Update on MEIC Nonlinear Dynamics Work V.S. Morozov Teleconference on Nonlinear Dynamics July 21, 2015 F. Lin

Complete Ring Lattice Two identical CCBs, one upstream and the other one downstream of the IP Optimal phase advances first obtained using thin trombones then implemented by adjusting phase advances of dispersion-free quadrupole sections Betatron tunes: x = 25.22, y = 23.16 IP

Tracking in Elegant Thick trombone case Betatron tunes: x = 25.22, y = 23.16 Thin RF cavity, h = 6832, V = 11.09 MV, s = 0.0367 @ 60 GeV/c x = 23.4 m, y = 4.7 m, p/p = 310-4 @ 60 GeV/c RF off RF on

MAD-X vs Elegant with RF Thick trombone case Betatron tunes: x = 25.22, y = 23.16 Thin RF cavity, h = 6832, V = 11.09 MV, s = 0.0367 @ 60 GeV/c x = 23.4 m, y = 4.7 m, p/p = 310-4 @ 60 GeV/c p/p = 0 p/p = 3p/p p/p = 10p/p

Exploring Nonlinear Properties Replaced thin multipoles with thick sextupoles and tweaked the optics to be able to calculate nonlinear parameters in Elegant (tedious otherwise) Used thin trombones to adjust the phase advance from IP to sextupoles to exactly (n+1/2), reoptimized sextupole strength for minimum W’s at IP and x,y = 1, tried different n to check cross-talk between CCB’s Betatron tunes: x = 25.22, y = 23.16 No significant impact on DA: solution not too sensitive to parameters but no improvement either IP

Some Non-Linear Parameters Chromaticities dnux/dp = 1.107578e+00; dnux/dp2 = 1.089866e+03; dnux/dp3 = -7.070816e+06 dnuy/dp = 1.054413e+00; dnuy/dp2 = 2.851418e+03; dnuy/dp3 = -9.016539e+06 Chromatic  function dependence dbetax/dp (m) = 7.512945e-02; dbetay/dp (m) = 8.869397e-03 Non-linear dispersion etax2 (m) = 1.215463e+00; etax3 (m) = -3.199603e+02 etay2 (m) = 0.000000e+00; etay3 (m) = 0.000000e+00 Tune dependence on amplitudes dnux/dJx (1/m) = -2.623351e+02; dnux/dJy (1/m) = -2.436476e+04; dnuy/dJy (1/m) = -8.473632e+02 1st-order driving terms h11001 = 6.907272e+01; h00111 = 6.158692e+01; h10100 = 0.000000e+00; h10010 = 0.000000e+00; h21000 (1/m1/2) = 2.717454e-02; h30000 (1/m1/2) = 5.928193e-03; h10110 (1/m1/2) = 3.324664e+01; h10020 (1/m1/2) = 1.858944e+01; h10200 (1/m) = 7.024785e+00; h20001 = 7.177547e+00; h00201 = 1.521199e+01; h10002 (1/m1/2) = 2.538938e+00; 2nd-order driving terms h22000 (1/m) = 2.060350e+02; h11110 (1/m) = 3.404719e+04; h00220 (1/m) = 3.991722e+02; h31000 (1/m) = 2.272050e+01; h40000 (1/m) = 5.213691e+02; h20110 (1/m) = 9.676610e+03; h11200 (1/m) = 1.209824e+04; h20020 (1/m) = 7.168240e+03; h20200 (1/m) = 7.269484e+03; h00310 (1/m) = 4.648071e+02; h00400 (1/m) = 8.771640e+01

Conclusions & Outlook MAD-X PTC and Elegant agree reasonably well with RF Seem to have narrowed down the problem with the CCB scheme: cross-talk between horizontal and vertical sextupoles; hope to be able to fix it by adjusting the phase advance between them Further work Straighten out the phase advances Do some reasonable optimization Check error sensitivity Compare the different schemes side by side: nonlinear performance, magnet parameters, error sensitivity