1. UPDATE IN PTC-ORBIT PSB STUDIES Space charge meeting (27-04-2012) * Vincenzo Forte * Follows LIS meeting presentation 16/04/2012

2. Preliminary results of the PTC/ORBIT convergence studies in the PSB - Vincenzo Forte Logical path* Lattice setup Inject starting 6-D matched distribution PTC ORBIT basic settings RMS emittancetunes Adding of space charge Orbit routines 1000 turns tracking 95-99% emittance Results analysis Best settings choose Externally created (MadX, …) Internally modified (tables) Externally created (Mathematica, …) PTC-ORBIT Plots and tunes footprints *From LIS meeting presentation 16/04/2012

3. Preliminary results of the PTC/ORBIT convergence studies in the PSB - Vincenzo Forte Results – first without space charge…* y *From LIS meeting presentation 16/04/2012 Why this transitory without space charge???

4. Preliminary results of the PTC/ORBIT convergence studies in the PSB - Vincenzo Forte D.O.E.* Lattice setup Inject starting 6-D matched distribution PTC ORBIT basic settings xx xx yy yy DxDx D px Lattice (PTC) 0.8762e-55.5940-0.22351e-33.6225-1.33400.13270e-3 250e3 (Matlab post p.) 1.0819e-45.58900.00223.6187-1.3372-9.4e-4 500e3 (Matlab post.p.) -3.0357e-45.5903-4.7075e-43.6186-1.34407.8642e-4 1000e3 (Matlab post p.) -0.00235.5901 *-1.81e-53.6219 *-1.34186.5791e-4 * Beta functions statistical precision increases with number of m.p. *From LIS meeting presentation 16/04/2012 The initial distributions, as usual, were matched to this initial parameters from PTC Twiss table output

5. Preliminary results of the PTC/ORBIT convergence studies in the PSB - Vincenzo Forte In the PSB study the introduction of time-dependent elements is useful to control some lattice’s elements during the simulations. This is obtained in PTC-Orbit through tables, that let us vary the waveform of magnets strengths and RF cavities to desired functions (like ramps or even non- linear) through linear interpolations in time. In the PSB the (LHC) beam will be injected horizontally into each PSB ring with a chicane using four dipole magnets (BS), and a painting bump using four kicker magnets (KSW). Then, we have also a double harmonic RF system that can be managed through tables (i.e. for acceleration). Regarding to our preliminary lattice (bumps at 0, kickers at 0, double harmonic without acceleration), we initially took a complete lattice (with bumps, kickers at non-0 value) and then applied tables to overwrite (at 0 value) the BS and KSW strengths and to define the RF cavity. Preliminary considerations

6. Preliminary results of the PTC/ORBIT convergence studies in the PSB - Vincenzo Forte *From LIS meeting presentation 16/04/2012 fractional tunes 0.277351800735185 0.431269833678875 name s betax betay alphax alphay eta_x etap_x PSBRING$START 0.0000 5.5940 3.6225 0.87260E-05 -0.22351E-03 -2.5655 0.25532E-03 xx xx yy yy DxDx D px Lattice (PTC) 0.8762e-55.5940-0.22351e-33.6225-1.33400.13270e-3 250e3 (Matlab post p.) 1.0819e-45.58900.00223.6187-1.3372-9.4e-4 500e3 (Matlab post.p.) -3.0357e-45.5903-4.7075e-43.6186-1.34407.8642e-4 1000e3 (Matlab post p.) -0.00235.5901 *-1.81e-53.6219 *-1.34186.5791e-4 The initial distributions, as usual, were matched to this initial parameters from PTC Twiss table output These dispersions values must be multiplied for  rel ~ 0.52

7. Preliminary results of the PTC/ORBIT convergence studies in the PSB - Vincenzo Forte And so… what generated the inital oscillations if the Twiss are matched? We made an attempt… what if it was just a mismatching? After 1000 turns, but even much before, the distribution seems to be matched At the beginning there seems to be a mismatching in vertical transverse plane Attempt: We took the distribution at turn 1000 and made a new run for 50 turns with this one as initial distribution y

8. Preliminary results of the PTC/ORBIT convergence studies in the PSB - Vincenzo Forte And so… what generated the inital oscillations if the Twiss are matched? Now it’s vertically matched … but w.r.t. which Twiss parameters ??? xx xx yy yy DxDx D px Lattice (Twiss PTC) 0.8762e-55.5940-0.22351e-33.6225-1.33400.13270e-3 1000e3 (init. unmatched) -0.00235.5901-1.81e-53.6219-1.34186.5791e-4 1000e3 (finally matched) 5.7977e-55.62774.8118e-43.2210-1.3443-1.715e-4 So… why are the values different from the PTC Twiss table ones??

9. Preliminary results of the PTC/ORBIT convergence studies in the PSB - Vincenzo Forte InitPTC("PSB_PTC_ORBIT_FLAT_427_443.TXT"); ReadPTCscript("fringe.ptc"); ReadPTCscript("chrom.ptc"); /////////////////////////////////////////////////////////// // (2) PTC scripts for tracking WITH time-dependent elements /////////////////////////////////////////////////////////// ReadPTCscript("PSB_PTC_TOTAL_RAMP_RFTable.ptc"); ReadPTCscript("twiss_script.ptc"); …. Tracking routines ReadPTCscript("twiss_script.ptc"); Diagnostic routines fractional tunes 0.276163580722948 0.416531295482894 name s betax betay alphax alphay eta_x etap_x PSBRING$START 0.0000 5.6285 3.2533 -0.23633E-14 0.31041E-14 -2.5877 0.16376E-14 W. Point tunes will be consequently modified too after applying tables It depends on the position where you put the ReadPTCscript("twiss_script.ptc") command: If you put before tracking routines you are still considering the complete lattice with bumps and kickers (at non-zero value) If you put after (or during) tracking loops, the tables will be effectively applied and the lattice will change (bumps and kickers at 0).