Preliminary results of the PTC/ORBIT convergence studies in the PSB LIS meeting 16/04/2012 Vincenzo Forte
OVERVIEW Aim of the study Logical path D.O.E. Results Conclusions and future implementations Preliminary results of the PTC/ORBIT convergence studies in the PSB - Vincenzo Forte
Aim of the study Preliminary study for finding the optimal conditions for PTC/ORBIT space-charge simulations in terms of convergence and computational costs How far do we have to push in simulations settings to obtain reasonable results with less computational costs? Preliminary results of the PTC/ORBIT convergence studies in the PSB - Vincenzo Forte
Logical path Externally created (MadX, …) Internally modified (tables) Lattice setup Inject starting 6-D matched distribution Externally created (Mathematica, …) PTC ORBIT basic settings Adding of space charge Orbit routines PTC-ORBIT 1000 turns tracking RMS emittance 95-99% emittance tunes Results analysis Plots and tunes footprints Best settings choose Preliminary results of the PTC/ORBIT convergence studies in the PSB - Vincenzo Forte
D.O.E. Made externally through Mad-X Lattice setup Modified internally through tables Lmax = 1, w.p. Qx = 4.27, Qy= 4.43 (“resonances - safe” area) Simple lattice (double harmonic, tables at 0 value, no acceleration, no C.O.D.) Inject starting 6-D matched distribution PTC ORBIT basic settings Adding of space charge Orbit routines 1000 turns tracking RMS emittance 95-99% emittance tunes Results analysis Best settings choose Preliminary results of the PTC/ORBIT convergence studies in the PSB - Vincenzo Forte
Inject starting 6-D matched distribution PTC ORBIT basic settings D.O.E. Lattice setup Externally-made distribution through Mathematica script Ekin = 160 MeV Normalized transverse emittances: ex=3 (mm-mrad) - ey=2 (mm-mrad) (source: official Excel datasheet on SC-webpage) Un-normalized transverse emittances: ex=4.9 (mm-mrad) - ex=3.3 (mm-mrad) Matched 6-D distribution (without SC) 250th, 500th, 1000th macro-particles used Number of particles per bunch = 1.5 * 1.65e12 (official) = 2.475e12 -> “extreme” conditions for space charge Fringe fields included Inject starting 6-D matched distribution PTC ORBIT basic settings ??? Preliminary results of the PTC/ORBIT convergence studies in the PSB - Vincenzo Forte
Inject starting 6-D matched distribution PTC ORBIT basic settings D.O.E. Lattice setup Externally-made distribution through Mathematica script Matched 6-D distribution (without SC) 250th, 500th, 1000th macro-particles used RF voltages (h=1) 8kV, (h=2) 4kV -> Ts ~ 750 turns Inject starting 6-D matched distribution PTC ORBIT basic settings ax bx ay by hx hpx Lattice (PTC) 0.8762e-5 5.5940 -0.22351e-3 3.6225 -1.3340 0.13270e-3 250 th (Matlab post p.) 1.0819e-4 5.5890 0.0022 3.6187 -1.3372 -9.4e-4 500 th (Matlab post.p.) -3.0357e-4 5.5903 -4.7075e-4 3.6186 -1.3440 7.8642e-4 1000 th (Matlab post p.) -0.0023 5.5901 * -1.81e-5 3.6219 * -1.3418 6.5791e-4 * Beta functions statistical precision increases with number of m.p. Preliminary results of the PTC/ORBIT convergence studies in the PSB - Vincenzo Forte
Inject starting 6-D matched distribution D.O.E. Lattice setup 1000th M.p. distribution Longitudinal dp/p = 0.002042, T = 185.606 ns 4T dW = 1.4129 eV.s Bunching Factor = <I>/Ipeak 0.6 (histogram analysis) Inject starting 6-D matched distribution PTC ORBIT pre-tracking settings Preliminary results of the PTC/ORBIT convergence studies in the PSB - Vincenzo Forte
Adding of space charge Orbit routines D.O.E. Lattice setup Inject starting 6-D matched distribution PTC ORBIT basic settings Longitudinal space charge adding Potential-based transverse space-charge (2 ½ D) adding “chamber” definition Nxbins, Nybins Adding of space charge Orbit routines 1000 turns tracking RMS emittance 95-99% emittance tunes Results analysis Best settings choose Preliminary results of the PTC/ORBIT convergence studies in the PSB - Vincenzo Forte
