Comparison of Linac Simulation Codes

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Comparison of Linac Simulation Codes

• S. Nath, R. Ryne, J. Stovall, H. Takeda,
• J. Qiang, L. Young, LANL
• K. Crandall, TechSource
• N. Pichoff, D. Uriot, CEA, Saclay

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PARMELA is the Most Detailed Simulation Code

• PARMELA Phase Radial Motion in Electron
  Linacs
• Originally written to simulate electron beam
  dynamics
• now extended to simulate ion dynamics
• It does not design linacs
• Main features
• time step integration
• composite E H fields
• 2-D 3-D space charge
• note that 3-D space-charge requires ?100k
  particles
• Er, Ez H? field maps computed by SUPERFISH

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PARMILA is the Design and Primary Simulation Code

• PARMILA Phase Radial Motion in Ion Linacs
• Initially written to design DTLs and simulate
  beam dynamics
• can now design integrated linacs including DTLs,
  CCLs, CCDTLs , SRFs transport systems
• includes large variety of design simulation
  options
• special quad phase laws, errors, phase advance,
  steering, ...
• Main features
• z-based with impulse approximations
• presently uses 2-D space charge (3-D pending)
• gap transformation includes transit time
  integrals T, T, S S
• off-axis fields derived using Bessel-function
  expansions
• 100k - 1M particle typical

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LINAC is a Code Similar to PARMILA

• Initially written for CCLs and CCDTLs only
• Now extended to integrated linacs including DTL,
  CCL, CCDTL SRF
• Does only simulation through linacs
• Dynamics similar to PARMILA
• uses only T in CCL SRF
• Can use either 2-D or 3-D space charge
• Includes large variety of simulation options
  including errors and steering

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PARTRAN is the CEA, Saclay Linac Code

• Design simulation functions are handled in two
  separate codes
• Written to be compatible with PARMILA
• Dynamics i.e., gap transformation, transport
  through other elements are treated as in PARMILA
• radial field treated via Bessel function
  expansion
• Can use either 2-D or 3-D space charge
• 3 options for SRF linacs
• use field per cavity, per cell or assume a
  sinusoidal field
• step integration (z) through SRF axial field from
  SUPERFISH
• More flexible and user friendly graphics than
  PARMILA
• Er, Ez H? field map (from SUPERFISH)
  integration (Pending)

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IMPACT Uses Parallel Computation

• IMPACT is a linac code written for parallel
  mode computation
• used for simulations only, no design
• Uses 3D space charge applied impulsively multiple
  times per element
• Transfers through the cell using linear transfer
  map
• map calculated from vector potential
• in between space-charge kicks, uses fine scale
  integration for computation of transfer-map for
  the external fields
• multipole expansion truncated at the quadratic
  term
• linear variation of Er and H? with r
• Can run very large particle arrays (could run 108)

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Key Features of the Codes

• Five linac codes, PARMILA, PARMELA, LINAC,
  PARTRAN, and IMPACT considered
• PARMELA a t-code all others z-code
• PARMELA uses time-step integration through field
  maps others use impulse approximation at the
  electrical center
• off-axis fields derived using Bessel-function
  expansions
• PARMILA and PARTRAN design and simulation, both
  Others only simulation
• IMPACT is specifically written for parallel mode
  computation
• can handle large array of particles i.e., 10 8
• Space-charge calculation PARMILA 2D (3D
  pending), IMPACT 3D, All others 2D or 3D

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Essential Differences Between the 5 Codes

• Primary differences between the 5 codes
• speed of execution
• 2 3-D space-charge, minor differences in method
  of field calculation
• time integration vs. impulse approximation
• number of particles usable in the calculation
• characterization of gap fields
• Main difficulty
• describing exactly the same linac to each code in
  its unique input format

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Acceleration Across Gaps

• PARMILA, PARTRAN and LINAC, all use about the
  same gap impulses applied at electrical center
• off-axis fields derived using Bessel-function
  expansions
• PARMELA does time-step integration thro composite
  field-maps
• 10 X 60 r,z grid for half DTL cell
• integration step-size 5 deg i.e.,72 steps
  through a DTL cell
• IMPACT transfers through the cell using linear
  transfer map
• map calculated from vector potential
• In between space-charge kicks, uses fine scale
  integration for computation of transfer-map for
  the external fields
• multipole expansion truncated at the quadratic
  term
• linear variation of Er and H? with r

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Simulations

• 1 M particle (4D Waterbag distribution) at the
  entrance to the RFQ
• Use TOUTATIS to get the RFQ output beam
• Use PARMELA (with 3D space-charge) Transport the
  beam through the MEBT in front of the DTL
• All codes start with the same distribution
• Transport beam through the 1st Tank with
  different codes
• Output at the mid-point between 1st and 2nd
  tanks.

