Abstract
In this section we demonstrate how Hamiltonian mechanics can be used to derive the trajectory of an electron in an undulator magnet and its coupling to the radiation field. For a thorough presentation of the Lagrange–Hamilton formulation of classical mechanics we refer to the textbooks by Landau and Lifshitz [1] and Goldstein [2].
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Notes
- 1.
In particle physics one looks along the direction of motion of the photon. In that case the electric vector at a fixed spatial position rotates in clockwise direction. In optics the convention is such that the observer is facing into the oncoming wave, and then the field vector at a fixed spatial position rotates counterclockwise, see Ref. [4].
References
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Schmüser, P., Dohlus, M., Rossbach, J., Behrens, C. (2014). Appendices. In: Free-Electron Lasers in the Ultraviolet and X-Ray Regime. Springer Tracts in Modern Physics, vol 258. Springer, Cham. https://doi.org/10.1007/978-3-319-04081-3_10
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DOI: https://doi.org/10.1007/978-3-319-04081-3_10
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