Scattering of Particles by the Gas in a Synchrotron

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Abstract
Successive elastic encounters of a proton with atoms of air in a proton synchrotron may build up a betatron oscillation whose amplitude exceeds the aperture of the vacuum chamber; in this case the particle is lost. The Rutherford scattering formula, suitably cut off at large and small scattering angles, is used to determine the r.m.s. amplitude of this oscillation as a function of the increasing kinetic energy of the particle. It reaches a maximum, given by Eq. (11), when the latter is four times its value at injection. The differential equation is found, which the distribution of amplitudes as a function of path length must obey, and it is solved, by use of appropriate boundary conditions, for the case in which damping of the oscillations is ignored. The solution makes possible an estimate of the fraction of the original particles which is scattered to the wall (Fig. 1). These results are applied to two proposed synchrotrons to determine the air pressures which gives a ten percent loss of particles.

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