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FNAL: September 11, 2001. ORBIT. J. A. HolmesORNL. Colleagues, Collaborators, Contributers. SNS, ORNL S. Cousineau, V. Danilov, J. Galambos, J. Holmes BNL J. Beebe-Wang, M. Blaskiewicz, A. Luccio, N. Malitsky, A. Shishlo TRIUMF F. Jones FNAL J. MacLachlan. Motivation for ORBIT.

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ORBIT

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FNAL: September 11, 2001

ORBIT

J. A. HolmesORNL


Colleagues, Collaborators, Contributers

  • SNS, ORNL

    • S. Cousineau, V. Danilov, J. Galambos, J. Holmes

  • BNL

    • J. Beebe-Wang, M. Blaskiewicz, A. Luccio, N. Malitsky, A. Shishlo

  • TRIUMF

    • F. Jones

  • FNAL

    • J. MacLachlan


Motivation for ORBIT

  • High intensity proton rings such as FNAL Booster, AGS Booster, PSR, and SNS are characterized by low energy, high beam intensity, and low beam loss requirements for high availability.

  • These requirements of high intensity and low losses necessitate a detailed understanding of beam dynamics in this regime.

  • Under these conditions collective effects due to space charge and wakefields will strongly affect the beam behavior, and single particle models alone will not apply.

  • Because of the complexity of collective phenomena for bunched beams in high intensity rings, a computational approach is productive.


ORBIT History

  • In response to this need, the SNS AP group at ORNL, with help from BNL colleagues, developed the ORBIT code.

  • We started with ACCSIM (provided by Fred Jones of TRIUMF) as the core to build a beam dynamics code around, but decided to begin again with an object-oriented approach. The basic classes are herds and nodes. Nodes operate on herds.

  • ORBIT began as a C++ rewrite of ACCSIM, developed under the SuperCode driver shell, but has since undergone extensive independent development.

  • With the completion of the 3D spacecharge routine, ORBIT has become a good candidate for massively parallel computing.

  • Because of the parallel computing need and the desire to inherit sophisticated mapping and general error treatment capabilities, ORBIT is now being included into the Unified Accelerator Libraries (UAL).


ORBIT: General Description and Approach

  • ORBIT is a particle (herd)-tracking code in 6D phase space.

  • ORBIT is designed to simulate real machines: it has detailed (node) models for

    • transport through various types of lattice elements

    • injection foil and painting

    • RF and acceleration

    • 2.5D space charge with or without conducting wall beam pipe

    • longitudinal impedance and 1D longitudinal space charge

    • Transverse impedance

    • 3D space charge

    • apertures and collimation

  • ORBIT has an excellent suite of routines for beam diagnostics.


  • ORBIT: Particle-Tracking in 6D Phase Space

    • ORBIT coordinates utilize the usual accelerator expansion

      • Transverse phase space horizontal x, x_prime

      • Transverse phase space vertical y, y_prime

      • Longitudinal phase space phi, dE

  • The coordinates are taken with respect to a reference particle on a reference closed orbit.

  • The independent variable is the machine location s. This has interesting implications in the representation of 3D space charge and transverse impedance.


  • ORBIT: Transport Through Lattice

    • ORBIT lattices can be constructed by reading MAD or DIMAD output files. There are also special facilities to specify lattices directly or to create uniform focusing channels.

    • Linear transport through drifts, bends, or quadrupoles is carried out through symplectic matrix multiplication.

    • Nonlinear elements, such as higher order multipoles, are evaluated in the thin lens approximation.

    • Higher order single particle transport terms, such as chromaticity, are evaluated using second order transport matrices.

    • There is no specific facility for the treatment of errors.

    • Inclusion of ORBIT in UAL will alleviate these last two shortcomings.


    ORBIT: Injection and Foil

    • ORBIT can inject particles turn-by-turn or utilize a complete distribution from the start.

      • A variety of distributions can be generated internally.

      • Any externally generated distribution can be read in.

  • Injection painting schemes can be simulated by time-dependent closed orbit bumps.

  • ORBIT contains an injection foil model taken from ACCSIM. Not all of the ACCSIM model physics has been implemented.

    • At present, the model keeps track of foil hits and applies transverse kicks based on multiple Coulomb scattering.

    • Particles that miss the foil at injection are removed from the beam.


  • ORBIT: RF and Acceleration

    • ORBIT contains an RF cavity model which provides longitudinal kicks based on a time-dependent waveform with multiple user-specified harmonics.

    • For nonaccelerating cases, the synchronous phase is assumed to be zero, and the harmonics and time-dependent voltages are all that need to be specified.

    • For accelerating cases, the harmonics, time-dependent voltages, and time-dependent dipole fields must be specified.

      • The synchronous phase and the resulting kicks are then solved by the model.

      • Transverse phase space is adjusted to conserve normalized emittance.


    ORBIT: 2.5D Transverse Space Charge

    • Particles are binned in 2D rectangular grid

      • 2nd order momentum-conserving distribution of charges to grid (see Hockney and Eastwood)

    • Potential is solved on transverse grid

      • Fast FFT solver is used

      • Conducting wall boundary conditions (circular, elliptical, or rectangular beam pipe)

    • Particle kicks are obtained by interpolating the potentials

      • 2nd order momentum-conserving interpolation scheme is used (see Hockney and Eastwood)

      • Kicks are weighted by the local longitudinal density to account for bunch factor effects

    • There is also a free space direct force solver without beam pipe.


    ORBIT: Longitudinal Impedance and Space Charge

    • ORBIT treats longitudinal impedances and/or space charge in a similar fashion as ESME.

