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I E and B fields for charged particle's parabolic motion

  1. Dec 28, 2016 #1
    I am looking to find a combination of electric and magnetic fields that create something similar to the (d) crests
    medium.png


    Currently, I have the cracks flipped clockwise 90deg, so that the crests are concave up. And each crest can be defined by a parabolic function (which are uniform with each new turn).

    If I look at one crest, treat it as a particle moving in a concave up parabola I have...

    $$\vec{E} = E\hat{y} , \vec{B} = B\hat{z}$$

    Now, this is only for a single parabola. I need to make it so that the particle reaches a turning point and goes backwards along the same parabola (to the left now). I think this can be done by making B oscillate between a positive and negative value.

    I also need to add a "group velocity" so that a string of these parabolas will create a chain like that seen in (d). In my example, though, the parabolas should be moving downwards.

    TO SIMPLIFY:
    1. What E and B fields (can be time dependent) will cause a charged particle to oscillate along a parabola
    2. What can be done to include a drift/ group velocity so that the parabolas move in one direction.
     
  2. jcsd
  3. Dec 29, 2016 #2

    mfb

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    Staff: Mentor

    Undulators give particle paths similar to (d): Alternating magnetic fields, the particles follow circle segments in each section. A fine-tuning of the magnetic fields can modify the path a bit more.
     
  4. Dec 29, 2016 #3
    Ok, so my research is basically modeling self replicating cracks with analog E and B fields. This means that I need an analytical expression (not experimental method).
     
  5. Dec 29, 2016 #4

    mfb

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    Staff: Mentor

    An analytical expression of what?
    You can make up magnetic fields (or electric fields) that lead to parabolic paths of particles moving through that field.

    Your question is quite vague.
     
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