By Professor Dr. Dr. Rer. Nat. Habil. Pierre Meystre, Professor Murray Sargent III Ph. D. (auth.)
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This structure exerts a Lorentz force on the moving electrons, forcing them to oscillate, similarly to the simple harmonic oscillators of Sec. 1-3. As discussed at the end of that section, oscillating electrons emit radiation with the field shown in Fig. 1-2. In the laboratory frame, this radiation pattern is modified according to Lorentz transformations. Note that in contrast to the case of radiative decay discussed in Sec. 1-3, the FEL electron velocity approaches that of light and the vxB factor in the Lorentz force of Eq.
Chapter 12-5 shows by a quantum- 20 CLASSICAL ELECTROMAGNETIC FIELDS Chap. I screen Fig. 1-4. Young double-slit experiment illustrating how coherent light can interfere with itself mechanical analysis of the detection process that these methods measure l£+(r,t)l 2 , rather than IE(r,t)l 2 • This is why we performed the decomposition in Eq. (10). Returning to Young's double-slit experiment, we wish to determine £+(r,t), where r is the location of the detector. £+(r,t) is made up of two components, each coming from its respective slit (76) where r 1 and r 2 are the locations of the slits and t 1 and t2 are the retarded times (77) s 1 and s2 being the distances between the slits and the detector.
114) Here A is the vector potential of the field. Using the prescription (114) in Eq. (113), we find the required Hamiltonian 30 CLASSICAL ELECTROMAGNETIC FIELDS Chap. 1 (115) Hamilton's equations of motion are . af/C aq; . af/C Q; = ap. , P·=-I (116) (117) I where the three components of the canonical momentum, P;, and the three electron coordinates, Q;, completely describe the electron motion. To obtain their explicit form, we need to know A. This consists of two contributions, that of the static periodic magnetic field, and that of the scattered laser field.