Coupling resonance 2νh - 2νv = 0 in the KEK proton synchrotron

The width of the fourth-order coupling resonance 2ν_H - 2ν_V = 0 is calculated for the KEK proton snynchrotron for the case of various octupolar nonlinear fields. The space charge nonlinear field has the largest effect and it may cause some beam loss for the diagonal tune ν_H /spl Litilde/ ν_V /spl Litilde/ 7.25 at a high intensity. This coupling resonance is avoided by choosing an offdiagonal tune νH /spl Litilde/ 7.25 and ν_V /spl Litilde/ 6.25. Even then, the linear tune shift and the tune spread due to space charge octupolar field are found to be rather large and these may be connected with the beam loss in the KEK proton synchrotron.