ORBIT

1
ORBIT
FNAL September 11, 2001

• J. A. Holmes ORNL

2
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

3
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.

4
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).

5
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.

6
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.

7
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.

8
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.

9
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.

10
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.

11
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.

12
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

13
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)

14
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.

15
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

16
Where Weve 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 -gt 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).

17
Where Were 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.

18
Where Were 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 -gt 25.6M
  macroparticles at finish.
• 300 transports / turn interspersed with space
  charge and impedance kicks.
• Run time gt1000 hours on my laptop (650 MHz
  Pentium III).

19
Where Were 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.