Abstract
The shape of the cross section of the electron beam of an electron synchrotron observed photographically (spot) is discussed in relation to the distribution function for the amplitude and the phase of the betatron oscillation and also that for the coordinates of a particle and the inclination of its orbit to the equilibrium orbit. It is found that the probability density that particles move on the quilibrium orbit is zero, when the observed spot has a non-cusped finite intensity at its center. For example, a gaussian distribution for the spot intensity results from the rayleighan distribution for the amplitude. In this case the full half-width of the spot is given by 4(ln 2/π)1/2 <A>, where <A> is the mean amplitude of the betatron oscillation.
Published Version
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