Filtered sum rules for synchrotron radiation in nonuniform field. Application to channeling radiation

Sum rules are derived which relate moments of the differential photon spectrum emitted by a classical moving point charge to the integral of the square of the apparent position, velocity or acceleration, as seen by the observer. Smoothing of the trajectory by means of a convolution with a function f(τ), where τ is the observer's time, results in a filtering of the spectrum by |f-tilde(ω)|2, f-tilde(ω) being the fourier transform of f(τ); this allows us to write filtered sum rules. Examples of applications of unfiltered and filtered sum rules to computer simulation of channeling radiation are presented. (author)