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SCHEFF

• The SCHEFF subroutine is widely used for applying
  space-charge impulses in many beam-dynamics codes
  
• It is a particle-in-cell (PIC) code that
  calculates the electric field components, Er and
  Ez, on a two-dimensional (2D) r-z grid, and
  interpolates these field components to get the
  force on each particle
• For purposes of calculating the space-charge
  fields, each particle is considered to be a ring
  of charge. The elliptical cross section on the
  x-y plane is taken into account when calculating
  the effective radius of the rings of charge

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SCHEFF (Continued)

• The amount of charge in each rectangular box of
  the grid is then determined. Er and Ez are
  calculated at every node in the vicinity of the
  beam
• The ellipticity of the beam cross section is
  taken into account when applying to each particle
  the impulse due to Er. The x, y and
  longitudinal energy of each particle is changed
  by applying the Er and Ez for a given time or
  distance interval
• Relativistic corrections are made for
  transforming the beam coordinates from the lab
  frame to the beam frame and back again

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PICNIC

• The PICNIC (Particle In Cell Numerical
  Integration between Cube) is a full 3D code
• As in SCEFFF, it applies the space charge
  impulses to a beam at a given z or time
• Particles in each cube formed by the 3D grid are
  counted
• The field is calculated at each node of the grid
  as the sum of the contributions from all the
  grid-cubes, each of which is assumed to be
  uniformly populated
• The field at the position of the particle is
  interpolated from the neighboring nodes, allowing
  a calculation of space-charge impulse

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PICNIC (Continued)

• The field acting on particles outside the mesh is
  the one of a Gaussian beam with the same RMS
  dimensions as the real beam
• Relativistic corrections are made by transforming
  the beam-coordinates from the lab frame to the
  beam frame and back again
• The mesh size is adjusted to ? 3.5 times the RMS
  beam-size in all directions

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Space-charge Force

• All use PIC method
• LINAC 3D (PICNIC) 3 space-charge kicks per cell
• PARTRAN 3D (PICNIC) 1 kick per cell (can use
  any no.)
• PARMILA 2D (SCHEFF) 1 kick per cell (can use
  any no.)
• PARMELA 3D 12 kicks per cell (can use any no.)
• IMPACT 3D 10 kicks per cell (can use any no.)

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Computation Time - PIC Code

• One part depends linearly on Np
• time needed to count particles in a cell (?10)
• time needed to compute field at each particle
  position (?90)
• Other part depends on the method of computing
  field at mesh nodes i.e., Nc
• For SCHEFF, ? Nc4
• For PICNIC, ? Nc6 (present version about Nc5 )
• For 1 M particle runs, with usual mesh-size
  choice nearly same computation time is needed for
  PICNIC and SCHEFF

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The Particle Distribution Developes a Halo in the
MEBT
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Transverse Phase Space at Input and Output, All
Codes
INPUT
PARMELA
PARTRAN
PARMILA
LINAC
IMPACT
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Longitudinal Phase Space at Input and Output, All
Codes
INPUT
PARMELA
PARTRAN
PARMILA
LINAC
IMPACT
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Emittance Profiles From 5 Codes
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Output Radial Distribution, All Codes
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IMPACT Gap Fields Er H? are Linear in r
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Phase Space at the OutputLINAC with SCHEFF and
PICNIC
SCHEFF
PICNIC
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Simulations Differ at the 10 nA Level in the
Distribution but Not in the Extent
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Small Large Distributions Yield Consistent
Results
1.25 GeV 6-D waterbag SRF only , no errors
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Summary

• Good qualitative and quantitative agreement
  between predictions from different codes
• no gross physics and/or coding errors in the
  codes
• Close agreement between results with t-code
  (PARMELA) and z-codes
• dynamics calculation seems not to be critically
  dependent on this issue
• Calculations with LINAC using 2D (SCHEFF) and 3D
  (PICNIC) show little difference
• needs to be pursued with other codes
• Phase -space plots from IMPACT show some
  differences
• assumption of linear variation of Er and H? with
  r should be replaced.

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Comments

• What Figure of Merit to use ?
• R density plot , ?99, ?99.9, x,y,? profile
  plots, phase space plots, xmax,, ymax profiles,
  kurtosis or a combination of them ?
• How to interpret differences quantitatively ?
  What percentage difference is significant ?
• need estimated confidence level on simulated
  prediction values
• Predictions from different codes differ in the
  nano-amp level. Absent experimental results, how
  to attach more confidence to one in preference to
  another ? Looking for More Physics is
  subjective and controversial.
• Need to focus on studies relevant to prediction
  of potential losses