Update on MEIC Nonlinear Dynamics Work V.S. Morozov Teleconference on Nonlinear Dynamics August 4, 2015 F. Lin

Nonlinear Parameter Study Continued Phase advance between the h and v sextupoles adjusted to exactly /2 in both planes Phase advance from IP to sextupoles adjusted to exactly (n+1/2) in appropriate planes W minimized at IP using “non-linear” sextupoles x,y = 1 using “linear” sextuples Betatron tunes: x = 25.22, y = 23.16 No significant improvement IP

Some Non-Linear Parameters Chromaticities dnux/dp = 9.998781e-01; dnux/dp2 = 1.109191e+03; dnux/dp3 = -7.024153e+06 dnuy/dp = 9.504664e-01; dnuy/dp2 = 2.601808e+03; dnuy/dp3 = -8.934732e+06 Chromatic  function dependence dbetax/dp (m) = 6.866690e-02; dbetay/dp (m) = 3.606922e-02 Non-linear dispersion etax2 (m) = 1.178847e+00; etax3 (m) = -3.103298e+02 etay2 (m) = 0.000000e+00; etay3 (m) = 0.000000e+00 Tune dependence on amplitudes dnux/dJx (1/m) = -2.680087e+02; dnux/dJy (1/m) = -2.469341e+04; dnuy/dJy (1/m) = -7.253478e+02 1st-order driving terms h11001 = 6.875269e+01; h00111 = 6.126258e+01; h10100 = 0.000000e+00; h10010 = 0.000000e+00; h21000 (1/m1/2) = 2.510811e-02; h30000 (1/m1/2) = 5.426073e-03; h10110 (1/m1/2) = 3.270516e+01; h10020 (1/m1/2) = 1.975800e+01; h10200 (1/m) = 6.228126e+00; h20001 = 6.955414e+00; h00201 = 1.548701e+01; h10002 (1/m1/2) = 2.460090e+00; 2nd-order driving terms h22000 (1/m) = 2.104914e+02; h11110 (1/m) = 3.400605e+04; h00220 (1/m) = 4.830917e+02; h31000 (1/m) = 2.323952e+01; h40000 (1/m) = 5.144545e+02; h20110 (1/m) = 9.568259e+03; h11200 (1/m) = 1.195545e+04; h20020 (1/m) = 6.952266e+03; h20200 (1/m) = 7.347341e+03; h00310 (1/m) = 4.868787e+02; h00400 (1/m) = 7.736146e+01

What Is the Issue? Second order amplitude dependent tune shift Consider a single CCB (the downstream one) with N = 3 h/v sextuple cross-talk within a single CCB explains the large x/Jy value: (x/Jy)21 and (x/Jy)23 independent of tune and add up x/Jy j Total 1 2 3 k 223.0 -8087.9 -223.0 -20.0 -1282.2 -17498.0

Conclusions & Outlook There seems to be a fundamental problem with the CCB scheme There appear to be no phase advance combination that would cancel sextupole contributions to x/Jy Additional sextupole(s) needed, this then starts resembling –I sext pair scheme x/Jy is the hardest to compensate with octupoles, would require three of them Important lesson: phase advance between sextupole pairs matters Further work Present a side by side comparison to the collaboration and make a down selection Get non-interleaved –I sextupole pair optics from SLAC for further studies Continue optimization Continue error studies Start thinking about the electron ring