PTC ½ day – Experience in PS2 and SPS

H. Bartosik, Y. Papaphilippou

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PTC – Introduction (I)• PTC (Polymorphic Tracking Code) is a tracking code – Written by E. Forest (“Introduction to the Polymorphic Tracking Code”, 2002)– Based on symplectic integration using maps– Order of symplectic integrator is defined by user allows to choose number of

integration steps– PTC is a very powerful tool not only for tracking itself

• PTC normal form analysis allows to compute lattice parameters up to any order– Hamiltonian driving terms– Chromaticities– Anharmonicities (detuning with amplitude coefficients)– …– This cannot be done with MADX alone …

• PTC provides a generic way to take fringe fields into account– Hard-edge kicks in either side of the magnets (see E. Forest book)– It would be nice to be able to include map from measured field profiles

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PTC – Introduction (II)• “Exact” (no expansion in momentum error) treatment of Hamiltonian– Can be of great important for small machines – Option “Exact” usually used for PS2 studies – Example drift space: user can choose between

– The map of the exact Hamiltonian is non-linear in the momenta!!!

• Magnetic errors can be assigned to “thick elements”– As opposed to MADX, multipole errors can be assigned to thick elements

instead of inserting thin lens kicks as used in MADX– Allows for better treatment of multipole errors

• PTC is very well suited for studying nonlinear dynamics in machines for which a detailed magnetic model exists (for example the LHC)

• However, PTC is not (yet) optimized for speed– Tracking with PTC is quite slow (many calls of “IF” routines)– Tracking with PTC a few times slower than with MADX

Exact Hamiltonian Expanded Hamiltonian

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PTC as library in MADX• PTC is used as a library in MADX, i.e. MADX can be used as front end

for PTC– Definition of lattice in MADX (lattice can also be defined in PTC directly,

however it is more complicated)

• Usual procedure for using PTC: – Creating “PTC-Layout” from existing accelerator structure within MADX– Normal form analysis or tracking can be done with PTC– Read the output back into MADX and provide to user

• No “matching” routine available in PTC– Matching is usually done in MADX– Matching of PTC parameters (like higher order chromaticity) can be done in

MADX by calling PTC within a macro

• Some features are not sufficiently documented and thus are not easy to use or not known to exist– Users would benefit a lot from a better documentation of PTC and MADX as

front end for PTC

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Tracking with PTC• Using PTC for PS2 tracking studies– Define lattice in MADX– Match working point, chromaticity, … , in MADX (with macro using PTC in

some cases)– Define multipole errors , misalign magnets in MADX and assign in PTC

• Simplest example: Tracking studies for finding dynamic aperture

Include

errors

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Frequency Maps – PS2 lattices• Plot “tune diffusion coefficient” d for generating Frequency map– Diffusion map shows d as function of initial condition for tracking in

configuration space– Frequency map shows d as function of tune – Useful for identifying resonances– Distinguish regular motion (small tune diffusion) from chaotic motion (large

tune diffusion)

tunes in first (second) half of total turns

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PSAmplitude detuning – PS2 lattices

• Normal form analysis in PTC can be used to calculate higher order anharmonicities (coefficients for detuning with amplitude) – Sufficiently far away from strong resonances and for sufficiently small

amplitudes (non-chaotic regime), anharmonicities can be used to reconstruct detuning with amplitude as found by tracking

• Example of PS2 lattice including misalignments and fictitious error table for particles up to 3σ

Analytic representation

using anharmonicities up to higher order

Nominal tune

Off momentum tunes

Nominal tune

Tracking From anharmonicities

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Nonlinear chromaticity - SPS• Normal form analysis in PTC provides directly nonlinear chromaticity

up to any order

• Example SPS: Establish “effective” machine model by matching multipole errors of main magnets to measured chromaticity– Was done in the past using MAD (G. Arduini et al., EPAC02) or using response

matrix approach using the calculations of PTC (R. Tomas et al., PAC07)– Can be done very conveniently by matching “directly” higher order

chromaticities using PTC macro in MADX

SPS Q20 optics

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Space charge simulations – PTC-ORBIT?

• ORBIT is a (macro particle) space charge simulation code developed for SNS– Written in a modular way can be extended or combined with other codes– Is compatible with parallel computing on a cluster – Is used at CERN for simulations of the PSB in combination with LINAC4

• Lattice imperfections and nonlinearities might play a key role for space charge effects– Defining magnet errors and misalignments in ORBIT is not easy– Properties of the lattice is not easily comparable with MADX simulations

• Idea of combining the power of MADX-PTC with the space charge calculations of ORBIT PTC-ORBIT (A. Molodozhentsev et al.)

• Basic idea: start with MADX-PTC (or PTC)– Generate lattice, match optics– Study impact of misalignments and magnet errors on single particle motion with

MADX-PTC– In case of existing machine: Develop “effective” machine model which is capable of

reproducing the measured imperfections and non-linear effects (closed orbit, higher order chromaticity, amplitude detuning, resonances, …)

– Dump lattice to PTC flat file

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PTC-ORBIT• Use PTC-ORBIT for space charge simulations– The exact same lattice as used in MADX-PTC can be used for the tracking in

space charge simulations full control of the lattice (instead of creating the lattice in ORBIT itself with all the complications)

– Many of the ORBIT standard routines are available in PTC-ORBIT

• First attempts with PTC-ORBIT were made with the SPS, PSB and PS lattices in 2010– Still in progress of optimizing PTC parameters (obtaining good machine models)

and implementing new features necessary for the CERN injector (time varying fields, double harmonic RF, travelling wave cavities, …)

– No robust and trustable simulation for CERN machines results up to now

• Down sides of PTC-ORBIT– Documentation: manual of ORBIT is from 1999– PTC-ORBIT is still in development some features don’t work– Up to now, a lengthy procedure of executing various small codes has to be

followed in order to generate input files in special formats needed for running PTC-ORBIT

– Tracking with PTC is slower than using the built in tracking of ORBIT

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PSPTC-ORBIT – Simulation procedure

• Use MADX PTC for generating lattice and do all the matching– Taking advantage of all the usual features of MADX PTC

• Create a PTC-flat file with all the lattice definitions – Define how many places should be foreseen for the insertion of space charge

calculation nodes– The modifications of the lattice (including error assignments for example) are

finished here– Exception: the feature of time varying fields in PTC-ORBIT allow to modify

magnet strengths even at a later stage in the execution of PTC-ORBIT

• Prepare “acceleration table”– This table contains the evolution of the magnetic field (energy) and the

parameters for the RF-cavities (phases, voltages)

• Use PTC-ORBIT for space charge simulations– Running PTC-ORBIT is very similar to running ORBIT itself, but basically all

routines related to the lattice are (or have to be) replaced by special routines for invoking PTC

– Many of the standard ORBIT features can be used also in PTC-ORBIT

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Summary• PTC is a tracking code which provides powerful tools as for example

normal form analysis– Very interesting for nonlinear dynamics analysis and lattice optimization– Very useful for developing effective nonlinear machine model

• PTC is usually used as library in MADX– Slower than other tracking codes– Big overhead of generating PTC environment, possibly several times per job

execution

• One of the big problems is documentation

• PTC-ORBIT is a very interesting development for future space charge studies– Still needs some further improvement and development– One of the main issues is again documentation