When the higher harmonics for the vertical field B y are not negligible, the peak field B 0 in Eq. The radiated photon energy e n for the nth harmonic on the z-axis is given by e n ( keV ) = n 9.498 E 2 ( GeV ) λ ( mm ) ( 1 + K 2 / 2 )with E as the electron beam energy, and the deflection parameter K defined as K = 0.0934 λ ( mm ) B 0 ( T ). In the midplane of a planar undulator, the vertical magnetic field variation has the form: B y = B 0 sin ( 2 π λ z )where B 0 is the peak magnetic field in the midplane of the undulator, and λ is the undulator magnetic period length along the electron-beam direction on the z-axis. For most synchrotron radiation sources and free-electron lasers, permanent magnet (PM) undulators are commonly used to produce photon beams from relativistic electron beams.
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