1. Ring tuning spread 2 MW beam at 1 GeV – Space charge tune spread about 0.2 (green) – Chromatic tune spread must be controlled by sextupoles (red: beam core Dp/p=+/-0.6%; pink: partial halo Dp/p=+/- 1.0%) Imperfection non-structure resonances are shown in black

6. Two regions of working points Imperfection resonances up to 3 rd orderImperfection resonances up to 4 th order

7. w.p.(6.4,6.3) Tune spread for 2MW beam with dp/p=0.6 %

8. Phase Advance A4 A6 B4 B6 C4 C6 D4 D6 A4-C4=19*2*  /2=18*  =  =B4-D4=A6-C6=B6-D6 A4-B6 =19*2*  /4 +3*  /2=10*  +  =B4-C6=C4-D6

9. Skew & Normal Sextupole A4-C4C6-A6B4-D4B6-D6 (A4-C4)-(B6- D6) (C6-A6)-(B4- D4) -5.84-1.20 = -7.04 0.33-(-2.45) =-2.87 2.03-0.92 =1.11 1.17-8.13 =-6.96 -7.04 –(-6.96) =-0.08 2.87-1.11 =1.76 -0.08-1.76 =1.84 -5.84-(-2.54) =-3.30 0.92-0.33 =0.59 2.03-1.20 =0.83 1.17-8.13 =-6.96 -3.30-(-6.97) =3.67 0.59-0.83 =-0.24 3.67-(-.24) =3.91 1.17-1.20 =-0.03 0.92-2.03 =-1.11 8.13-(-5.84) =13.97 0.33-(-2.54) =2.87 -0.03-(-2.87) =-2.90 -1.11-(13.97) =15.08 -2.90-15.08 =17.98 2.05-(-.90) =2.95 -0.20-1.96 =-2.16 -1.87-(- 1.06)=-0.81 0.72-1.41 =-0.69 2.95-(-.69) =3.66 -2.16-(-.81) =-1.35 3.66-(-1.35) =5.01 2.05-0.20 =2.25 1.96-(-1.06) =3.02 -1.82-(-.9) =-0.92 0.72-1.41 =-0.69 2.25-(-.69) =2.94 3.02-(-.92) =3.94 2.94-3.94 1.00 0.72-(-.9) =1.62 -1.87-1.96 =-3.83 1.41-2.05 =-0.64 -1.06-(-.2) =-0.86 1.62-(-.86) =2.48 -3.83-(-.64) =-2.19 2.48-(-2.19) =4.67 0.8% 1.1% 6%