Beam Based Measurements of Field Multipoles in the RHIC Low Beta Insertions and Extrapolation of the Method to the LHC

The multipolar content of the dipoles and quadrupoles is known to limit the stability of the beam dynamics in super-conducting machines like RHIC and even more in LHC. The low-beta quadrupoles are thus equipped with correcting coils up to the dodecapole order. The correction is planned to rely on magnetic measurements. We show that a relatively simple method allows an accurate measurement of the multipolar field aberrations using the beam. The principle is to displace the beam in the non-linear fields by local closed orbit bumps and to measure the variation of sensitive beam observable. The resolution and robustness of the method are found appropriate. Experimentation at RHIC showed clearly the presence of normal and skew sextupolar field components in addition to a skew quadrupolar component in the interaction regions. Higher-order components up to decapole order appear as well.