Beam size enhancement due to the presence of sextupole magnets in a ring

A perturbation method using the Green's function of the Fokker-Planck equation is applied to evaluate an enhancement of the vertical beam size of a bunch due to the presence in a storage ring of sextupolar magnetic fields. This paper considers the beam size in function of the machine tune. The resulting curve will correctly describe the size enhancement only if tune is not too close to a resonance. In the immediate vicinity of the resonance the beam size will deviate from correct values because at this point the assumption underlying these values becomes invalid; namely, the perturbed distribution function will deviate strongly from its unperturbed value. Since perturbation theory cannot be used near the resonance, other methods are needed to treat beam size enhancement at this range; however, at ranges far from resonance, the assumption regains its validity and the method of perturbation gives an accurate estimate of the perturbed beam size. The size of the bunch is presented as the power series in sextupole strength parameters. A numerical example of the beam enhancement due to the presence of sextupole magnets in a PEP storage ring is presented, and includes, among its parameters, particle motion described by the Courant-Snyder variables, the perturbed distribution function, and the vertical beam emittance