TREDI test for Photo-injectors

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TREDI test forPhoto-injectors

• L. Giannessi M. Quattromini
• C.R. ENEA-Frascati

Presented at
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TREDI

• is a multi-purpose macroparticle 3D Monte
  Carlo, devoted to the simulation of electron
  beams through

• Rf-guns
• Linacs (TW SW)
• Solenoids
• Bendings
• Undulators
• Quads

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Motivations

• Three dimensional effects in photo-injectors
• Inhomogeneities of cathode quantum efficiency
• Laser misalignments
• Multipolar terms in accelerating fields
• 3-D injector for high aspect ratio beam
  production
• . on the way
• Study of coherent radiation emission in
  bendings and interaction with beam emittance and
  energy spread

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History

• 1992-1995 - Start EU Network on RF-Injectors
• Fortran / DOS (PC-386 20MHz)
• Procs VII J.D'Etude Sur la Photoem. a Fort
  Courant Grenoble 20-22 Septembre 1995
• 1996-1997 - Covariant smoothing of SC Fields
• Ported to C/Linux (PC-Pentium
  133MHz)FEL
• 1996 - NIM A393, p.434 (1997) - Procs. of 2nd
  Melfi works. 2000 - Aracne ed.(2000)
• 1998-1999 - Simulation of bunching in low energy
  FEL Added Devices (SW Linac Solenoid - UM)
  (PC-Pentium 266MHz)
• J.B.Rosenzweig P. Musumeci, PRE 58, 27-37,
  (1998) Diamagnetic fields due to finite
  dimensions of intense beams in high-gain FELs
• FEL 1998 - NIM A436, p.443 (1999) (not
  proceedings )
• 2001-2002 - Italian initiative for Short ? FEL
• Today Many upgrades - First tests of CSR in
  new version

Contributions from A. Marranca Contributions
from P. Musumeci
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Features

• 15000 lines in C language
• Scalar Parallel (MPI 2.0)
• Unix Windows versions
• Tcl/Tk Gui (pre-processing)
• Mathematica MathCad frontends
  (post-processing)
• Output format in NCSA HDF5 format (solve
  endian-ness/alignement problems)

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TREDI FlowChart

• Start
• Load configuration
• init phase space

Charge distribution external fields known at
time t
Adaptive algorithm tests accuracy evaluates
step length ?t
Exit if ZgtZend
Trajectories are intagrated to t ?t
Self Fields are evaluated at time t ?t
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Parallelization
Present Beam
Time
NOW
Particle trajectory 1
Particle trajectory 2
Particle trajectory 3
Particle trajectory k-2
Particle trajectory k-1
Particle trajectory k
Self Fields
..

Node 3
Node 2
Node 1
Node n
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Upgrades to be done (six months ago, in Zeuthen)

• Accomodate more devices (Bends, Linacs,
  Solenoids )
• Load field profiles from files
• Point2point or Point2grid SC Fields evaluation
  (NxN ? NxM)
• Allowed piecewise simulations
• Graphical User Interface for Input File
  preparation (TCL/Tk)
• Graphical Post Processor for Mathematica /
  MathCad / IDL
• Porting to MPI for Parallel Simulations
• SDDS support for data exchange with FEL code
• Fix Data/Architectural dependences
  (portability of data)
• Introduce radiative energy loss
• Smooth (regularize) acceleration
  fields (for CSR tests)

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six months later, Chia Laguna

• SDDS support for data exchange with FEL code
• Fix Data/Architectural depences done,
  now use HDF5 data format support to fix
  endian-ness/alignments problems (output
  portability to different platforms)
• Introduce radiative energy loss
  done
• ? Smooth acceleration fields (for CSR tests)
  done (more work required, no manifestly
  covariant, CPU consuming)
• Big speed up (improved retarded time condition
  routine)
• Zeuthen 300 particles ? 4h on
  IBM-SP3/16x400MHz)
• Chia Laguna 1000 particles ? 35m
• 10000 particles in 27h on a
  32CPUs platform!
• Many improvements and bug fixes (surely many
  still lurking in the code) recently introduced
  a Parmela-like mode (instantaneous
  interactions,MUCH faster still experimental)

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Eqs Of motion
N.B. t ct
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SELF FIELDS
Self Fields are accounted for by means of
Lienard-Wiechert retarded potentials
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Retard Condition
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EM fields
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Problem fields regularization

• Real beam 1010 particles
• Macroparticles 103-106 huge charges
• Pseudo-collisional effects

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Known therapy

• Share charge among vertices of a regular grid
  (require a fine mesh to reduce noise)
• Typical problems
• non Lorentz invariant
• assume instantaneous interactions
• sensible for quasi-static Coulomb fields, low
  energy spread etc.

