Beam energy measurements

It turns out that beam energy measurements seems to be the easiest in theory yet quite difficult in practice. Ideed, one can simply use a spectrometer , to get the beam energy value through the simple dependency P~300BR. However, the beam energy is such a critical parameter to e-beam controls and applications, that as a rule it has to be known with better than 2-digits accuracy. One can estimate the relative error in a spectrometer measurement:

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First term is a field error minimized by careful field mapping , and second is a beam launching angle error which can be small for large bending angles. However, operational problems, such as degaussing errors can easily make the error big. For instance at VISA I experiment, due to lack of degaussing and dipole alignment error, the energy uncertainty was about 2%, so the measurement was not very informative. In that particular case, for better accuracy, the spectrum of the on-axis FEL radiation was measured and energy determined as

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