1. Tools for loss analysis and studies PS2/PS2+ Meeting 23 rd of May of 2007 Javier Barranco AB/ABP

2. Acknowledgements Thanks to O. Berrig, S. Gilardoni, Y. Papaphilippou, G. Robert-Demolaize, T. Risselada, F. Schimdt, J. B. Jeanneret, R. De Maria, P. Skowronski.

3. Goal Numerical tools have been developed for the design and optimization of the LHC collimation system through the production of detailed loss maps (see G. Robert-Demolaize, PhD thesis, 2006) Our ultimate goal is to have robust tools for beam loss studies in low energy synchrotrons and use them for the design of the collimation system in the new PS2 machine. These tools were adapted to the PS machine by using the detailed aperture model (O. Berrig) and a thin lens version for tracking with SIXTRACK. Serious debugging was necessary in order to understand the implications of adapting the tools to low energy rings. A benchmarking campaign was initiated in order to reproduce the loss patterns simulated and observed in the PS complex (see APC talks by S. Gilardoni).

4. Flow diagram Lattice Thick Elements MADX “makethin” Lattice Thin Elements MADX “sixtrack” SIXTRACK input files (fort.2 fort.3) …… Aperture Model Particles tracked SIXTRACK LOSS LOCATION Particle, S, X, X’,Y,Y’, E PTC Thick Elements SIXTRACK tracking + K2 scattering

5. Tracking with SixTrack (I) SixTrack is a single particle tracking code which in its primary version allows to track a maximum of 32 particle couples (64 particles). CollTrack, a new module developed for collimation studies, increases considerably the number of particles (~10 6 particles) and gives the possibility to track an external distribution (2x10 3 particles) over hundreds of turns. Possibility to insert collimators and use particle scattering codes (like K2). Interaction with machine aperture model. The loss location of the particles tracked is given with an accuracy of 10cm. Among other input files, it is necessary to provide a thin lens model of the lattice, through the MAKETHIN command in MAD-X. Some problems were encountered while trying to do the conversion.

6. Thin Lens Model (I) In MAD-X, the combined function magnets are modeled as sector bends (SBEND), with a quadrupole component and pole face angles describing the edge focusing. MAKETHIN ignores completely the effect of the fringe fields (edge focusing and higher order effects). The DIPEDGE element in MAD-X can solve the problem of the edge focusing when passing to thin lenses, by adding it on either side of an SBEND (with a zero pole face angle). label : DIPEDGE, h=real, e1=real, fint=real, hgap=real, tilt=real; DIPEDGE is limited to only linear terms…

7. Edge Focusing in MAD-X Transfer maps for dipoles in MAD are composed of three maps, fringe field at entrance F (1), body of the dipole B and fringe field at the exit F (2), using TRANSPORT formalism F= F (1) *B*F (2) Working only with the fringe fields. Linear terms due to the pole face angle Non-linear term coming from the gradient of the quadrupole Term due to the curvature of the pole face, Term due to the pole face angle itself Term due to the longitudinal dependence of the field

8. Thin Lens Model (II) Notice that the effect of both, linear and non-linear terms, is greater in small machines (small ρ, h=1/ρ). If pole face angles are zero, just terms containing only the secant remain. DIPEDGE only includes edge focusing term MADX simulation for CT extraction. Note that the difference in tunes comes from not including the non- linear component of the fringe-field (sextupole-like) and having the extraction bumps on (quadrupole feed-down).

9. Thin lens model revision Previously, it was shown that some high-order terms were absent in the thin lens conversion made by MADX to Sixtrack. In absence of a correct implementation (e.g. with PTC), the sextupole-like fringe field effects in the thin lens model will be approximated by means of thin lens multipoles giving the equivalent effect in chromaticity. In what follows, beam loss studies with Sixtrack + detailed Aperture Model will be discussed, as well as some features of PTC.

10. Tracking with Sixtrack (II) In order to evaluate the validity of the results, the reference used is the losses measured by the BLMs during CT extraction (*) (*) S. Gilardoni (APC meeting 06/10/2006) Unknown losses SS5-SS10 SS41-SS45 SS85

11. Tracking with Sixtrack (III) Following Simone’s studies (APC 06/10/06), a scattered particle distribution (MARS) was provided by him, coming from the blade of Septum31, in order to be tracked.

12. Tracking with Sixtrack (IV) Beam losses obtained after tracking with Sixtrack (only Slow Bump) The loss pattern is very similar to the measured one Losses in sections 9, 41-45 and 85 do not appear.

13. Some comments regarding the simulation In this simulation only particles produced in scattered processes in Septum 31 are tracked. The rest of elements are considered as black absorbers. Some considerations have to be taken into account when interpreting these results (see also Simone’s talk on APC 6/10/06 ).  The closed orbit used for tracking is an ideal and not the measured one.  It is not possible to include the real effect of the electrostatic septum’s field in the scattered particles.  There is some uncertainty regarding the angle between the beam and the blade.  Possible activation of the magnets or others regions that could generate showers of particles cannot be included by this method. One would need a complete modeling of the PS with a scattering code like MARS.

14. Tracking with PTC PTC track module is the symplectic thick-lens tracking tool in MAD-X. Fringe field effects are treated correctly. For beam loss studies, it was not directly useful, as it was necessary to place markers in all positions were tracking data is needed. In addition, it was not possible to follow the particle trajectory inside an element because of the thick lens nature of the code. Recently P. Skowronski (AB/OP), responsible for the track module of PTC, made possible to track the particles inside the elements (still some debugging needed) The loss location will be established using the detailed aperture model (as with SIXTRACK). PTC it is not designed for large number of particles. For each particle one tracking simulation has to be launched. In all the cases, the distribution should be generated externally to PTC.

15. Scattering codes adaptation to low energies K2 has been extensively used for LHC studies (energies of 450 GeV or higher and certain materials). For lower energies and different materials some changes are needed. For example, for the PS (1.4 GeV – 26 GeV):  Septum Material -> Molybdenum (Mo): Input parameter needed Z, W, ρ, Radiation length,…  Processes: Multiple Coulomb Scattering (MCS) -> Material’s Radiation length Ionization (dE/dx) -> Stopping Power for Protons (1.4 – 26 GeV)) in Mo.  For LHC energies (>100 GeV) can be considered as constant value. Not for lower energies.  Experimental Values difficult to find for that range of energy in Mo.  Bethe-Bloch formula which fits well for that range. Point-like interactions -> To be checked.

16. Conclusions & Further Steps At present, results from SIXTRACK simulations have already shown a good agreement with measured losses (even with the described model approximations). GEANT4 will be used to provide data necessary for scattering processes in any material or energy. When the revision of the scattering processes is finished, K2 will be ready for collimation studies in low energy synchrotrons. After debugging PTC, will become another powerful tool for tracking (thick elements) which may be used together with an updated K2 for collimation studies. Concerning to PS2 studies, the important inputs are:  A lattice for placing the collimators and optimizing their position  A rough aperture model for the loss location studies.