Abstract
The width of the fourth-order coupling resonance 2ν <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">H</sub> - 2ν <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">V</sub> = 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 <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">H</sub> /spl Litilde/ ν <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">V</sub> /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 <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">V</sub> /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.
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