Bremsstrahlung photon intensity and energy

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Does the timescale over which a charge decelerates determine the energy and intensity of brem photons?

Consider two electrons, one is decelerated over a large distance and relatively long period of time. A second electron is involved in fast scattering event and loses its energy relatively quickly and is ultimately left with the same final energy as the first electron.

Does the first electron emit a continuum of low energy photons through its deceleration, as compared to the second one? What ultimately determines the ratio of photon energies and intensities?
 

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In Bremsstrahlung, a continuous frequency spectrum of photons is emitted because the electron is not decelerating sinusoidally. Larger decelerations lead to higher energy photons.
 

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