Two-family compensation of linear horizontal/vertical coupling

Many existing circular accelerators have been able to adequately compensate their horizontal/vertical coupling by one or two families of skew-quadrupole corrector magnets. For example, the HERA proton storage ring at DESY has used just two skew quadrupoles correctors, the SPS at CERN can operate with just one skew quadrupole corrector, and the Tevatron at Fermilab with two families of skew quadrupoles. At first sight just two corrector families seem unlikely to be enough, since there are four independent horizontal/vertical coupling coefficients in the 4 x 4 transfer from one point to any other in the ring. Thus, for the general case four families of correctors would seem to be necessary. It will be shown that the adequacy of two-family correction for storage rings in a consequence of operating near the diagonal of the tune diagram