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Relationship between Mean Radiated Energy, Mean Squared Radiated Energy, and Spontaneous Power Spectrum in a Power Series Expansion of the Equations of Motion in a Free Electron Laser,
HIGH TEMPERATURE MATERIALS INC BOSTON MASS
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To lowest order in the electric field and the inverse electron energy, the classical mean energy radiated by electrons in a free electron laser with a symmetric magnet is equal to one-half the derivative, with respect to energy, of the classical mean-squared radiated energy. The integral for the mean squared energy is also shown to be identical to the integral for the classical spontaneous power spectrum. Author
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