511keV.

    Also, even the radiation at one single magnet depends strongly on the electron's energy.

    A less obvious reason: if you take non-relativistic electrons, the period of the magnetic poles is short, but you need magnets wide apart in the transverse direction because the beam can't be concentrated at will - and as static magnetic fields can't be short and wide, this is incompatible.

    The lower-energy variant is called Bremsstrahlung (or braking radiation, no idea why it isn't translated). There you may take lower energies and still have a significant radiated power, with or without the magnetic wiggler.

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