D.O.E. 1000 turns tracking RMS emittance 95-99% emittance tunes Results analysis Best settings choose no. sc. 64 x 64 128 x 128 256 x 256 250th 500th 1000th Nxbins/Nybins N.mp. Preliminary results of the PTC/ORBIT convergence studies in the PSB - Vincenzo Forte
D.O.E. Computational costs criteria Best settings choose Lattice setup Inject starting 6-D matched distribution PTC ORBIT basic settings Adding of space charge Orbit routines 1000 turns tracking RMS emittance 95-99% emittance tunes Results analysis Computational costs criteria Convergence criteria Best settings choose Preliminary results of the PTC/ORBIT convergence studies in the PSB - Vincenzo Forte
Results – first without space charge… y Preliminary results of the PTC/ORBIT convergence studies in the PSB - Vincenzo Forte
Results – first without space charge… If NoSc. with 1000th is our reference -> Error’s order ~ 10^-3 Preliminary results of the PTC/ORBIT convergence studies in the PSB - Vincenzo Forte
Results – computational time criteria On lxbatch machines, “engpara” queue, 8 nodes required, over 1000 turns Preliminary results of the PTC/ORBIT convergence studies in the PSB - Vincenzo Forte
Results – convergence criteria – best cases – a footprint… - 4th order resonances plotted Preliminary results of the PTC/ORBIT convergence studies in the PSB - Vincenzo Forte
Results – convergence criteria – the best two cases… Preliminary results of the PTC/ORBIT convergence studies in the PSB - Vincenzo Forte
Results – convergence criteria – best cases difference The error is in the order of 10^-3 (same as in the linear case !!!) Preliminary results of the PTC/ORBIT convergence studies in the PSB - Vincenzo Forte
Results – convergence criteria – best cases – 95, 99% x emittances In horizontal 95% emittance is better for 1000th – 256 x 256 Preliminary results of the PTC/ORBIT convergence studies in the PSB - Vincenzo Forte
Results – convergence criteria – best cases – 95, 99% y emittances In vertical 95% emittance is good enough even for 500 th M.p. – 256 x 256 Preliminary results of the PTC/ORBIT convergence studies in the PSB - Vincenzo Forte
Results – worst case Preliminary results of the PTC/ORBIT convergence studies in the PSB - Vincenzo Forte
Results – a little better… Preliminary results of the PTC/ORBIT convergence studies in the PSB - Vincenzo Forte
Results – “a little better” vs. best cases… 128 x 128 growth ratio order ~10^-2 (RMS) 256 x 256 growth ratio order ~10^-3 (RMS) -> better accuracy Preliminary results of the PTC/ORBIT convergence studies in the PSB - Vincenzo Forte
Conclusions Thanks to this preliminary study we had an indication for a starting setting for transverse space charge simulations: 500th – 256x256 could be almost ever enough for RMS emittance behavior and halo formation studying… We should increase the computational power for longer simulations. Question #1 -> Between 95% or 99% emittance, which should we choose to study the halo formation? Preliminary results of the PTC/ORBIT convergence studies in the PSB - Vincenzo Forte
Future implementations Question #2 -> Which basic settings should we use (i.e. intensity and starting emittance) in the future as “final” PSB characteristics? Longer simulations required (more turns, i.e. a few synch. periods) “Lmax” effect -> beta function w-length is about 40 m in PSB ->Lmax up to 4 m (now 1 m) -> less S.C. nodes for integration! -> less CPU time but … what about physics? Bumps introduction (static -> dynamic tables) New scripts creation for “off-line” post-processing (FFT analysis for tunes, …) Effects of shorter dipole magnets on the emittance growth with space charge Errors in lattice introduction (misalignments and field errors) -> resonance analysis… long term Preliminary results of the PTC/ORBIT convergence studies in the PSB - Vincenzo Forte