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Alternative

• Get rid of 3-anything (i.e. quantities not
  possessing a definite Lorentz character)

• Use 4-quantities instead

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Field strength produced by an accelerated charge
(covariant form)
(see e.g. Classical Electrodynamics, J. D.
Jackson)
t is the (source) proper time and V is the
(source) 4-velocity
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Separation in vel.accel. terms
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Separation in vel.accel. terms (contd)

• Where
  

Note
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The natural decomposition of EM fields can be
cast in a covariant form!
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Velocity term
Lorentz scalar
Lorentz scalar
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Smoothing of vel. fields

• Solution source macro particles are given a form
  factor (i.e. a finite extension in space Debye
  screening, Q.E.D. f.f. corrections to current
  M.E.)
• Effective charge
• A scaled replica of the (retarded) beam
• Same aspect ratio

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Boosts change macroparticles shape
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Smoothing of vel. fields (contd)

• Velocity (static,Coulomb) fields travel at speed
  of light, too! introduce a
  covariant (4D) generalization of purely geometric
  form factor

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Smoothing of vel. fields (contd)
e.g. gaussian shape
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Smoothing of vel. fields (contd)

• Effective charge total charge included by
  the iso-density surface associated to the value
  of ? (?) at observer point

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Smoothing of vel. fields (contd)
Un-smoothed (1/R2) fields
Eff. Charge
Effective vel. field
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Acceleration term
Lorentz scalars
Lorentz scalars
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Smoothing of accel. fields

• Fields blow up when (collinear
  divergencies)
• Solution target macro particles are given a
  finite extension in space
• Let be

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Smoothing of accel. fields (contd)

Where and G3 is a too complicated to be worth
seeing

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Effectiveness of smoothing

• S0 10-5 (collinear)

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Effectiveness of smoothing (contd)

• S0 10-3 (non collinear)

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SPARC INJECTOR
(BNL RfGunSolenoidDrift)
Gradient 140 MV/m
Charge 1nC
Pulse length 10 ps (flat top)
Spot radius 1 mm
Extraction phase 35º (center)
Solenoid field 0.3 T
104 macro-particles x 3103 grid points 13h
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Energy Spread
Tredi Homdyn
Homdyn data courtesy of M. Ferrario
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Envelopes
Tredi Homdyn Parmela
Parmela data courtesy of C. Ronsivalle
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The emittance in the GunSol
Tredi Homdyn
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Sol. at standard position
Tredi Homdyn
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Sol. 2cm ahead
Tredi Tredi, sol 2cm ahead Homdyn
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Sol. 1cm ahead
Tredi Tredi, B 2cm ahead Tredi, B 1cm ahead Homdyn
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The emittance in the Gun revisited
Tredi Tredi, B 2cm ahead Tredi, B 1cm ahead Homdyn
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TODOs

• The nature of discrepancies with other codes
  (Parmela, Homdyn) need to be investigated and/or
  explained
• Test results obtained in Parmela-like mode
• Speed up the code (Accel. Fields, OpenMP version?
  3D runs with 105 -106 particles?)
• Make smoothing of Accel. Fields manifestly
  covariant
• Save SC fields onto output to estimate noise

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CONCLUSIONS

• Some internals of the code need to be fully
  understood but
• TREDI proved to be an usable tool for
  simulations of quasi-rectilinear set of devices
  from mildly-to-wildly relativistic regimes
  (5-5000 MeV)
• Start-to-end simulations?

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Acknoledgements

• M. Ferrario, P. Musumeci, C.Ronsivalle, J.B.
  Rosenzweig, L. Serafini
• For providing results (Homdyn, Parmela), support,
  hints, feedback or directly partecipating to the
  development of TREDI.

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Energy spread (contd)
Tredi Homdyn