      • The longitudinal impedance is represented by its harmonic content in terms of the fundamental ring frequency.

      • Particles are binned longitudinally.

      • The binned distribution is Fourier transformed.

      • The space charge contribution to the impedance is combined with the external impedance.

      • The Fourier transformed distribution is multiplied by the impedance and the results applied to give longitudinal kicks to the particles.

    • Typically (for SNS anyway), it is sufficient to evaluate the longitudinal impedance and space charge kicks once each turn, since the synchrotron period is more than a thousand turns. More evaluations may be required for applications with higher synchrotron frequencies.


    ORBIT: Transverse Impedance Model

    • Transverse impedance treated as localized node in ORBIT

      • Element length must be short compared to betatron oscillation wavelength

      • If physical impedance is not short, multiple impedance nodes are required

    • Impedance representation

      • User inputs Fourier components of impedance at betatron sidebands of the ring frequency harmonics

      • Velocities less than light speed included in formulation

    • Particle kicks

      • Convolution of beam current dipole moment with impedance

      • Current evaluation assumes dipole moment evolves from previous turn according to simple betatron oscillation


    ORBIT: 3D Space Charge Model

    • Particles are binned in 3D rectangular grid

      • 2nd order momentum-conserving distribution of charges to grid (see Hockney and Eastwood)

      • Typically, for rings, longitudinal spacing greatly exceeds transverse spacing

    • Potential is solved on transverse grid for each longitudinal slice

      • Fast FFT solver is used

      • Conducting wall boundary conditions (circular, elliptical, or rectangular beam pipe) “tie together” the transverse solutions

    • Particle kicks are obtained by interpolating the potentials in 3D

      • 2nd order momentum-conserving interpolation scheme is used (see Hockney and Eastwood)


    ORBIT: Apertures and Collimation

    • Apertures can be defined in ORBIT.

      • The apertures can be circular, elliptical, or rectangular.

      • The apertures can be set either to allow particles to pass through and simply tabulate the hits, or

      • to remove the particles from the beam and tabulate the locations.

    • A collimation model has been added to ORBIT.

      • In addition to the aperture shapes, the collimators can include single or combinations of edges at arbitrary angles.

      • Physics includes multiple Coulomb scattering, ionization energy loss, nuclear elastic and inelastic scattering, and Rutherford scattering.

      • Monte Carlo algorithms are used for particle transport inside the collimator, and step sizes are carefully adjusted near collimator boundaries.


    ORBIT: Diagnostics

    • A list of useful diagnostics in ORBIT includes the following:

      • Dumps of particle coordinates.

      • Dumps of particle tunes.

      • Dumps of particle emittances.

      • Histograms of particle distributions in x, y, phi, and emittance.

      • rms emittances versus turn or versus position

      • Beam moments versus turn or versus position

      • Statistical calculation of beta functions

      • Longitudinal harmonics of the beam centroid


    Where We’ve Been: Typical High Intensity Ring Tracking Simulation, SNS Injection.

    • Linear transports.

    • Nonlinear 2(+) D transverse space charge, evaluated using periodic FFT solver with 128 x 128 grid, as described by Hockney and Eastwood.

    • Longitudinal dynamics including RF and longitudinal space charge.

    • Beam accumulation ~1000 turns.

    • Inject ~200 macroparticles / turn -> 200K macroparticles at finish.

    • ~300 linear transports / turn interspersed with nonlinear space charge kicks.

    • Run time ~6 hours on my laptop (650 MHz Pentium III).


    Where We’re Going: New Physics in High Intensity Ring Tracking Code.

    • Impedance models - longitudinal and transverse.

      • Longitudinal involves straightforward combination with longitudinal space charge.

      • Transverse requires dipole moment of current resolved along the bunch. Proper treatment of space charge in presence of transverse impedance requires

  • 3D space charge model.

    • This involves binning the beam longitudinally.

    • Each bin will contain a complete 2D space charge solution.

  • Higher order maps (nonlinearities) in particle transport.

    • This will increase time for transports.

  • Error terms.

    • This will increase time for transports.

  • Electron cloud model - this is another subject, and work is just beginning.


  • Where We’re Going: Typical Future Ring Tracking Simulation, SNS Injection.

    • Nonlinear map transports with errors.

    • Longitudinal and transverse impedances.

    • 3D space charge, evaluated using 128 longitudinal bins (this may not be enough - aspect ratio), each with periodic 2D FFT solver with 128 x 128 grid, as described by Hockney and Eastwood, and conducting wall boundary correction as described by Jones.

    • Longitudinal dynamics including RF and longitudinal impedance.

    • Beam accumulation ~1000 turns.

    • Inject ~200 macroparticles / turn / bin -> 25.6M macroparticles at finish.

    • ~300 transports / turn interspersed with space charge and impedance kicks.

    • Run time >1000 hours on my laptop (650 MHz Pentium III).


    Where We’re Going: Merger With Unified Accelerator Library (UAL).

    • We have been working with our SNS colleagues (N. Malitsky and A. Shishlo) at BNL to incorporate the ORBIT models into their Unified Accelerator Library.

    • In addition to all the ORBIT capabilities described above the resulting product will support

      • An MPI parallelization of the time-consuming space charge routines.

      • TEAPOT and ZLIB for nonlinear symplectic tracking.

      • Other capabilities of UAL, including errors.

  • Status

    • ORBIT impedance and space charge routines have been implemented, parallelized, and tested in UAL.

    • Some ORBIT diagnostic routines have been implemented, but this task remains to be completed.

    • Collimation and aperture routines have not yet been implemented.


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