0.4229 (7) points The 6 fixed points other than the origin R = 0 are given dR 3by de = de =

The 3 stable fixed points recede to CT0 and the 3 unstable fixed points are exactly at Ru = z and strength of the resonance exciting sextupole magnet We would like the beam to pass the electrostatic septum at zero angle. This implies that at the septum px = 0 hence -5- TM-271 0402 $I = $. (Equ. (7)) for the phase points streaming out along the separatrix. With no octupole field the separatrices in the (R, @) plane are shown in Figure

octupole magnets. The effect of the octupole field is to move the 3 stable fixed point inward from 03 and to close the separatrices on the outside (dotted lines in Figure 1). The extreme tolerance condition is that the separatrix should not curve back before x s has reached the desired maximum value x smax m for the main ring). But, in practice, the curvature of the separatrix caused by the octupole field becomes appreciable even at R % Rs. If the value of R corresponding to xsmax is larger than Rs the quality of the extracted beam will suffer. At xs = xSmax = 0.04 m -9- TM-271 0402 X R = Rmax 5 smax = 0.04 m /q cos f = 6.91 x 10v3 m1'2 J98 m cos 0.9465 The condition Rs 2 2r > Rmax z 6.91 x 10m3 m1'2 gives r = - & > 3.46 x 10 -3,1/2 OP -B < - A 2 x

0.67 x 10' kGm and the tolerance on B$ is (21) We note here that because of the difference in B values at the F and the D quadrupoles the contribution to B comes mainly from the F quadrupoles. The measured Blsris about 10 times this tolerance value indicates that correcting octupole magnets are necessary. Assuming for the correcting octupoles $ aperture = 6 cm radius Bf'f = lo5 kG/m3 (3.6 kG on pole tip) located near B = 98 m to compensate for -Bz' = -1000 kG/m3 (say) in the sixteen 7 ft long F quadrupoles in one superperiod we have a length of 3 loookG'm xl6x7ft=l.l2ft 105 kG/m3 Thus, to correct for the octupole error field at 200 BeV we need a