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

2. 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

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

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

5. 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

6. Some Non-Linear Parameters
Chromaticities
dnux/dp = e+00; dnux/dp2 = e+03; dnux/dp3 = e+06
dnuy/dp = e+00; dnuy/dp2 = e+03; dnuy/dp3 = e+06
Chromatic  function dependence
dbetax/dp (m) = e-02; dbetay/dp (m) = e-03
Non-linear dispersion
etax2 (m) = e+00; etax3 (m) = e+02
etay2 (m) = e+00; etay3 (m) = e+00
Tune dependence on amplitudes
dnux/dJx (1/m) = e+02; dnux/dJy (1/m) = e+04; dnuy/dJy (1/m) = e+02
1st-order driving terms
h11001 = e+01; h00111 = e+01; h10100 = e+00;
h10010 = e+00; h21000 (1/m1/2) = e-02; h30000 (1/m1/2) = e-03;
h10110 (1/m1/2) = e+01; h10020 (1/m1/2) = e+01; h10200 (1/m) = e+00;
h20001 = e+00; h00201 = e+01; h10002 (1/m1/2) = e+00;
2nd-order driving terms
h22000 (1/m) = e+02; h11110 (1/m) = e+04; h00220 (1/m) = e+02;
h31000 (1/m) = e+01; h40000 (1/m) = e+02; h20110 (1/m) = e+03;
h11200 (1/m) = e+04; h20020 (1/m) = e+03; h20200 (1/m) = e+03;
h00310 (1/m) = e+02; h00400 (1/m) = e+01

7. 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